QETools Tutorial - Part I

QE Tools Software Tutorial

An Excel-based Statistical Software Add-In for Lean-Six Sigma

qetools.com

Topics

Note: Not all tools are shown in this tutorial. See help files for additional examples. 2

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Topics (Continued)

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QE Tools Menu of Tools

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QE Tools Tutorial Part 1 – Getting Started and Data Manipulation

1.1 Getting Started 1.2 Data Manipulation Tools Subset Data Split Data by Group 1.3 Six Sigma Methods – Tool Roadmap

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1.1 Getting Started Excel Menu

QE Tools appears as a menu option in the main Excel toolbar

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1.1 Getting Started New Data Sheet

QE Tools uses a dedicated data sheet (own worksheet) for performing analyses.

Begin by creating an initial blank datasheet using the New Data Sheet menu pick.

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1.1 Getting Started Data Sheet

. A new, pre-formatted worksheet is inserted with name “Datasheet” (Warning: Do not change sheet name). . After you create a data sheet, you can add and manipulate data in ways familiar to you in Excel (e.g., copy, paste, add formulas, etc.) . Note: You must define a variable name for each data series (Datasheet Row: “Var Name”) . Optional, may include Upper and Lower specification Limits (USL and LSL) as well as a Target (nominal) value for each variable. . These will automatically be referenced for those tools that use specification limits for analysis.

TIP: Use Datasheet to only store raw data 8

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1.1 Getting Started Macro-Enabled File Format

 Be sure to save the file as a “.xlsm” macro- enabled format file to ensure the QETools functionality works properly

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1.1 Getting Started Entering Data – “Datasheet”

. If all data in a column are numerical values, QETools will recognize as “Data” in the “Var Type” row. . Otherwise, data will be listed as “Text.” . Important: Certain tools are restricted to the use of Data Variables Only.

Note: You may also copy data from other locations (e.g., Excel File). TIP: Do not copy entire worksheet. First rows on data sheet are reserved for data characteristics

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1.1 Getting Started Data Format in “DataSheet”

. Variables may include Text or Data Variables . Data variables may either be values or calculations (Excel Formulas). Examples: • ‘TotalVisit’ has data values • ‘TotalWait’ and ‘WaittoVisit’ are formula. . Data for any variable may be constructed using standard Excel commands.

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1.1 Getting Started Variable Names

 When entering variable names, QE Tools may update after you enter them or paste from another worksheet

 QE Tools uses an algorithm to standardize variable names:

 Certain characters are not allowed in variable names and are removed:

 ":", "\", "/", "?", "*", "[", "]", "'", " ", "(", ")", "`", "~", "@", "#", "$", "%", "^", "&", "-", "+", "=", "{", "}", "|", "<", ">")

 Duplicate names are not allowed to insure QE Tools knows which variable you wish to analyze when running a tool

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1.1 Getting Started Number of Worksheet Warnings

 QETools warns of too many active worksheets because performance may be diminished with increasing file size

 After 30 worksheets, QETools issues a warning message

 Recommend creating a second analysis file or removing unused worksheets

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1.2 Data Manipulation

 Sorting and other data manipulation may be done using normal Excel Functionality, OR

 QE Tools has a data manipulation tool for:

 Subset Data by Variable

 Split Data Set by Variable

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1.2 Data Manipulation Subset Data – Dialogue Box

 May create a subset of data rows (Select Variables) based on condition(s) satisfied

Sample Excel Data File: qetools-sampledata.xlsx 15

1.2 Data Manipulation Subset Data – Sample Result

 Data are stored on datasheet in next open column to the right with new variable names (suffix added)

. Subset to only include data for each row where Team = C

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1.2 Data Manipulation Split Data by Group – Dialogue Box

 Split command creates data subsets of all selected rows of data

 Select Variables for each unique value of the Grouping Variable identified

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1.2 Data Manipulation Split Data by Group – Sample Result

 Data are stored on datasheet in next open column to the right with new variable names (suffix added)

The output is separate columns for each Output Variable . ‘TimeWaitingRoom’ . ‘WaitClinician1’ . WaitClinician2’) for each of the selected Grouping Variable . Team A . Team B . Team C

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1.3 Six Sigma Methods – Tool Road Map

 QE Tools also provides a Six Sigma problem solving roadmap with common analysis steps and hyperlinks to analysis tools and templates

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1.3 Six Sigma Methods – Tool Road Map Tool Roadmap: Define/Measure

Phase Task Task Description and Tool Road Map (with Hyperlinks)

DEFINE Define Problem Identify Problem, key customers, and assess impact in terms of $$ if possible – Tools:

Project Charter SIPOC QFD - House of Quality Scorecard Analysis Pareto Chart Other Tools: Value Stream Map, Flow Chart, Swim Lane Diagram, Affinity Diagram, Cost-Benefit Analysis, Project Plan

Identify Critical Y and assess its current state (e.g., Data Pattern, Process Stability, Process Capability/DPM/DPMO). MEASURE: Identify Key Output Note: select method based on Y data type (continuous/discrete, binary, or binary w/ multiple opportunities)

Assess Current State Compute DPM, DPMO, Sigma Level, Yield (Unit-based, Rolled Throughput), or Process Capability Index (e.g., Pp, Ppk) Performance Process Capability Process Capability Process Capability Sigma Level and Graphical Summary Graphical Summary Graphical Summary Binary Tabulation DPM Converter (Normal) (Non-Normal) (Binary) FMEA Analysis Scorecard Analysis Yield Analyzer

Assess stability of Y Plot Y versus time ( X-axis in time order) and assess if problem is chronic and/or sporadic. (time order) Assess if any trends in data over time (may include comparison to target performance levels or specification limits). Run Chart Blue Text representsAssess hyperlinksif process is in-statistical to controlvarious (process stability analysis). Select appropriate SPC chart based on the if Y is continuous variable data (or may be modeled as continuous)? analysis and templates in QEToolsIf subgroup size = 1 (or unknown), use: I / MR If subgroup size = 2 - 10, use: X-Bar / Range If subgroup size > 10, use X-Bar / S If Y relates to yield or % defective (each unit is defective or not)? If subgroup size is not constant, use: P-Chart If subgroup size is constant, use: P-Chart NP-Chart If Y relates to DPMO (1 or more defect opportunities per unit)? If subgroup size is NOT constant, use: U-Chart If subgroup size is constant, use: U-Chart C-Chart Describe Distribution of Perform distribution analysis. Select method based on Y-data type Y (non-time order) 20 If Y is categorical data (with multiple categories) --> use: Pareto Chart If Y is a set of proportions --> show distribution of sample proportions using: Histogram If Y is discrete/continuous --> show distribution using: Process Capability Process Capability Histogram Single Box Plot Graphical Summary Graphical Summary Dot Plot (Normal) (Non-Normal)

Summarize Data and Assess if Mean and/or Compute descriptive statistics of Y and assess if mean and/or variation concern. 10 www.qetools.com Variation Concern Process Capability Process Capability Descriptive Graphical Summary Graphical Summary Statistics (Normal) (Non-Normal)

Measurement Systems Assess quality of the measurement data for Y – verify if measurement system is effective (preferably quantitatively Analysis using measurement system analysis techniques) Paired (Repeated) Attribute Matching Gage R&R Study Measurements Study Study

ANALYZE: Qualitative Analysis Identify possible key X’s (usually prior to Quantitative Analysis): Possible tools include: Cause-and Effect FMEA Other Tools: P-Diagram, Affinity Diagram

Collect Data (check sheets, observational study of X's and Y's, controlled experiment). Quantitative Analysis: Analyze data to identify cause of the problem (key X's). Possible analysis tools include: Stratify Y by a grouping variable X (Stratification Analysis) Desc Statistics Mulitple Box Plot Scatter Plot Pareto Chart Multiple Tabulation (Grouping) Cross Tabulation Binary Tabulation

Test for a Statistically Significant Difference Using Hypothesis Test. Select appropriate test on the following: Test variance effect on Y for X at 2 levels (variance Group A vs. Variance B): F-test

Test mean effect on Y for X at 2 levels using paired data: Paired t-test

Independent Test mean effect on Y for X at 2 levels: Samples t-test Test two proportions (Proportion Group A vs. Proportion Group B): Two proportion test Test mean effect on Y for X at 2 or more levels using independent samples: One-Factor ANOVA Test mean effect on Y for two X variables at 2 or more levels each: Two-Factor ANOVA

Examine relationship between a single Y and X variable (prediction equation, Correlation, and R-squared): Scatter Plot Simple Regression

Examine relationship between a single Y and mulitple X variables: Multiple Run Chart Multiple Regression Correlation Matrix Queuing Analysis Perform a Controlled Design of Experiment: Control Chart Create an Define Existing Analyze QETools DOE Analysis Experiment Experiment Experiment

Other Tools: Multi-vari analysis, stepwise regression

IMPROVE: Identify Improvement Identify improvement countermeasure (new procedure, change process setting, poke yoke, process monitoring Compare alternative solutions using tools from analyze phase or evaluate alternatives using: Pugh Matrix Assess the before/after effect of improvement recommendation relative to current state Process Capability Process Capability Process Capability Sigma Level Graphical Summary Graphical Summary Graphical Summary Binary Tabulation Calculator (Normal) (Non-Normal) (Binary) FMEA Analysis Scorecard Analysis Simulation Analysis

Other Tools: Future State Map, Revised Process Flow Chart

CONTROL: Create Control Plan Prepare a process control plan or document method of control. Control Plan Control Plan Transactional Manufacturing QETools Tutorial - Part I

QE Tools Tutorial Part 2 – Define: Project Charter and SIPOC

2.1 Project Charter 2.2 SIPOC

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2.1 Project Charter

Project Charter Template

Project Information Resources Project #: Project Leader: Project Name: Black Belt: Project Start Date: Champion: Project End Date: Process Owner:

Team Members: QETools Project Charter Template fields: . Project Information- identifying project number and Problem Statement: name, with the start/end dates, and the resources assigned to the project . Problem Statement- brief description of the problem and impact on the business . Goal Statement- desired improvement in key process metrics and financial benefits . Project Scope- start/end points of the process and Goal Statement: what is included/excluded

Project Scope

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2.2 SIPOC Dialogue Box

 Select variables using the SIPOC dialogue box

 Identify the title of the SIPOC

 Optional: state the start and end boundaries

Note: Examples in the tutorial use the excel file “qetools-sampledata”

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SIPOC Diagram shows 2.2 SIPOC . Suppliers, Inputs, Process, Sample Result Outputs, and Customers . Start/End Boundaries . Process Steps Title SIPOC Diagram - Loan Process

Suppliers Inputs Process Outputs Customers

• Appraisers • Lender Programs • Loan Documents • Mortgage Customers

• Insurance Companies • Interest Rates • Mortgage • External Underwriter

Customer Loan is complete • Title Companies • Type of Loan requests loan • Lending Institution

• Government • Loan Value

Step 1: Step 2: Step 3: Step 4: Final:

Prepare Process Underwr Clear Close Loan Loan Loan ite Loan Conditio ns

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QE Tools Tutorial Part 3 – Basic Graphical Tools & Descriptive Statistics

3.1 Basic Descriptive Statistics 3.2 Basic Graphical Tools Run Charts Histograms Box Plot (Single or Multi) Individual Values Plot (Single or Multi) Dot Plot qetools.com 25

3.1 Basic Descriptive Statistics Dialogue Box

 Select one or more variables from the list to analyze (Output Variables) Note: All output appear on a single table

 May enter multiple Output Variables or a Grouping Variable

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3.1 Basic Descriptive Statistics Sample Results

Multiple Variables Variable: Group: ALL TimeWaitingRoom WaitClinician1 WaitClinician2 TotalWait TotalVisit Sample Size, N 345 69 69 69 69 69 Mean 57.9 30.3 13.4 21.9 65.7 158.0 Single Variable Median 30.0 25.0 13.0 18.0 56.0 143.0 StDev, S 61.3 20.7 10.4 16.1 39.0 49.0 TimeWaitingRoom Variance 3763.3 429.8 108.5 259.1 1523.0 2401.8 Sample Size, N 69 Min 0.0 2.0 1.0 0.0 15.0 73.0 Mean 30.3 Max 273.0 82.0 48.0 60.0 147.0 273.0 Median 25.0 Range 273.0 80.0 47.0 60.0 132.0 200.0 StDev, S 20.7 Sum 19960.0 2091.0 926.0 1513.0 4530.0 10900.0 Variable: TimeWaitingRoom TimeWaitingRoom TimeWaitingRoom Variance 429.8 Skewness 1.41 0.70 1.31 0.67 0.44 0.56 Min 2.0 Group:Kurtosis ALL 1.27 A-0.52 1.87B -0.47 C -1.01 -0.53 Max 82.0 Sample Size, N 69 15 28 26 Range 80.0 Mean 30.3 11.5 24.2 47.8 Sum 2091.0 Median 25.0 10.0 25.0 53.0 Skewness 0.70 StDev, S 20.7 3.9 12.5 20.5 Kurtosis -0.52 Variance 429.8 15.1 157.4 418.3 Min 2.0 5.0 2.0 7.0 Max 82.0 17.0 45.0 82.0 Range 80.0 12.0 43.0 75.0 Sum 2091.0 172.0 677.0 1242.0 Skewness 0.70 0.03 0.02 -0.40 Kurtosis -0.52 -1.21One Variable (TimeWaitingRoom)-0.64 -0.71 with Grouping (Team) 27

3.2 Basic Graphical Tools

Graphical Tools Menu:

 Run Chart

 Histogram

 Box Plot (Single or Multi)

 Individual Values Plot (Single or Multi)

 Dot Plot

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3.1 Basic Graphical Tools Run Chart – Dialogue Box

 Select one or more variables from the list to analyze (Output Variables) Note: All output appear on a single run chart

 Optional: Modify the scale setting for the Y axis

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3.1 Basic Graphical Tools Run Chart – Sample Results

Single Variable

NOTE: Specification Limits are added if listed on data sheet. May exclude/hide using drop down box on output sheet.

Lower Multiple Variables Target Upper 20

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3.1 Basic Graphical Tools Histogram – Dialogue Box

 Select the variable from the list to analyze (Output Variables) Note: Output for multiple variables appear on multiple charts

 Use either Absolute or Relative Frequency for Y-axis

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3.1 Basic Graphical Tools Histogram – Sample Result

Adjust Bin Width

- + TimeWaitingRoom Histogram 10 OR Enter Min and Width Cumulative 1st Bin: Hidden 9 WIDTH: The Histogram output contains:

Total: 69 8 . Frequency table (frequency of Relative Cumulative Rel Bin Frequency Frequency Freq 7 observations falling within a certain 5.0 3 4.35% 4.35% 8.0 6 8.70% 13.04% 6 data range or bin) 11.0 6 8.70% 21.74% 14.0 3 4.35% 26.09% 5 . Histogram 17.0 9 13.04% 39.13% 20.0 1 1.45% 40.58% Frequency 4 23.0 0 0.00% 40.58% 26.0 7 10.14% 50.72% 3 29.0 3 4.35% 55.07% 32.0 8 11.59% 66.67% 2 35.0 1 1.45% 68.12% 38.0 1 1.45% 69.57% 41.0 1 1.45% 71.01% 1 44.0 1 1.45% 72.46% 47.0 4 5.80% 78.26% 0

50.0 0 0.00% 78.26%

5.0 8.0

14.0 20.0 29.0 35.0 50.0 65.0 80.0 11.0 17.0 23.0 26.0 32.0 38.0 41.0 44.0 47.0 53.0 56.0 59.0 62.0 68.0 71.0 74.0 77.0 53.0 3 4.35% 82.61% more 56.0 1 1.45% 84.06% Bin 59.0 2 2.90% 86.96% 62.0 2 2.90% 89.86% 65.0 2 2.90% 92.75% Sample, N 69 68.0 2 2.90% 95.65% Mean 30.3 71.0 1 1.45% 97.10% Median 25.0 Histogram Table/Graph options: 74.0 0 0.00% 97.10% StDev 20.7 77.0 1 1.45% 98.55% Variance 429.8 . Adjust Bin Width with scroll bar (+/-) 80.0 0 0.00% 98.55% Min 2.0 more 1 1.45% 100.00% Max 82.0 or WIDTH field Range 80.0 st Sum 2091.0 . Enter 1 Bin value to adjust Skewness 0.70 Kurtosis -0.52 table/graph to desired cutoff values

Alpha, a 0.05 . Show or Hide Cumulative line and Skewness - (1-a%) Est Lower CI 0.13 Skewness - (1-a%) Est Upper CI 1.27 axis label Significant? Significant

Kurtosis - (1-a%) Est Lower CI -1.64 32 Kurtosis - (1-a%) Est Upper CI 0.59

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3.1 Basic Graphical Tools Box Plot (Single) – Dialogue Box

 Select the variable from the list to analyze (Output Variables)

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3.1 Basic Graphical Tools Box Plot (Single) – Sample Result

TimeWaitingRoom USL 20 The Box Plot output contains: LSL Sample, N 69 . Box Plot graph & table Mean 30.3 Q1 13.0 Median 25.0 Q3 45.0 StDev 20.7 Variance 429.8 Min 2.0 The Box Plot option: Max 82.0 . Include or exclude the specification Range 80.0 limit lines on the graph Sum 2091.0 Skewness 0.70 Kurtosis -0.52

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3.1 Basic Graphical Tools Box Plot (Multi) – Dialogue Box

 Select the variable from the list to analyze (Output Variables) Note: All output appear on a single chart

 May enter multiple Output Variables or a Grouping Variable

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3.1 Basic Graphical Tools Box Plot (Multi) – Sample Result

Output Variable: TimeWaitingRoom Grouping Variable: Team

Output Variable: TimeWaitingRoom & WaitClinician1 Grouping Variable: Team

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3.1 Basic Graphical Tools Individual Values Plot – Dialogue Box

 Select one or more variables from the list to analyze (Output Variables) Note: All output appear on a single chart

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3.1 Basic Graphical Tools Individual Values Plot – Sample Result

Individual Values Plot with 3 variables: . TimeWaitingRoom . WaitClinician1 . WaitClinician1

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3.1 Basic Graphical Tools Individual Values Plot – Dialogue Box

Grouping Option:

 Select one Output and one Grouping variable from the list to analyze

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3.1 Basic Graphical Tools Individual Values Plot – Sample Result

Individual Values Plot with 1 Output variable (TimeWaitingRoom) and Grouping Variable (Team)

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3.1 Basic Graphical Tools Dot Plot – Dialogue Box

 Select the variable from the list to analyze (Output Variables)

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3.1 Basic Graphical Tools Dot Plot – Sample Result

TOTAL 69 Relative Cumulative TimeWaitingRoom Frequency Frequency Rel Freq 2 1 1.4% 1.4% Dot Plot with Output Variable 3 1 1.4% 2.9% 5 1 1.4% 4.3% (TimeWaitingRoom) 7 4 5.8% 10.1% 8 2 2.9% 13.0% 9 1 1.4% 14.5% 10 5 7.2% 21.7% 12 2 2.9% 24.6% 13 1 1.4% 26.1% 15 6 8.7% 34.8% 9 16 1 1.4% 36.2%

Frequency 7 17 2 2.9% 39.1% 20 1 1.4% 40.6% 5 25 7 10.1% 50.7% 28 3 4.3% 55.1% 3 30 5 7.2% 62.3% 32 3 4.3% 66.7% 1 35 1 1.4% 68.1% 0 10 20 30 40 50 60 70 80 90 38 1 1.4% 69.6% 39 1 1.4% 71.0% TimeWaitingRoom 43 1 1.4% 72.5% 45 4 5.8% 78.3% 51 1 1.4% 79.7% 53 2 2.9% 82.6% 54 1 1.4% 84.1% 57 2 2.9% 87.0% 62 2 2.9% 89.9% 63 1 1.4% 91.3% 65 1 1.4% 92.8% 67 1 1.4% 94.2% 68 1 1.4% 95.7% 71 1 1.4% 97.1% 76 1 1.4% 98.6% 82 1 1.4% 100.0%

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QE Tools Tutorial Part 4 – Process Capability (DPMO, PPM Defective, Capability Indices) 4.1 Sigma Level and DPM Converter (DPMO) 4.2 Process Capability Summary Process Capability Summary – Normal Process Capability Summary – Non-Normal (Weibull) Process Capability Summary – Binary (Binomial)

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4. Process Capability DPMO, PPM Defective, Capability Indices

 Data Analysis Tools

 Sigma Level and DPM Converter (DPMO)*

 Process Capability Graphical Summary*

 Variable is Normal

 Variable is Non-Normal – Best Fit with Weibull Distribution

 Variable is Binary – Assume Binomial Distribution

*DPM – Defects per Million (same as PPM Defective) 44

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4.1 Sigma Level and DPM Converter (DPMO)

 Sigma Level and DPM Converter is a template which may be used to perform various calculations for PPM, DPMO, Yield and Sigma Level

Note: Tolerance and Process Capability Converter is also a template used to calculate tolerance and mean allowance

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4.1 Sigma Level and DPM Converter (DPMO) Sample Result

Enter Values in White Boxes Five different methods

PPM Defective = DPM Sigma Level Converter are available to (Defects per Million) (enter values in white boxes) Sigma Level from Total Opportunities and Defects (each unit may have 1 or more opportunities for a defect) calculate the “sigma Total Opportunities Defects DPMO Yield Sigma Level level” depending on the 4,050 15 3,703.7 99.630% 4.18 format of information example 3200 5 1562.5 99.844% 4.46available from your Sigma Level from Units and Defects (each unit may have 1 or more of the same opportunities for a defect) process. Enter the Total Units Defects DPU Yield Sigma Level

1,350 5 0.004 99.630% 4.18 appropriate information example 800 5 0.006 99.377% 4.00in white boxes and Sigma Level from Total Units and Total Defective Units (each unit is defective or not defective) sigma level is calculated Total # Units # Units Defective PPM Defective Yield Sigma Level automatically. 1,350 5 3,703.7 99.63% 4.18 example 1350 5 3703.7 99.63% 4.18

Sigma Level from Quality Yield (Yield = 1 - % defective)

Quality Yield % Non-Conforming PPM Defective Z Sigma Level

0.9999966 0.0003400% 3.4 4.50 6.00 example 0.9999966 0.00 3.40 4.50 6.00

Sigma Level from PPM for Non Centered Process - Assumes 1.5 sigma shift (Normal Distribution)

PPM Defective Yield Prob Z Sigma Level

6,210.0 99.38% 0.0062100 2.499980907 4.00 example 6210 99.38% 0.00621 2.499980907 4.00 46

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4.1 Sigma Level and DPM Converter (DPMO) Sample Result Continued Enter Values in White Boxes

PPM Converter Assuming Normal Distribution (enter values in white boxes) PPM Defective (Defects per Million) given Average, Sigma, USL, LSL

Upper Specification Nominal or Lower Specification Average Standard Deviation Limit (USL) Target (optional) Limit (LSL)

16 2 20 15 10

Pp Ppk Predicted PPM Quality Yield

0.83 0.67 24,100.0 97.59%

PPM Probability Defect PPM

PPM > USL 0.022750 22,750.1

PPM < LSL 0.001350 1,349.9

PPM Total 0.024100 24,100.0

Note: Parts per Million Defective (PPM Defective) = Defects per Million (DPM) Option to calculate the PPM (DPMO) given the process average, standard deviation, and specification limits.

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4.2 Process Capability Summary*

 Different Process Capability Summaries are available depending on data/distribution

 Continuous Variable and Normal Distribution

 Continuous Variable and Non-Normal – Best Fit with Weibull Distribution

 Binary Variable – Distribution assumed Binomial

*Note: Process Capability Summary includes: summary statistics, observed DPM, expected DPM (distribution),

histogram, run charts, box plot, control charts where applicable 48

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4.2 Process Capability Summary Normal – Dialogue Box

 Select one or more variables from the list to analyze (Output Variables) Note: Output for multiple variables appear on separate worksheets

 Select type of control chart Note: Subgroup size is assumed 1 for IMR unless otherwise specified Options: . Show out-of-control patterns . Manual scale (min/max) run chart . Enter specification limits if not already entered on the “data sheet” 49

4.2 Process Capability Summary Normal – Sample Results

Process Capability Graphical Summary TimeWaitingRoom Normal

Summary Statistics Histogram USL 20 Target LSL Sample Size, N 69 12 Mean 30.3 Median 25.0 The Process Capability output contains: 10 USL Stdev (Within) 15.2 Stdev (Overall, S ) 20.7 Range 80.0 8 . Statistical summary Process Capability Cp Cpk -0.23 6 Pp . Expected Defects per Million Ppk -0.17 Frequency 4 Expected Overall Performance PPM < LSL (distribution) PPM > USL 690423.3 2 PPM Total Expected 690423.3

Observed Performance 0 . Observed Defects per Million PPM < LSL 5.9 13.7 21.5 29.3 37.1 44.9 52.7 60.5 68.3 76.1 more PPM > USL 594202.9 PPM Total Observed 594202.9 First Bin 5.9 Yield (%) Observed 40.58% Width 3.9 . Histogram # Observed Defective 41

. Run chart Box Plot 90 Run Chart . Box plot 80 90 70 80 70 60 . Control charts 60 50 50

Value 40

30 Value 40 20 10 30 0 0 10 20 30 40 50 60 20 Observation 10

0

Control Chart - Individuals Control Chart - Moving Range Chart

90 70 75.99 70 60 56.12 50 50 40 30 30.30 30 10

MovingRange 20 -10 17.18 -15.38 IndividualValue 10 -30 Subgroup 0 0.00 Subgroup

Outside Control Limit

consecutive9 consecutive points points on on same same side side of ofCL CL 9

consecutive6 consecutive points points increasing increasing or ordecreasing decreasing 6

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4.2 Process Capability Summary Normal – Sample Results (Summary Stats and Histogram)

Process Capability Graphical Summary TimeWaitingRoom Normal

Summary Statistics Histogram USL 20 Target LSL Sample Size, N 69 12 Specification Limit are displayed Mean 30.3 Median 25.0 on the chart Stdev (Within) 15.2 10 USL Stdev (Overall, S ) 20.7 Range 80.0 8 Process Capability Cp Cpk -0.23 6 Pp

Ppk -0.17 Frequency 4 Expected Overall Performance PPM < LSL PPM > USL 690423.3 2 PPM Total Expected 690423.3

Observed Performance 0 PPM < LSL 5.9 13.7 21.5 29.3 37.1 44.9 52.7 60.5 68.3 76.1 more PPM > USL 594202.9 PPM Total Observed 594202.9 First Bin 5.9 Yield (%) Observed 40.58% Width 3.9 # Observed Defective 41

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4.2 Process Capability Summary Normal – Sample Results (Run Chart and Box Plot)

. The Run Chart displays in datasheet order . Box Plot summarizes distribution (Example shown is skewed right)

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4.2 Process Capability Summary Non-Normal (Weibull)

May perform similar analysis assuming data are non-normal (QE Tools fits Weibull)

Process Capability Graphical Summary Non-Normal TimeWaitingRoom Summary Statistics USL 20 Histogram Target LSL Sample Size, N 69 12 Mean 30.3 Median 25.0 Stdev, S 20.7 10 USL Shape (beta) 1.48 Scale (alpha) 33.50 Predicted 6s Spread 79.4 8 Range 80.0 Distribution: Weibull 6 Process Capability Pp Ppk -0.09 4

2 Expected Overall Performance PPM < LSL 0 PPM > USL 627650.4 PPM Total Expected 627650.4 5.9 13.7 21.5 29.3 37.1 44.9 52.7 60.5 68.3 76.1 more

Observed Performance First Bin 5.9 PPM < LSL Width 3.9 PPM > USL 594202.9 PPM Total Observed 594202.9 Yield (%) Observed 40.58% # Observed Defective 41 Box Plot 90

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4.2 Process Capability Summary Binary (Binomial)

Process Capability may be performed on Binary data (assume Binomial)

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QE Tools Tutorial Part 5 – Statistical Process Control (Control Charts)

5.1 Binary (Attribute) Variable Charts P-Chart & NP-Chart 5.2 Poisson (Attribute) Variable Charts U-Chart & C-Chart 5.3 Continuous Variable Charts Individual / Moving Range Chart, X-Bar / Range Chart, & X-Bar / S Chart qetools.com 55

5. Statistical Process Control (Control Charts)

 Attribute Charts

 P-Charts

 U-Charts

 Variable Control Charts

 Individual/Moving Range

 X-Bar/Range

Note: Other charts available but not demonstrated here (See Help File) 56

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5.1 Binary (Attribute) Variable Charts P-chart – Dialogue Box

 For unequal sample size, select two variables:

 number of units inspected

 number of defective units Note: Do not enter the “Percent Defective (p)” – QE Tools calculates this

 For constant sample size, specify a constant sample size and select a single variable:

 number of defective units Note: Similar to Attribute NP-Chart 57

5.1 Binary (Attribute) Variable Charts P-chart – Sample Results Note: after creating a chart, you may Exclude Points Unequal sample size and hit “UPDATE CHARTS” to reconfigure charts Include/ Subgroup Units Events Proportion (P) Comment Control Chart for Attributes Exclude 1 465 133 0.286 Include P Chart 2 425 124 0.292 Include 3 500 170 0.340 Include 0.40 4 505 184 0.364 Include 0.38 0.376 5 425 137 0.322 Include 0.36 0.34 6 430 116 0.270 Include 0.32 0.312 7 425 136 0.320 Include 0.30 8 465 126 0.271 Include 0.28 9 500 165 0.330 Include 0.26 0.249 10 455 99 0.218 Include 0.24 11 425 136 0.320 Include Samplep 0.22 0.20 12 465 156 0.335 Include 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 13 483 173 0.358 Include 14 425 136 0.320 Include Subgroup 15 480 150 0.313 Include 16 510 185 0.363 Include 17 425 125 0.294 Include 18 455 122 0.268 Include Outside Control Limit 19 425 115 0.271 Include 20 465 145 0.312 Include 9 consecutive points on same side of CL 21 465 138 0.297 Include 22 500 169 0.338 Include consecutive points increasing or decreasing 6 23 515 175 0.340 Include 24 465 154 0.331 Include 25 480 149 0.310 Include Proportion Vs. Subgroup Size 0.40 0.38 The P-Chart output contains: 0.36 0.34 . Table of values 0.32 0.30 . Control Chart Samplep 0.28 0.26 . Proportion vs Subgroup size (only 0.24 0.22 0.20 appears in unequal sample size) 425 435 445 455 465 475 485 495 505 515 Subgroup Size 58

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5.1 Binary (Attribute) Variable Charts P-chart – Sample Result (for constant sample size) Constant sample size

The P-Chart output contains: . Table of values . Control Chart

Proportion Include/ Subgroup Units Events Comment Control Chart for Attributes Defective (P) Exclude 1 500 133 0.266 Include P Chart 2 500 124 0.248 Include 3 500 170 0.340 Include 0.40 4 500 184 0.368 Include 0.35 0.350 5 500 137 0.274 Include 6 500 116 0.232 Include 0.30 0.289 7 500 136 0.272 Include 0.25 8 500 126 0.252 Include 0.229 9 500 165 0.330 Include 0.20 10 500 99 0.198 Include 0.15 11 500 136 0.272 Include Samplep 0.10 12 500 156 0.312 Include 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 13 500 173 0.346 Include 14 500 136 0.272 Include Subgroup 15 500 150 0.300 Include 16 500 185 0.370 Include 17 500 125 0.250 Include 18 500 122 0.244 Include Outside Control Limit 19 500 115 0.230 Include 20 500 145 0.290 Include 9 consecutive points on same side of CL 21 500 138 0.276 Include 22 500 169 0.338 Include consecutive points increasing or decreasing 6 23 500 175 0.350 Include 24 500 154 0.308 Include 25 500 149 0.298 Include 59

5.2 Poisson (Attribute) Variable Charts U-chart – Dialogue Box

 Enter variable with the # units (subgroup sizes) or constant sample size

 Enter # defects (errors) Note: Similar to Attribute C-Chart

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5.2 Poisson (Attribute) Variable Charts U-chart – Sample Results Unequal sample size Include/ Subgroup Units Events Sample U Comment Control Chart for Attributes Exclude 1 1354 13 0.00960 Include U Chart 2 1535 16 0.01042 Include 3 1237 12 0.00970 Include 0.020 4 1677 17 0.01014 Include 0.018 0.01799 5 2036 20 0.00982 Include 0.016 0.014 6 1591 16 0.01006 Include 0.012 7 1408 14 0.00994 Include 0.010 0.01004 8 1672 17 0.01017 Include 0.008 9 1611 16 0.00993 Include 0.006 10 1145 12 0.01048 Include 0.004 11 1840 19 0.01033 Include Sampleu 0.002 0.00208 0.000 12 1428 14 0.00980 Include 1 2 3 4 5 6 7 8 9 10 11 12 Subgroup

Outside Control Limit The U-Chart output contains: 9 consecutive points on same side of CL . Table of values consecutive points increasing or decreasing 6 . Control Chart Defects per Unit by Subgroup Size . Defects per Unit vs Subgroup size 0.020 0.018 0.016 0.014 0.012 0.010

Sampleu 0.008 0.006 0.004 0.002 0.000 1145 1245 1345 1445 1545 1645 1745 1845 1945 Subgroup Size 61

5.2 Poisson (Attribute) Variable Charts U-chart – Sample Results Constant sample size

The U-Chart output contains: . Table of values . Control Chart

Include/ Subgroup Units Events Sample U Comment Control Chart for Attributes Exclude 1 1250 13 0.0104 Include U Chart 2 1250 16 0.0128 Include 3 1250 12 0.0096 Include 0.030 4 1250 17 0.0136 Include 0.025 5 1250 20 0.0160 Include 0.0218 6 1250 16 0.0128 Include 0.020 7 1250 14 0.0112 Include 0.015 8 1250 17 0.0136 Include 0.0124 9 1250 16 0.0128 Include 0.010 10 1250 12 0.0096 Include 0.005 11 1250 19 0.0152 Include Sampleu 0.0030 0.000 12 1250 14 0.0112 Include 1 2 3 4 5 6 7 8 9 10 11 12 Subgroup

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5.3 Continuous Variable Charts Individual/Moving Range – Dialogue Box

 Select one or more variables from the list to analyze Note: Output for multiple variables appear on separate worksheets

 Check this box to show out- of-control data points on the control charts

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5.3 Continuous Variable Charts Individual/Moving Range – Sample Results The IMR-Chart output contains: . Table of values . Individuals Chart . Moving Range Chart

Moving Include/ Subgroup Ind Comment Control Chart for Variables Range Exclude 1 25.0 Include Individuals Chart 2 17.0 8.0 Include 3 20.0 3.0 Include 200 4 19.0 1.0 Include 175.2 150 5 45.0 26.0 Include 6 106.0 61.0 Include 100 7 26.0 80.0 Include 50 65.7 8 49.0 23.0 Include 0 9 51.0 2.0 Include 10 37.0 14.0 Include -50 -43.9 11 56.0 19.0 Include -100 12 31.0 25.0 Include IndividualValue 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869 13 83.0 52.0 Include 14 64.0 19.0 Include Subgroup 15 35.0 29.0 Include 16 24.0 11.0 Include Moving Range Chart 17 91.0 67.0 Include 18 62.0 29.0 Include 160 19 45.0 17.0 Include 140 134.6 20 104.0 59.0 Include 120 21 56.0 48.0 Include 100 22 85.0 29.0 Include

MR 80 23 123.0 38.0 Include 60 24 28.0 95.0 Include 25 119.0 91.0 Include 40 41.2 26 79.0 40.0 Include 20 27 147.0 68.0 Include 0 0.0 28 73.0 74.0 Include 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869 29 21.0 52.0 Include Subgroup 30 34.0 13.0 Include 64

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5.3 Continuous Variable Charts X-bar/Range – Dialogue Box (1 Column)

All Data in 1 Column

 Select one variables from the list to analyze

 Check this box to show out-of-control data points on the control charts

 Select the sub group size (every # of rows) Note: Similar to Attribute X-bar/S Chart

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5.3 Continuous Variable Charts X-bar/Range – Dialogue Box (Multiple Columns)

Data Across Columns (each row is a subgroup)

 Select two or more variables from the list to analyze

 Check this box to show out-of-control data points on the control charts

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5.3 Continuous Variable Charts X-bar/Range – Sample Results The X-bar/R-Chart output contains: All Data in 1 Column . Table of values . X-bar Chart . Range Chart

Include/ Subgroup X-bar Range Comment Control Chart for Variables Exclude 1 21.0 8.0 Include X-bar Chart 2 19.5 1.0 Include 3 75.5 61.0 Include 200 4 37.5 23.0 Include 150 5 44.0 14.0 Include 132.4 6 43.5 25.0 Include 100

7 73.5 19.0 Include 50 64.6 bar 8 29.5 11.0 Include - X 0 -3.2 9 76.5 29.0 Include 10 74.5 59.0 Include -50 11 70.5 29.0 Include -100 12 75.5 95.0 Include 1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435 13 99.0 40.0 Include 14 110.0 74.0 Include Subgroup 15 27.5 13.0 Include 16 82.0 40.0 Include Range Chart 17 76.0 40.0 Include 18 56.5 23.0 Include 140 19 73.0 96.0 Include 120 117.8 20 93.0 52.0 Include 21 44.5 57.0 Include 100 22 59.0 82.0 Include 80 23 53.5 17.0 Include 60

24 78.5 45.0 Include Range 40 25 101.0 12.0 Include 36.1 26 17.5 3.0 Include 20 27 111.0 36.0 Include 0 0.0 28 44.5 57.0 Include 1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435 29 63.0 96.0 Include Subgroup 30 43.5 3.0 Include 67

Control Limits Calculations

 May adjust control limits by using only a subset of subgroups for calculations (Note: All points will still display on graph) Subgroups for Control Limit Calculations (Note: May exclude additional subgroup using Include/Exclude in Column D)

# Subgroups 69 # Subgroups 69

Start Subgroup 1 Start Subgroup 1 End Subgroup 69 End Subgroup 33 X-bar Control Limits X-bar Control Limits UCL 45.37 UCL 41.59 CL 21.88 CL 20.35 LCL -1.60 LCL -0.88 Range Control Limits Range Control Limits UCL 59.09 UCL 53.43 CL 22.96 CL 20.76 LCL 0.00 LCL 0.00 68

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QE Tools Tutorial Part 6 – Measurement System Analysis (Gage R&R)

6.1 Gage R and R 6.2 Paired (Repeated) Measurement Study 6.3 Attribute Matching Study

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6. Measurement System Analysis (MSA)

 Measurement Systems Analysis Tools

 Gage R&R Template

 Paired (Repeated) Measurement Study

 Attribute Matching Study (Agreement Study)

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6.1 Gage R&R Template Overview

Gage R & R Study Worksheet

Date:

Gage Number: Part Number: Gage Cert. Level: Part Name: Gage Cert. Date: Characteristic: Gage Build Source: Engineering Level:

Operator: A B C

Number of Operators: Tolerance Width: Study Variation: 6.00 # of standard deviations

Number of Trials: Number of Parts: Trial Part Operator Number 1 2 3 4 5 6 7 8 9 10 Average A 1 2 3 Average X-bar Range R-bar Trial Part Operator Number 1 2 3 4 5 6 7 8 9 10 Average B 1 2 Gage R&R Template fields: 3 Average . Header- gage, part, and operatorX-bar information Range R-bar Trial Part . Data Entry- part measurements for multiple Operator Number 1 2 3 4 5 6 7 8 9 10 Average C 1 operators and multiple trials 2 3 . Calculations- R&R, repeatability, and reproducibility Average X-bar Range R-bar Part Average Rp

Equipment Variation: Enter # Trials srepeatability %EV-Tol Enter Tol %EV-TV R-Dbl-Bar

Appraiser Variation: Enter # Op's sreproducibility %AV-Tol Enter Tol %AV-TV X-bar Diff

R & R: sR&R %RR-Tol Enter Tol %RR-TV UCL R chart

Part Variation: Enter # Parts sPV %PV-TV LCL R Chart 0.00 Max Range Total Variation: sTV Pass/Fail Enter Tol Pass/Fail Range Acceptance Criteria < 30% Stable? 71

6.1 Gage R&R Template – Header Section

Gage R & R Study Worksheet

Date:

Gage Number: Part Number: Gage Cert. Level: Part Name: Gage Cert. Date: Characteristic: Gage Build Source: Engineering Level:

Operator: A B C

Number of Operators: Tolerance Width: Study Variation: 6.00 # of standard deviations

Number of Trials: Number of Parts:

. Number of Trials & Number of Parts needed for calculations . Tolerance width = USL – LSL . Study Variation Multiplier: K=5.15 or 6 . 5.15 (predict 99% of the area under normal distribution curve), or 6 (predict 99.73% of the area under normal distribution curve)

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6.1 Gage R&R Template – Data Entry Section

Data Entry Section for Measurement System Study . Max 10 parts . 3 Operators . 3 Trials

Trial Part Operator Number 1 2 3 4 5 6 7 8 9 10 Average A 1 2 3 Average X-bar Range R-bar Trial Part Operator Number 1 2 3 4 5 6 7 8 9 10 Average B 1 2 3 Average X-bar Range R-bar Trial Part Operator Number 1 2 3 4 5 6 7 8 9 10 Average C 1 2 3 Average X-bar Range R-bar

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6.1 Gage R&R Sample Result – Data

. Enter Data in White Cells . Calculations done automatically in Yellow

Gage Number: X235 Part Number: 22561089 Gage Cert. Level: 3 Part Name: Door Gage Cert. Date: 8/1/2001 Characteristic: Feature #1 Gage Build Source: UM Engineering Level: 3

Operator: A Drake B Kramer C

Number of Operators: 2 Tolerance Width: 1.4 Study Variation: 6.00 # of standard deviations

Number of Trials: 3 Number of Parts: 5 Trial Part Operator Number 1 2 3 4 5 6 7 8 9 10 Average A 1 -0.32 -0.13 -0.36 -0.22 -0.33 -0.27 2 -0.25 -0.17 -0.39 -0.19 -0.26 -0.25 3 -0.29 -0.19 -0.34 -0.18 -0.29 -0.26 Average -0.29 -0.16 -0.36 -0.20 -0.29 X-bar -0.26 Range 0.07 0.06 0.05 0.04 0.07 R-bar 0.06 Trial Part Operator Number 1 2 3 4 5 6 7 8 9 10 Average B 1 -0.14 -0.13 -0.35 -0.24 -0.26 -0.22 2 -0.13 -0.18 -0.37 -0.25 -0.30 -0.25 3 -0.20 -0.19 -0.37 -0.17 -0.27 -0.24 Average -0.16 -0.17 -0.36 -0.22 -0.28 X-bar -0.24 Range 0.07 0.06 0.02 0.08 0.04 R-bar 0.05

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6.1 Gage R&R Sample Result – Calculations

Sample Output based on SPC Average and Range Method

Part Average -0.22 -0.17 -0.36 -0.21 -0.29 Rp 0.20

Equipment Variation: 0.20 srepeatability 0.03 %EV-Tol 14.0% %EV-TV 37.2% R-Dbl-Bar 0.06

Appraiser Variation: 0.09 sreproducibility 0.01 %AV-Tol 6.3% %AV-TV 16.9% X-bar Diff 0.02

R & R: 0.21 sR&R 0.04 %RR-Tol 15.3% %RR-TV 40.8% UCL R chart 0.14

Part Variation: 0.48 sPV 0.08 %PV-TV 91.3% LCL R Chart 0.00 Max Range 0.08 Total Variation: 0.53 sTV 0.09 Pass/Fail Pass Pass/Fail Fail Range Acceptance Criteria < 30% Yes Stable?

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6.2 Paired (Repeated) Measurements Study Template Overview

Paired (Repeated) Measurements Study

Part Number: Study Date: Part Name: Gage Certification Level: Gage Build Source: Operator(s):

Comments:

Part Measure 1 Measure 2 Difference (+/-) Abs Difference Variable Name: 1 LSL: 2 USL: 3 TOLERANCE WIDTH: 4 5 1 6  Enter data in White 7 0.9 8 0.8 9 10 0.7 11 2 0.6 12 Cells, 13 0.5 14 0.4 15 Measure 16 0.3 17 0.2 18 19 0.1 OR 20 0 21 22 0 0.2 0.4 0.6 0.8 1 23 Measure1 24 25 26 Note: Dashed Line Represents Perfect Match, Solid Line Represents best fit.  Select two variables 27 28 Hide Perfect Match Line Show Best Fit Line 29 30 R-Sq= 31 from the list to 32 Study 33 Source Sigma (s) Variation (Ks) % Study Variation % Tolerance 34 Meas Sys Variation 35 Part-to-Part analyze 36 37 Total Variation 38 39 40 % Contribution: Measurement System to Total Variance 41 42 Study Variation (# of "K" Sigma's) 6 (default = 6) 43 44 alpha (a) = 0.05 (default = .05) 45 p-value = 46 for Paired t-test comparison 47 48 Test Result =

49 Test: Difference =0; MeanMeasure 1 - MeanMeasure 2 50 Measure 1 Measure 2 Range, Diff Range, Abs Diff Average StDev s (MS - abs diff) s pooled Measurement System (Meas Sys) 76

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6.2 Paired (Repeated) Measurements Study Sample Result

Part Measure 1 Measure 2 Difference (+/-) Abs Difference Variable Name: 1 0.86 0.92 -0.06 0.06 LSL: -1 2 0.82 0.88 -0.06 0.06 USL: 1 3 0.96 0.88 0.08 0.08 TOLERANCE WIDTH: 2 4 0.76 0.80 -0.04 0.04 5 0.72 0.70 0.02 0.02 6 0.10 0.14 -0.04 0.04 1.00 Variable Name: 7 0.15 0.18 -0.03 0.03 8 0.16 0.12 0.04 0.04 0.80 LSL: -1 9 0.14 0.08 0.06 0.06

10 0.18 0.18 0.00 0.00 2 11 0.15 0.13 0.02 0.02 0.60 USL: 1 12 0.12 0.08 0.04 0.04 13 0.14 0.12 0.02 0.02 TOLERANCE WIDTH: 2

14 0.10 0.16 -0.06 0.06 Measure 0.40 15 0.12 0.16 -0.04 0.04 16 17 0.20 18 19 20 0.00 Note: Need Specifications 21 0.00 0.20 0.40 0.60 0.80 1.00 22 Measure1 23 24 (OR, tolerance width) for 25 26 Note: Dashed Line Represents Perfect Match, Solid Line Represents best fit. 27 28 Hide Perfect Match Line Show Best Fit Line some calculations 29 30 R-Sq= 98.2% 31 32 Study 33 Source Sigma (s) Variation (Ks) % Study Variation % Tolerance 34 Meas Sys Variation 0.0361 0.2163 10.45% 10.82% 35 Part-to-Part 0.3433 2.0596 99.45% 102.98% The Paired Measurement 36 37 Total Variation 0.3451 2.0709 Study output contains: 38 39 40 % Contribution: Measurement System to Total Variance 1.1% . Scatter Plot 41 42 Study Variation (# of "K" Sigma's) 6 (default = 6) . R-squared value 43 44 alpha (a) = 0.05 (default = .05) 45 p-value = 0.787 . Tolerance & Variation for the 46 for Paired t-test comparison 47 Measurement System and Part- 48 Test Result = No Difference

49 Test: Difference =0; MeanMeasure 1 - MeanMeasure 2 to-Part 50 Measure 1 Measure 2 Range, Diff Range, Abs Diff Average 0.37 0.37 0.00 0.04 . P-value and Test Result StDev 0.34 0.35 s (MS - abs diff) 0.036 s pooled 0.343 77

6.3 Attribute Matching Study Template Overview

Attribute Matching Study: Appraiser Vs. Standard

Ratings Sample Standard Appraiser 1 Appraiser 2 Appraiser 3 1 2 Appraiser vs. Standard 3 Attribute Matching 4 CL upper lowr 5 100% Appraiser 1 6 90% Appraiser 2 7 80% Appraiser 3 8 9 70% N 10 60% m 11 50% v1lower #VALUE! #VALUE! #VALUE! 12 v2lower #VALUE! #VALUE! #VALUE! 40%  Enter data in White Cells 13 v1upper #VALUE! #VALUE! #VALUE!

14 30% v2upper #VALUE! #VALUE! #VALUE! % Agreement . Agreement % 15 20% alpha 0.05 0.05 0.05 16 Flower #VALUE! #VALUE! #VALUE! 10%  Must include a standard (or 17 Fupper #VALUE! #VALUE! #VALUE! 18 0% st 19 Appraiser 1 Appraiser 2 Appraiser 3 reference) in 1 Column 20 21 22 23  Enter data for 1-3 Appraisers 24 25 Sample Size 26 alpha = 0.05 in additional columns 27 28 Appraiser 1 Appraiser 2 Appraiser 3 29 # Matches - Standard 30 % Match-Standard Note: Max 50 samples 31 32 Lower Bound 33 Upper Bound 34  Enter Alpha (Type I) error 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Note: Calculations In yellow box 49 50

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6.3 Attribute Matching Study Sample Result

Attribute Matching Study: Appraiser Vs. Standard

Ratings Sample Standard Appraiser 1 Appraiser 2 Appraiser 3 1 10 10 10 9 2 9 9 9 8 Appraiser vs. Standard 3 1 1 1 2 Attribute Matching 4 3 3 3 2 CL upper lowr 5 5 5 5 5 100% Appraiser 1 0.8 0.09 0.12 6 10 10 10 9 90% Appraiser 2 0.86 0.07 0.11 OK, if 7 9 9 10 9 80% Appraiser 3 0.36 0.13 0.11 8 8 8 8 8 confidence 9 4 3 4 2 70% N 50 50 50 10 6 6 6 7 60% m 40 43 18 11 5 5 5 6 50% v1lower 80 86 36 intervals 12 2 2 2 2 v2lower 22 16 66 13 1 2 1 1 40% v1upper 82 88 38

14 8 8 8 9 30% v2upper 20 14 64 overlap % Agreement . Agreement % 15 7 6 7 8 20% alpha 0.05 0.05 0.05 16 6 6 5 5 Flower 0.5964 0.5674 0.6020 10% 17 1 1 1 2 Fupper 1.9199 2.1944 1.5910 18 10 10 10 10 0% 19 9 9 8 8 Appraiser 1 Appraiser 2 Appraiser 3 20 6 7 6 6 21 4 4 5 4 22 3 3 3 4 23 8 8 8 7 24 2 1 2 1 25 6 6 6 5 Sample Size 50 26 5 6 5 5 alpha = 0.05 27 4 4 4 3 28 3 3 3 2 Appraiser 1 Appraiser 2 Appraiser 3 29 1 1 1 2 # Matches - Standard 40 43 18 30 1 1 1 1 % Match-Standard 80.0% 86.0% 36.0% 31 9 9 9 8 32 1 1 1 2 Lower Bound 68.44% 75.31% 24.72% 33 3 3 3 2 Upper Bound 88.73% 93.24% 48.58% 79

QE Tools Tutorial Part 7 – Cause and Effect (Fishbone Diagram)

7.1 Cause-Effect Diagram 7.2 Cause-Effect Matrix

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7.1 Cause-Effect Diagram Dialogue Box

Manually Enter

 Choose to ‘Enter Text’

 Enter ‘Effect’

 Manually enter potential root causes into the dialog box

 Cause Branch Categories on tabs

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7.1 Cause-Effect Diagram Dialogue Box

Select Variables

 Choose to ‘Select Variables’ Note: New dialog box opens

 Select variables from the list for each applicable category

 Cause Branch Categories on tabs

 Enter ‘Effect’

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7.1 Cause-Effect Diagram Sample Result

Cause and Effect Diagram

Man Method

Late Crew Boarding Process

Late Pilot Gate Blocked

Late Cleaning

Late Airline Flight

FAA Delay Late Baggage Mechanical

Weather Late Meals Gate Not Working

Late Fuel

Environment Material Machine 83

7.2 Cause-Effect Matrix Template & Sample Result

Cause and Effect Matrix Add Column

Key Process Output Variables Customer Importance 8 10 1 2

Process Step Process Input Loan Documents Mortgage Total Rank 1 Prepare Loan Prospect Customer 0 0 0 8 Interest Rates, Type of 2 Prepare Loan 9 9 162 1 Loan The Cause-Effect Matrix 3 Prepare Loan Submitted Application 1 3 38 6 template contains: Additional 4 Process Loan 3 3 54 4 Documentation . Process Inputs listed by 5 Process Loan Home Appraisal 3 9 114 3 Process Step Additional 6 Underwrite Loan 3 3 54 4 . Process Outputs Documentation 7 Clear Conditions Flags on Loan 1 1 18 7 . Outputs rated for Customer Prepared and Cleared Importance 8 Close Loan 9 9 162 1 Process Steps & Key Process Input Variables Process Key & Steps Process Loan . Process Inputs related to Reverse Total 232 370 Reverse Rank 2 1 Customer Requirements Specification 84

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QE Tools Tutorial Part 8 – Tabulation and Pareto Analysis

8.1 Tabulation One Way Tabulation Multiple Tabulation w/Pareto Cross Tabulation w/Chi Squared (2 Variables) Binary Tabulation 8.2 Pareto Analysis

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8.1 Tabulation

 One Way Tabulation –

 Obtain summary counts for a single text or data variable (w/Pareto)

 Multiple Tabulation –

 Obtain summary counts for multiple variables and create Pareto

 Cross Tabulation –

 Perform cross tabulation analysis with Chi-Square Test for 2 Variables

 Binary Tabulation –

 Obtain summary counts for 1 or more Binary Variables (0/1) with DPMO

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8.1 Tabulation One Way Tabulation – Dialogue Box

 Select one variable from the list (Output Variables) Note: May be Text or Data

 Check the box to automatically save summary count data to a new variable on the datasheet

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8.1 Tabulation One Way Tabulation – Sample Results

The One Way Tabulation contains: . Count, Percent and Cumulative percent for each category One-Way Tabulation . Pareto Chart Variable: Team

Count Total 69

Values Count Percent Cumulative B 28 40.6% 40.6% Pareto Chart C 26 37.7% 78.3% 45.0% 100.0% A 15 21.7% 100.0% 40.0% 90.0%

35.0% 80.0% 70.0% 30.0% 60.0% 25.0% 50.0% 20.0% C 40.0% C 15.0% 30.0% B RelativeFrequency . A 10.0% 20.0% Cumulative RelFrequency . A 5.0% 10.0% C B 0.0% 0.0% B B C A B

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8.1 Tabulation Multiple Tabulation – Dialogue Box

 Select one or more variables from the list (Output Variables)

 Optional: Select a Grouping Variable from the list

 Check the box to create a Pareto Chart

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8.1 Tabulation Multiple Tabulation – Sample Results (Output Tables)

No Grouping Variable The Multiple Tabulation contains: . Count Summary Table Multiple Tabulation . Pareto Chart Input: TimeWaitingRoom WaitClinician1 WaitClinician2

Output TimeWaitingRoom WaitClinician1 WaitClinician2 Row Count Count_ALL 69 69 69 207 Sum_ALL 2091 926 1513

Output TimeWaitingRoom Output WaitClinician1 Output WaitClinician2 Count_ALL 69 Count_ALL 69 Count_ALL 69

Value Count Percent Value Count Percent Value Count Percent 2 1 1.4% 1 6 8.7% 0 2 2.9% 3 1 1.4% 3 7 10.1% 1 2 2.9% 5 1 1.4% 5 5 7.2% 2 1 1.4% 7 4 5.8% 7 4 5.8% 3 5 7.2% 8 2 2.9% 8 5 7.2% 5 1 1.4% 9 1 1.4% 11 5 7.2% 6 2 2.9% 10 5 7.2% 13 11 15.9% 8 3 4.3% 12 2 2.9% 14 4 5.8% 9 1 1.4% 13 1 1.4% 15 5 7.2% 10 2 2.9% 15 6 8.7% 18 5 7.2% 13 6 8.7% 16 1 1.4% 24 1 1.4% 14 2 2.9% 17 2 2.9% 25 1 1.4% 15 5 7.2% 20 1 1.4% 30 7 10.1% 16 1 1.4% 25 7 10.1% 33 1 1.4% 18 5 7.2% 28 3 4.3% 47 1 1.4% 23 4 5.8% 30 5 7.2% 48 1 1.4% 24 1 1.4% 32 3 4.3% 25 1 1.4% 35 1 1.4% 26 1 1.4% 90 38 1 1.4% 27 5 7.2% 39 1 1.4% 30 1 1.4% 43 1 1.4% 32 1 1.4% 45 4 5.8% 33 1 1.4% 51 1 1.4% 36 3 4.3% 53 2 2.9% 39 1 1.4% 54 1 1.4% 40 1 1.4% 57 2 2.9% 43 1 1.4% 62 2 2.9% 46 2 2.9% 45 www.qetools.com 63 1 1.4% 47 2 2.9% 65 1 1.4% 48 1 1.4% 67 1 1.4% 51 1 1.4% 68 1 1.4% 52 1 1.4% 71 1 1.4% 54 1 1.4% 76 1 1.4% 59 1 1.4% 82 1 1.4% 60 1 1.4% QETools Tutorial - Part I

8.1 Tabulation Multiple Tabulation – Sample Results (Pareto Output)

No Grouping Variable The Multiple Tabulation contains: . Count Summary Table . Pareto Chart

Pareto Analysis Category: Cat_Output_Cpy1 Frequency: Sum_ALL_Cpy1

TOTAL 4530 Pareto Chart 50.0% 100.0% Relative Cumulative Category Frequency 45.0% 90.0% Frequency Rel Freq 40.0% 80.0% TimeWaitingRoom 2091 46.2% 46.2% 35.0% 70.0% WaitClinician2 1513 33.4% 79.6% 30.0% 60.0% WaitClinician1 926 20.4% 100.0% 25.0% 50.0% 20.0% 40.0% 15.0% 30.0% 10.0% 20.0% 5.0% 10.0%

0.0% 0.0%

RelativeFrequency .

Cumulative RelFreq .

WaitClinician2 WaitClinician1 TimeWaitingRoom

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8.1 Tabulation Multiple Tabulation – Sample Table with Grouping

Grouping Variable: Team The Multiple Tabulation contains: . Count Summary Table . Pareto Chart

Multiple Tabulation Input: TimeWaitingRoom WaitClinician1 WaitClinician2 Group by: Team

Variable TimeWaitingRoom WaitClinician1 WaitClinician2

Count (All) 207 Count 69 69 69 Group Row Count Row Percent By Group: Category TimeWaitingRoom WaitClinician1 WaitClinician2 A 45 21.74% Team A 15 15 15 B 84 40.58% B 28 28 28 C 78 37.68% C 26 26 26

Sum (All) 4530 Sum 2091 926 1513 Group Row Sum Sum Percent By Group: Category TimeWaitingRoom WaitClinician1 WaitClinician2 A 346 7.64% Team A 172 78 96 B 1732 38.23% B 677 443 612 C 2452 54.13% C 1242 405 805

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8.1 Tabulation Cross Tabulation – Dialogue Box

 Select two variables from the list (Output Variables) st  1 Variable: Row Variable in Matrix nd  2 Variable: Column Variable in Matrix

 Check the box to perform Chi-Square Test of Independence between Variables

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Cross Tabulation Input: OverallSsfaction LikelyReturn

Output OverallSsfaction LikelyReturn 8.1 Tabulation Count_ALL 1000 1000 Cross Tabulation – SampleChi-Sq Statistic Result 29.263 P Value 0.000 Alpha 0.05 ConclusionThe CrossFail to reject Tabulation hypothesis of contains: independence . Chi Square Test of Independence . Cross Tabulation Matrix Cross Tabulation Input: OverallSsfaction LikelyReturn LikelyReturn OverallSsfaction Count 0 1 All Output OverallSsfaction LikelyReturn 1 Count 9 19 28 Count_ALL 1000 1000 Column % 32.1% 67.9% Row % 2.2% 3.2% 2.8% 2 Count 15 39 54 Chi-Sq Statistic 29.263 Column % 27.8% 72.2% P Value 0.000 Row % 3.7% 6.6% 5.4% Alpha 0.05 3 Count 84 71 155 Conclusion Fail to reject hypothesis of independence Column % 54.2% 45.8% Row % 20.7% 12.0% 15.5% 4 Count 253 345 598 Column % 42.3% 57.7% Row % 62.3% 58.1% 59.8% 5 Count 45 120 165 LikelyReturn Column % 27.3% 72.7% OverallSsfaction Count 0 1 All Row % 11.1% 20.2% 16.5% 1 Count 9 19 28 Column % 32.1% 67.9% Count All 406 594 1000 Row % 2.2% 3.2% 2.8% Percent 40.6% 59.4% 2 Count 15 39 54 Column % 27.8% 72.2% 94 Row % 3.7% 6.6% 5.4% 3 Count 84 71 155 Column % 54.2% 45.8% Row % 20.7% 12.0% 15.5% 4 Count 253 345 598 Column % 42.3% 57.7% 47 www.qetools.com Row % 62.3% 58.1% 59.8% 5 Count 45 120 165 Column % 27.3% 72.7% Row % 11.1% 20.2% 16.5%

Count All 406 594 1000 Percent 40.6% 59.4% QETools Tutorial - Part I

8.1 Tabulation Binary Tabulation – Dialogue Box

 Select one or more variables from the list (Output Variables)

 Note: Data must be binary (0/1)

 Optional: Select a Grouping Variable from the list

 Check the box to create a Pareto Chart

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8.1 Tabulation Binary Tabulation – Sample Results (Table) The Binary Tabulation contains: No Grouping Variable . Overall DPMO . Row and Column % Calculations Binary Tabulation . Overall Data Summary Variable: PoorHouseKeeping Problemsrvations LongCheckIn LongCheckOut. Pareto Chart

Value PoorHouseKeeping Problemsrvations LongCheckIn LongCheckOut Row Count OK 0 918 966 904 942 3730 Defects 1 82 34 96 58 270

Column Count (Non-Blanks) 1000 1000 1000 1000 4000 Row % (=1) 30.4% 12.6% 35.6% 21.5% Column % (=1) 8.2% 3.4% 9.6% 5.8%

Total Opportunities 4000 Total (=1) 270 DPMO 67500 Overall DPMO is Data are tallied by 0/1 and totaled for Binary data and overall calculated when a each variable. Row% and Column% data are summed to the defect (failure) is are also calculated. right coded as 1 Ex: Poor Housekeeping Row% = 82/270 Column% = 82/1000 96

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8.1 Tabulation Binary Tabulation – Sample Results (Pareto Chart) The Binary Tabulation contains: No Grouping Variable . Overall DPMO . Row and Column % Calculations . Overall Data Summary . Pareto Chart Pareto Analysis Category: CatColCK Frequency: FreqColCL

TOTAL 270 Pareto Chart 40.0% 100.0% Relative Cumulative Category Frequency 35.0% 90.0% Frequency Rel Freq 80.0% 30.0% LongCheckIn 96 35.6% 35.6% 70.0% PoorHouseKeeping 82 30.4% 65.9% 25.0% 60.0% LongCheckOut 58 21.5% 87.4% 20.0% 50.0% Problemsrvations 34 12.6% 100.0% 15.0% 40.0% 30.0% 10.0% 20.0% 5.0% 10.0%

0.0% 0.0%

RelativeFrequency .

Cumulative RelFreq .

LongCheckIn

LongCheckOut

Problemsrvations PoorHouseKeeping

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8.2 Pareto Analysis

Input for Pareto Analysis:

 Column: Category

 “ReasonExercise”

 Column: Counts

 “ReasonCount”

Note: May calculate sum of data columns for different categories using the tabulation tool and adding Pareto to Output (See Multiple or Binary Tabulation) 98

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8.2 Pareto Analysis Dialogue Box

 Select one (Data) variable and one (Category) variable from the list

 Optional: Modify the output setting for the left and right Y-axes

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8.2 Pareto Analysis Sample Result

The Pareto Analysis output contains: . Table of Category frequencies . Pareto Chart Pareto Analysis Category: ReasonExercise Frequency: ReasonCount

TOTAL 265 Pareto Chart 25.0% 100.0% Relative Cumulative Category Frequency 90.0% Frequency Rel Freq 20.0% 80.0% Patient with extensive support needs 57 21.5% 21.5% 70.0% 15.0% 60.0% MD with another patient 54 20.4% 41.9% 50.0% Supplies not in exam room 47 17.7% 59.6% 10.0% 40.0% High patient acuity 36 13.6% 73.2% 30.0% Patient slow to complete forms 12 4.5% 77.7% 5.0% 20.0% Patient needs further education 8 3.0% 80.8% 10.0% 0.0% 0.0% Equipment not available 7 2.6% 83.4% Unable to find necessary supplies 6 2.3% 85.7% Paging interrupted visit 6 2.3% 87.9% Shared toilet caused delay 5 1.9% 89.8%

Consent needs signature 5 1.9% 91.7% Patientwith…

RelativeFrequency .

Cumulative RelFreq .

Unable to find…

Equipmentnot… Patientslow to…

Clerical staff with another patient 4 1.5% 93.2% Consentneeds…

MDwith another…

Longdistance to…

Clerical staff with… Aidewith another…

Long distance to exam room 4 1.5% 94.7% Additionalclerical…

High patient acuity Staff needs further…

Nursewith another…

Exam room needed…

Shared toilet caused… Patientneeds further…

Exam room needed clean or prep 3 1.1% 95.8% Supplies not in exam… Computersystem slow Staff needs further inservice 3 1.1% 97.0% Paginginterrupted visit Computer system slow 2 0.8% 97.7% Nurse with another patient 2 0.8% 98.5% Aide with another patient 2 0.8% 99.2% Additional clerical forms needed 2 0.8% 100.0%

Note: Option to Show Absolute or Relative Frequency. Or to add Cumulative Relative Frequency 100

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QE Tools Tutorial Part 9 – Hypothesis Testing (F-Test, T-Test, 2-Prop. & ANOVA) 9.1 F-Test (Differences in Variance) 9.2 T-Test (Differences in Means) 9.3 Proportions One & Two Proportions 9.4 ANOVA One-Way ANOVA & Two-Way ANOVA

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9. Hypothesis Tests

 May perform various one and two sample tests using either individual data or summary data

Difference in Variances • Test Variance – Standard (1 Sample) • Test Two Variances Difference in Means • Test Mean – Standard (1 Sample) • Test Two Means – Independent • Test Paired Data Proportions • Test One Proportion • Test Two Proportions

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9.1 F-Test (Differences in Variances) Test Variance-Standard (1 Sample) – Dialogue Box

 Select one variable from the list to be analyzed OR Enter the Summary Statistics

 Enter the Hypothesized Statistic

 Enter the Alpha Type I error (default = 0.05)

Note: Similar Menus for Test 1 Mean and 1 Proportion 103

9.1 F-Test (Differences in Variances) Test Variance-Standard (1 Sample) – Sample Result

Test Variance-Standard The Test Variance-Standard output Variable: TimeWaitingRoom contains: Hypothesized Variance: 25 . Degree of Freedom Hypothesis Test: Variance to Standard . Test Statistic . P value & Statistical Conclusion (Assume random sample from a Normal Population)

Data: Input Value Comments

Sample Size, N 69 sample size Variance, S 2 429.774 sample variance (stdev^2) 2 s0 25.000 hypothesized variance

a 0.050 alpha error May Change to “1” not equal Alternative for a 1-Tail Test Two Tail: Calculations: # tails 2 2 2 Ho: σ = σ 0 v 68 degree of freedom (n-1) 2 2 2 Ha: σ ≠ σ 0 c Test statistic 1168.984 test statistic c2 critical 47.092 - 92.689 critical value based on alpha One Tail: 94.9999999254941% 315.299 - 620.586 H : σ2 = σ2 Conf Int o 0 p-value 0.0000 p-value for statistical test 2 2 Ha: σ < σ 0 Statistical Conclusion? Difference exists (p <= a --> difference) 104

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9.1 F-Test (Differences in Variances) Test Two Variances – Dialogue Box

 Select variables to be analyzed

 Two Variables

 1 Output & 1 Group

 Summary Statistics

 Select one or two-tail hypothesis test

 Two-tail 2 2 Ha: σ A ≠ σ B  One-tail 2 2 Ha: σ (lg) > σ (sm)

 Enter the Alpha Type I error (default = 0.05)

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9.1 F-Test (Differences in Variances) Test Two Variances – Sample Results

Test Two Variances The Test Two Variance output Variable: WaitClinician1, WaitClinician2 contains: Hypothesis Test: Two Variance Test . Degree of Freedom . Test Statistic Data: Input WaitClinician1 WaitClinician2 . P value & Statistical Conclusion . Box Plot of differences Sample Size, n 69 69 i 70 StDev, S 10.42 16.10 2 Variance, S 108.51 259.07 60

# tails to evaluate 2 a 0.050 50

40 Calculations: Max Variance Min Variance

Variance 259.07 108.51 Value 30 degrees of freedom, n 68 68

20 Test Hypothesis: Var 1 = Var 2 Vs: not equal F: Test statistic 2.387 F: critical 1.615 10 F: p-value 0.000 WaitClinicia Statistical Conclusion? Difference exists (p <= a --> difference) 0 WaitClinicia n1 n2 Two Tail: One Tail: 2 2 2 2 Ho: σ A = σ B Ho: σ A = σ B 2 2 2 2 106 Ha: σ A ≠ σ B Ha: σ (lg) > σ (sm)

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9.2 T-Test (Differences in Means) Test Mean-Standard (1 Sample) – Dialogue Box

 Select one variable from the list to be analyzed OR Enter the Summary Statistics

 Enter the Hypothesized Statistic

 Enter the Alpha Type I error (default = 0.05)

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9.2 T-Test (Differences in Means) Test Mean-Standard (1 Sample) – Sample Result

The Test Mean-Standard Hypothesis Test: Mean to Standard (1-Sample test of mean) output contains: (Assume random sample from a Normal Population) . t-testDegree of Freedom Data: Input Value .CommentsTest Statistic

Sample Size, N 69 sample size . P value & Statistical Conclusion Mean 30.3043 sample mean

Standard Deviation 20.7310 sigma for test

Mean (Standard) 25.000 hypothesized mean to test

a 0.050

Alternative not equal

Calculations: May Change to “1” for a 1-Tail Test Two Tail: # tails 2 v 68 degree of freedom (n-1)

Ho: µ = µ0 t test statistic 2.125 test statistic

Ha: µ ≠ µ0 |t critical| 1.995 critical value based on alpha, df 94.9999999254941% 25.324 - 35.284 One Tail: Conf Int p-value 0.037 p-value for statistical test Ho: µ = µ0 Statistical Conclusion? Difference exists (p <= a --> difference) Ha: µ < µ0 108

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9.2 T-Test (Differences in Means) Test Two Means-Independent – Dialogue Box

 Select variables to be analyzed

 Two Variables

 1 Output & 1 Group

 Summary Statistics

 Select one or two-tail hypothesis test

 Two-tail

Ha: µA ≠ µB  One-tail

Ha: µ(lg) > µ(sm)

 Enter the Alpha Type I error (default = 0.05)

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9.2 T-Test (Differences in Means) Test Two Means-Independent – Sample Results

Test Two Means - Independent The Test Two Means-Independent Variable: WaitClinician1, WaitClinician2 output contains: Hypothesis Test: Two Means Test (Independent) . Degree of Freedom Data: Input WaitClinician1 WaitClinician2 . Test Statistic Sample Size, ni 69 69 . P value & Statistical Conclusion Mean 13.42 21.93 70 StDev, S 10.417 16.096 . Box Plot of differences # tails to evaluate 2 60 a 0.050 50 Variance Calculations: F 2.387 40 F critical (two-tail) 1.615 F (p-value) 0.00 Value 30 Conclusion (two-tail)? VAR different 20 Mean Difference: 8.51 S (assume equal var): 13.56 pooled 10 Assume Equal Variance Assume Unequal Variances WaitClinicia degrees of freedom, n 136 132 WaitClinicia 0 n1 n2 t: Test statistic 3.69 3.69 Results: Test Hypothesis: M1 = M2 Vs: not equal t: p-value - assume equal var 0.000 Statistical Conclusion? Difference exists (p <= a --> difference)

t: p-value - assume unequal var 0.000 Statistical Conclusion? Difference exists (p <= a --> difference) Two Tail: One Tail:

Ho: µA = µB Ho: µA = µB 110 Ha: µA ≠ µB Ha: µ(lg) > µ(sm)

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9.2 T-Test (Differences in Means) Test Two Means-Independent – Dialogue Box Input Summary Statistics Test Two Means-Independent Variable: Summary Data

Hypothesis Test: Two Means Test (Independent)

Data: Input Group1 Group2

Sample Size, ni 85 67 Mean 62.20 57.70 StDev, S 8.370 7.020 # tails to evaluate 2 a 0.050 Variance Calculations: F 1.422 F critical (two-tail) 1.593 F (p-value) 0.13 Conclusion (two-tail)? VAR not different

Mean Difference: 4.50 Spooled (assume equal var): 7.80 Assume Equal Variance Assume Unequal Variances degrees of freedom, n 150 149 t: Test statistic 3.53 3.60 Results: Test Hypothesis: M1 = M2 Vs: not equal t: p-value - assume equal var 0.001 Statistical Conclusion? Difference exists (p <= a --> difference)

t: p-value - assume unequal var 0.000 Statistical Conclusion? Difference exists (p <= a --> difference) 111

9.2 T-Test (Differences in Means) Test Paired Data – Dialogue Box

 Select two variables from the list to be analyzed OR Enter the Summary Statistics

 Select one or two-tail hypothesis test

 Recommend 2 tail for paired

 Enter the Alpha Type I error (default = 0.05)

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9.2 T-Test (Differences in Means) Test Paired Data – Sample Results

The Test Paired Data output Test Paired Data contains: Variable: pair1, pair2 . Degree of Freedom Hypothesis Test: Paired Means Test . Test Statistic . P value & Statistical Conclusion Data: Input Value Comments . Box Plot of differencesDifference: pair1 - pair2 Average difference 0.274 Average difference (X1 - X2) N 9 sample size for each group 0.6 StDev (difference) 0.135 Std deviation of differences # tails to evaluate 2 0.5 a 0.050

0.4 Results: Test Hypothesis: Difference = 0 Vs: not equal t: Test Statistic 6.08 0.3

t: p-value 0.000 Value Statistical Conclusion? Difference exists (p < a --> difference) Two Tail: 0.2 X1 X2 H : µ = µ Difference pair1 pair2 o A B 0.1 Sample Size, N 9 9 Ha: µA ≠ µB Mean 1.340 1.066 0 StDev, S 0.146 0.049 SE Mean 0.049 0.016

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9.3 Proportions Test One Proportion – Template & Sample Result

One Sample Template: Hypothesis Test: One Proportion Test (X = 1)

Data: po Sample p X (=1) 111

Sample Size, ni 447 sample p 0.050 0.248

# tails to evaluate 1 a 0.05

Proportion Difference: 0.198 p 0 0.050 . Enter Data in White Cells Zo: Test Statistic 19.239 . Number of defects (X)

Results: Test Hypothesis: P > Po Vs: <= . Sample size (n) Z: p-value 0.000 . Select one or two-tail test Two Tail: Statistical Conclusion? Difference exists (p < a --> difference). Calculations done Ho: p = p0 automatically in Yellow Ha: p ≠ p0 Normal Approximation? Large Sample Normality Condition Satisfied Select Type of Test: Large Sample Test One Tail:

Ho: p = p0 Test (nipi > 5 and niqi > 5) Sample p Ha: p < p0 Sample Size* p 111.0 Sample Size* (1-p) 336.0 114

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9.3 Proportions Test Two Proportions – Dialogue Box

 Select variables to be analyzed

 Two Variables Note: Data must be binary (0/1)

 1 Output & 1 Group

 Summary Statistics

 Select one or two-tail hypothesis test

 Two-tail

Ha: pA ≠ pB  One-tail

Ha: p(lg) > p(lg)

 Enter the Alpha Type I error (default = 0.05) 115

9.3 Proportions Test Two Proportions – Sample Results

The Test Two Proportions output contains: . Test Statistic . P value & Statistical Conclusion

Hypothesis Test: Two Proportion Test (X = 1) Hypothesis Test: Two Proportion Test (X = 1)

Data: Group1 Group2 Data: Group1 Group2 X (=1) 111 82 X (=1) 111 82

Sample Size, ni 447 1000 Sample Size, ni 447 1000

sample p i 0.248 0.082 sample p i 0.248 0.082

# tails to evaluate 2 # tails to evaluate 1 a 0.050 a 0.050

Proportion Difference: 0.166 Proportion Difference: 0.166 p-hat 0.133 pooled estimate p-hat 0.133 pooled estimate Zo: Test Statistic 8.598 Zo: Test Statistic 8.598

Results: Test Hypothesis: P1 = P2 Vs: not equal Results: Test Hypothesis: P(Large) > P(small) Vs: <= Z: p-value 0.000 Z: p-value 0.000 Statistical Conclusion? Difference exists (p <= a --> difference) Statistical Conclusion? Difference exists (p <= a --> difference)

Two Tail: May Change to “1” One Tail:

Ho: pA = pB for a 1-Tail Test Ho: pA = pB Ha: pA ≠ pB Ha: p(lg) > p(sm) 116

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9.3 Proportions Test Two Proportions – Low Sample Size Warning

Example Shown Below: Data fail normal approximation test for Test Two Proportions Variable: Summary Data proportions (warning is given)

Hypothesis Test: Two Proportion Test (X = 1)

Data: Group1 Group2 X (=1) 2 1

Sample Size, ni 30 30

sample p i 0.067 0.033

# tails to evaluate 2 a 0.05

Proportion Difference: 0.033 p-hat 0.050 pooled estimate Zo: Test Statistic 0.592

Results: Test Hypothesis: P1 = P2 Vs: not equal Z: p-value 0.554 Statistical Conclusion? No difference (p <= a --> difference)

Normal Approximation? Warning: Large Sample Normality Condition Not Satisfied Select Type of Test: Large Sample Test Variance Assumption: Equal

Test (nipi > 5 and niqi > 5) Group 1 Group 2 Sample Size* p 2.0 1.0 117 Sample Size* (1-p) 28.0 29.0

9.4 ANOVA

 May perform ANOVA test for 1 or 2 Factors

ANOVA Test • One-Way ANOVA • One-Way ANOVA Table (Multiple Outputs with common X Factor)* • Two-Way ANOVA

Note: Not demonstrated here (See Help File)

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9.4 ANOVA One-Way ANOVA – Dialogue Box

 Select variables to be analyzed

 Two or more variables

 One Output and one Group Variable

 Select either Main Effect Plot (mean only) or Individual Plot (all data)

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9.4 ANOVA One-Way ANOVA – Sample Results Main Effect Plot The One-Way ANOVA output contains: . Statistical Results One-Way Anova . Main Effect Plot or Individual Plot Variable: TimeWaitingRoom Group by: Team

One-way ANOVA Output: TimeWaitingRoom by Team

SUMMARY Mean Confidence Interval Groups Count Sum Average Variance Lower Upper A 15 172.0 11.5 15.1 2.6 20.4 60 TimeWaitingRoom by Team B 28 677.0 24.2 157.4 17.7 30.7 C 26 1242.0 47.8 418.3 41.0 54.5 50 Alpha 0.05 ANOVA 40 Source of Variation SS df MS F P-value F crit Between Groups 14304.153 2 7152.076 31.637 0.000 3.136 30

Within Groups 14920.456 66 226.068 Response 20 Total 29224.609 68 10 DESCRIPTIVE STATISTICS N 69 0 Mean 30.3043 A B C StDev(Pooled) 15.0355 StDev(Overall) 20.7310

MODEL PREDICTION R-squared 48.95% R-squared(Adj) 47.40%

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One-Way Anova Table Variable: TimeWaitingRoom 9.4 ANOVA Group by: Team One-Way ANOVA Table – Dialogue Box & SummaryOne-way ANOVA Report DESCRIPTIVE STATISTICS TimeWaitingRoom N 69 Mean 30.3 StDev(Pooled) 15.04 StDev(Overall) 20.73

MODEL PREDICTION Alpha 0.05 F 31.64  Select one or P-valuemore variables0.000 F Crit 3.13 R-squared 48.95% from the list R-squared(Adj) 47.40%

ANOVA Sum of Squares Variation SS  Select one Group Between GroupsVariable 14304.15 Within Groups 14920.46 One-Way Anova Table Total 29224.61 Variable: TimeWaitingRoom Degrees of Freedom df Group by: Team Between Groups 2 Within Groups 66 Total 68 One-way ANOVA Mean Square Variation MS Between Groups 7152.08 DESCRIPTIVE STATISTICS TimeWaitingRoom Within Groups 226.07 N 69 Mean 30.3 Groups Count StDev(Pooled) 15.04 Team_A 15 StDev(Overall) 20.73 Team_B 28 Team_C 26 MODEL PREDICTION Sum Alpha 0.05 Team_A 172.0 F 31.64 Team_B 677.0 P-value 0.000 Team_C 1242.0 F Crit 3.13 Average R-squared 48.95% Team_A 11.5 R-squared(Adj) 47.40% Team_B 24.2 ANOVA Team_C 47.8 Sum of Squares Variation SS Variance Between Groups 14304.15 Team_A 15.12 Within Groups 14920.46 Team_B 157.41 Total 29224.61 Team_C 418.34 Degrees of Freedom df 121 Between Groups 2 Within Groups 66 Total 68 Mean Square Variation MS Between Groups 7152.08 Within Groups 226.07

Groups Count Team_A 15 Team_B 28 Team_C 26 Sum Team_A 172.0 Team_B 677.0 Team_C 1242.0 Average Team_A 11.5 Team_B 24.2 9.4 ANOVA Team_C 47.8 Two-Way Anova FactorVariance 1 (row): A Factor 2 (col): B Team_A Response: Y1 15.12 Two-Way ANOVA – Dialogue Box Team_B & Sample157.41 Results Team_C Two Way 418.34ANOVA Summary B_-1 B_1 Totals A_-1 Count 1.0 1.0 2.0 Sum 10 12 22.000 Average 10.000 12.000 11.000 2.000

A_1 Count 1.0 1.0 2.0 Sum 15 20 35.000 Average 15.000 20.000 17.500 12.500

Total Count 2.0 2.0 Sum 25 32 Average 12.500 16.000

Alpha 0.05

ANOVA Sources of Variation SS df MS F P-value F crit A 42.250 1 42.250 18.778 0.144 161.448  Select rowB factor,12.250 1 12.250 column5.444 0.258 161.448 Within 2.250 1 2.250

Total 56.750 3

factor, andS response1.500 R-sq 96.04% R-sq(Adj) output88.11%

TABLE OF MEANS Two-Way Anova Combination B_-1 B_1 Total A_-1 10.000 12.000 11.000 Factor 1 (row): A A_1 15.000 20.000 17.500 Factor 2 (col): B Total 12.500 16.000 Response: Y1 MAIN EFFECTS PLOTs Y1 by A Y1 by B Two Way ANOVA 20.000 20.000

15.000 15.000 Summary B_-1 B_1 Totals A_-1 10.000 10.000

Count 1.0 1.0 2.0 Response

Sum 10 12 22.000 Response 5.000 5.000 Average 10.000 12.000 11.000 0.000 0.000 2.000 A_-1 A_1 B_-1 B_1

A_1 INTERACTION PLOT Count 1.0 1.0 2.0 Sum 15 20 35.000 A by B Interaction Plot Average 15.000 20.000 17.500 A_-1 A_1 12.500 25.000 20.000 Total 15.000

Count 2.0 2.0 10.000 Response Sum 25 32 5.000 Average 12.500 16.000 0.000 B_-1 B_1

Alpha 0.05

ANOVA Sources of Variation SS df MS F P-value F crit A 42.250 1 42.250 18.778 0.144 161.448 B 12.250 1 12.250 5.444 0.258 161.448

Within 2.250 1 2.250

Total 56.750 3

S 1.500 R-sq 96.04% R-sq(Adj) 88.11%

TABLE OF MEANS Combination B_-1 B_1 Total A_-1 10.000 12.000 11.000 A_1 15.000 20.000 17.500 Total 12.500 16.000

MAIN EFFECTS PLOTs 122 Y1 by A Y1 by B 20.000 20.000

15.000 15.000

10.000 10.000 Response

Response 5.000 5.000

0.000 0.000 A_-1 A_1 B_-1 B_1

INTERACTION PLOT A by B Interaction Plot 61 A_-1 A_1 www.qetools.com 25.000 20.000 15.000

10.000 Response 5.000 0.000 B_-1 B_1 QETools Tutorial - Part I

QE Tools Tutorial Part 10 – Regression, Scatter Plot, and Correlation

10.1 Linear Regression 10.2 Scatter Plot 10.3 Correlation Matrix

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10. Regression, Scatter Plot, and Correlation

 Regression and Correlation

 Linear Regression

 Correlation Matrix

 Graphical Tools

 Scatter Plot

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10.1 Linear Regression Dialogue Box

 Select one or more variables from the list (X)

 For simple regression, enter only 1 X variable

 For multiple regression, enter up to 10 X variables

Note: Equation solver options are available for simple regression

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10.1 Linear Regression Sample Results

The Linear Regression output contains: . Regression Statistics . Scatter Plot . Response Optimizer (enter either X or Y Linear Regression and solve for the other based on best fit Variable: Underwringdays Response: TotalTime equation)

Regression Analysis

Regression Statistics TotalTime Underwringdays Regression R Square 0.7771 Correl (R) 0.8815 70 y = 1.0447x + 20.068 Adjusted R Square 0.7768 R² = 0.7771 Standard Error 2.8582 Observations 749 60

ANOVA 50 df SS MS F Significance F Regression 1 21278.74 21278.74 2604.69 0.000 Residual 747 6102.53 8.17 40 Total 748 27381.27

Coefficients Standard Error t Stat P-value 95% CI-Lower 95% CI-Upper 30 Intercept 20.0675 0.3209 62.542 0.000 19.347 20.788

Underwringdays 1.0447 0.0205 51.036 0.000 0.999 1.091 (Y) TotalTime 20

10 0 10 20 30 40 Underwringdays (X)

Response Optimization Enter values below Underwringdays Y 126

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10.2 Scatter Plot Dialogue Box

 Select one input variable (X) and one output variable (Y) from the list

 Scatter Plot Options:

 Trend line – linear, quadratic, or no trend line 2  Show R

 Show best fit equation

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10.2 Scatter Plot Sample Result

The Scatter Plot output contains: Scatter Plot . Correlation Coefficient, R X(Category): Underwringdays . R-squared Y(Value): TotalTime . Scatter Plot

X Y Linear Model 2 19 39 Include R R Underwringdays TotalTime Scatter Plot 21 39 Include 0.88 0.777 23 40 Include 70 21 38 Include 20 37 Include 6 25 Include 60 y = 1.0447x + 20.068 6 22 Include R² = 0.7771 8 24 Include 6 23 Include 50 14 34 Include 7 30 Include 5 23 Include 40 10 28 Include 9 31 Include

13 35 Include TotalTime 30 12 26 Include 17 39 Include 8 31 Include 20 14 30 Include 9 28 Include 12 32 Include 10 13 34 Include 0 10 20 30 40 6 27 Include 12 30 Include Underwringdays 23 42 Include

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10.3 Correlation Matrix Dialogue Box

 Select one or more variables from the list (Output Variables)

 Variables must contain numeric data to be included. “Text” data will be omitted.

 Enter threshold to highlight data with a strong correlation

 Typically 0.7 is used to indicate a strong correlation 129

10.3 Correlation Matrix Sample Result

The Correlation Matrix output contains: . All pairwise comparisons of selected variables (max 50 variables) . Data with a correlation stronger than the threshold is emphasized with bold text. Either strong positive or strong negative will Correlation Matrix be emphasized Variable: LoanPrepmedays Internalaldays Underwringdays TotalTime

Correlation Matrix LoanPrepmedays Internalaldays Underwringdays TotalTime LoanPrepmedays 1 Internalaldays -0.07 1 Underwringdays -0.02 0.07 1 TotalTime 0.04 0.46 0.88 1

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QE Tools Tutorial Part 11 – Tolerance Analysis & Simulation

11.1 Tolerance Analysis Worksheet 11.2 Tolerance Simulation – Linear

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11. Tolerance Analysis & Simulation

 Perform tolerance analysis via the worksheet using stack-up methods (Worst Case or Statistical) or using the tolerance simulator

Tolerance Analysis • Tolerance Analysis Worksheet • Tolerance Simulation – Linear (Monte Carlo)

Note: Tolerance Calculator Tool under QE Tools > Process Capability Summary

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11.1 Tolerance Analysis Worksheet Template Overview

Tolerance Analysis

Date: Other Generic Assumptions Part:

Analyst: Customer: Final Tolerance Specification (Assembly) Componet Tol Method: Statistical (RSS) Nominal +/- t -OR- Lower (LSL) Upper (USL) Width (T) Assumed Cp Assumption: Normal 1.33

Proposed Tolerance Predicted Manual Data Add/ Weight St Dev* Entry -OR- -OR- Item # : Description Source Subtract Nominal +/- t tLOWER (-) tUPPER (+) Width (Default=1) (from Cp & tol) St Dev 1 + 1.0  Select Worst 2 + 1.0 3 + 1.0 Case, Statistical 4 + 1.0 5 + 1.0

(RSS), or Gilson 6 + 1.0

7 + 1.0

Method to 8 + 1.0 perform stack- 9 + 1.0 10 + 1.0 up calculations 11 + 1.0 12 + 1.0

13 + 1.0 Predicted Stack Up 0.000 * Predicted Overall St Dev Predicted Specifications (Assumes Normality) LSL USL

 Enter data in LSL USL Width Tolerance Analysis (Enter Proposed)--> 0.000 Out-of-Spec Categories White Cells % < LSL % > USL Overall  1% Predicted Percent Out of Spec --> 0.00% >1,  5% (Assumes Normality) > 5%

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11.1 Tolerance Analysis Worksheet Sample Result

The Tolerance Analysis Worksheet contains: . Stack Up Tolerance . Predicted St Dev Tolerance Analysis . Predicted Percent Out of Spec Date: Other Generic Assumptions Part:

Analyst: Customer: Final Tolerance Specification (Assembly) Componet Tol Method: Worst Case Nominal +/- t -OR- Lower (LSL) Upper (USL) Width (T) Assumed Cp Assumption: Normal 0.1 0.1 0 0.2 0.2 1.33

Proposed Tolerance Predicted Manual Data Add/ Weight St Dev* Entry -OR- -OR- Item # : Description Source Subtract Nominal +/- t tLOWER (-) tUPPER (+) Width (Default=1) (from Cp & tol) St Dev 1 Hole + 10.1 0.05 0.1 1.0 0.013

2 Pin - 10 0.05 0.1 1.0 0.013

3 + 1.0

4 + 1.0

5 + 1.0 Predicted Stack Up 0.100 -0.100 0.100 * Predicted Overall St Dev 0.018 Predicted Specifications (Assumes Normality) LSL 0.000 USL 0.200

LSL USL Width Tolerance Analysis (Enter Proposed)--> 0.2 0.200 Out-of-Spec Categories % < LSL % > USL Overall  1% Predicted Percent Out of Spec --> 0.00% 0.00% >1,  5% (Assumes Normality) > 5%

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11.2 Tolerance Simulation – Linear Dialogue Box

 Enter Number of Simulation Runs

 Optional: Enter Specification Limits for Components and/or Assembly to obtain PPM Defective

 For each variable, assign a Probability distribution and enter distribution parameters to simulate

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11.2 Tolerance Simulation – Linear Sample Result

Response Response 2 Response 3 1 2 Distribution Normal Normal Auto Calculate Param 1 10.1 10 Param 2 0.02 0.02 Param 3 Param 1 Mean Mean Param 2 Sigma Sigma The Tolerance Simulator Param 3 Valid Params? Valid Valid contains: % Out-of Spec Criteria: . Predicted Percent Out of Spec OK <= 1% Weight 1 1 Marginal <= 5% Operand + - . PPM (if specification limits Fail > 5% Include? Yes Yes

provided) Description Response Response 2 Response 3 Hole Pin N 1,000 Mean 0.101 10.1009 9.9997 St Dev 0.028 0.0198 0.0198 Min 0.009 10.0443 9.9401 Max 0.205 10.1719 10.0588 # Out-of-Spec 1 % Out-of Spec 0.1% PPM 1,000.0

LSL 0

USL 0.2 UPDATE Response Response 2 Response 3 Hole Pin 0.114 10.0870 9.9728 The 'Response' has been 0.084 10.0716 9.9879 created based on the Distribution, 0.122 10.1289 10.0071 Distribution Parameters, 0.097 10.0856 9.9889 Weight, Operand and 0.130 10.0898 9.9603 Inclusion (Yes/No). You may 0.072 10.0740 10.0022 enter a custom response 0.051 10.0817 10.0304 function and click 'Update' to 0.077 10.1092 10.0320 run the simulation. 0.068 10.0956 10.0273 0.092 10.1046 10.0126 136

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11.2 Tolerance Simulation – Linear Custom Equations

Click Update to create equation for all samples

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QE Tools Tutorial Part 12 – Pugh Matrix and Scorecard (Desirability)

12.1 Pugh Matrix 12.2 Scorecard (Desirability)

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12.1 Pugh Matrix Template Overview and Sample Result

Pugh Matrix Template fields: . Header- title, project, name, date . Requirements- list requirements, importance, and decision criteria . Pugh Matrix Output- Total of Sums (red- negative)

Pugh Selection Matrix

Title Solftware Solution Delete Project Name A. Vandalay Make Date Datum Add Col Decision Criteria Overall Excel-based Desktop Item Requirement Web-based Importance Add-in Application Counts Real-time Multi-User Data Input/Output from Count of Pluses 2 3 1 Multiple Locations to centralized database 20 -1 +2 Count of Minuses 5 1 2 Document Control and electronic information submittal 15 D -2 +1 Count of Same (0) 1 4 3 Encryption & Secured Access 10 a -1 0 Pluses - Minuses -3 2 4 Ease of Navigation 15 t +1 0 5 Search Speed 10 u -2 +1 Sums 6 Report Generator: standard 10 m 0 0 Sum of Pluses 3 4 7 Report Generator: custom analysis 5 +2 -1 Sum of Minuses -7 -1 Total -4 3 8 Query feature to consolidate reports for multiple parts 15 -1 0 100 Weighted Sums Add Weighted Sum of Pluses 25 65 Weighted Sum of Minuses -95 -5 Row Total -70 13960

12.2 Scorecard (Desirability) Dialogue Box and Sample Result

 Enter Requirements

 Provide Details for each Requirement

 Metric, Importance, Weight, Improvement Direction, Target and Specification Limits, Actual Value

Desirability Goal Desirability Item Requirements Group Importance (Benchmark) Index 1 Productivity - Weekly Invoices 1 0.59 2 Inventory 1 0.47 Total Desirability Index 0.53

1 Productivity - Weekly Invoices Improvement Target Lower Upper Actual Level Detail Requirements Metric/Units Importance Weight Desirability, d Direction (Value) Limit Limit (Avg) 1.1 Weekly Output # of Invoices 4 1 0.59 Larger is Better 3750 3000 3443

Total D 0.59

2 Inventory Improvement Lower Upper Actual Level Detail Requirements Metric/Units Importance Weight Desirability, d Target Direction Limit Limit (Avg) 2.1 Average WIP Dept # of Invoices 3 1 0.80 Target is Best 200 150 250 210 2.2 Ave WIP System # of Days 4 1 0.32 Smaller is Better 5 30 22 140 Total D 0.47

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Summary

 For additional support, please reference help menus or go to qetools.com

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