The that summarize a population are referred to as categorical statistics probabilistic statistics control statistics 1 The following was developed by a team to measure reactions on two different products.

In this chart, temperature represents the repetition factor response level 2 Which of the following measures is increased when process performance is improved? Variability Capability index Repeatability index Specification limits 3 Which of the following tools can be used to identify and quantify the source of a problem? Affinity diagram Quality function deployment 4 A correlation analysis is used to provide a numeric value for which of the following type s of relationships between two variables? Random Linear Curvilinear Causation 5

Which of the following tools is used to translate broad requirements into specific requirements? A plan The theory of constraints (TOC) A critical to quality (CTQ) tree A process 6 Which of the following tools is used extensively in quality function deployment (QFD)? Affinity diagram Matrix diagram Cause and effect diagram Activity network diagram 7 Which of the following control is used to monitor discrete ? p I & mR X̄ X̄ – R 8 Which of the following shapes is used to present a termination point in a flowchart? Rectangle Diamond Arrow Oval 9 For a normal distribution, two standard deviations on each side of the would include what percentage of the total population? 95% 68% 47% 34% 10 Which of the following is a commonly accepted level for alpha risk? 0.05 0.50 0.70 0.95 11 When the method used creates a difference between the result obtained from the sample and the actual population value, the difference is known as correlation precision accuracy bias 12 Which of the following is an example of mistake-proofing? Using an X̄ - R chart to prevent errors Using 100% inspection to detect and contain defects Using color coding as an error signal Having the team that created the errors repair them 13

Which of the following is the key objective of a six sigma project? Developing detailed control charts for critical processes Developing a matrix to understand the how’s and what’s of a problem process Reducing variation in critical processes Reducing investment costs while improving output quality 14 Which of the following tools is used to identify potential events and contingencies for an implementation plan? PERT chart Process decision program chart Fishbone diagram House of quality 15 Which of the following measures is used to show the ratio of defects to units? DPU DPO DPMO PPM 16 Which of the following terms is used to describe the risk of a type I error in a hypothesis test? Power Confidence level Level of significance Beta risk 17 Positional, cyclical, and temporal variations are most commonly analyzed in SPC charts multi-vari charts cause and effect diagrams run charts 18 In order for value flow analysis to be effective, a team must take which of the following steps first? Define the value stream Eliminate backlogs in the value stream Identify overlapping functions in the value stream Identify specific work practices within the value stream 19 When an inspection process rejects conforming product, what type of error is being made? α β σ

H0 20 The critical path for a project is best described as the sequence of steps with the highest costs tasks in the project that have the highest risk of failure sum of the tasks with the shortest time requirements longest path from the start to the completion of the project 21

Which of the following graphs represents a factorial with the strongest ?

22 Statistical process control (SPC) is best defined as the use of Pareto charts to understand and control a process inputs to control critical and complex processes statistical methods to identify and remove manufacturing errors statistical methods to understand and control a process 23 A measurement system analysis is designed to assess the statistical properties of gage variation process performance process stability engineering tolerances 24 When calculating the Cp index, what does the represent in the formula

? The The for the result The range of the process The of the index 25 Why do organizations use Six Sigma (6σ)? Bottom Line Benefits Customer Satisfaction Continuous Improvement All of the above

Six Sigma is a methodology for pursuing continuous improvement in customer satisfaction and profit that goes beyond defect reduction and emphasizes improvement in general. Six Sigma enables quality and continuous improvement to achieve the highest level of customer satisfaction. 26

Corporate scorecards are organized around financial, customer, internal process, learning and growth metrics. As these areas are broken down into components, projects are NOT limited to: Sigma quality level, defect rate Ease and quickness of completion Profit and loss None of the above

Organizations should not just measure against sigma quality levels and/or process output defect rates. 27 What is the best way to select six sigma projects when addressing customer satisfaction issues? Problem Focus Product Focus Project Cost Savings Focus Process Focus

The correct answer is: D –Process Focus –Overall, this is the best way to the root causes of defects and customer satisfaction issues. The key is identifying the processes that are critical to satisfaction and are operating at low sigma level. A, B, C –are all ways to select the projects, however when it comes to addressing customer satisfaction issues, the process approach is the best. 28 What is the Goal of ? Reduction of defects Elimination of waste Increased profits All of the above

Lean Manufacturing intents to reduce waste in all its forms 29 Which of the following is a value-added activity? Inspection Just-In-Time Inventory Defect Correction Waiting

Just in time, yields exactly the right product inexactly the right place and exactly the right time 30 The “Theory of Constraints” Focuses its continual improvement on: Empowering the employee Removing system bottlenecks Reducing defect Improving the bottom line

By Definition, the theory removes bottlenecks, the other choices relate to other quality methods 31 Quality Function Deployment (QFD) is commonly referred to as: The House of Quality Listening to the Quality Fundamentals A and B

QPD Often referred to as listening to the voice of the customer and QFD (Quality Function Deployment or the house of quality, a term coined QFD because of the shape of its matrix 32 The primary purpose of a Failure Modes and Effects Analysis is to: Solve Problems Manage the Product or Service to Be Delivered Manage Failure Risks Satisfy the Customer

“FMEA is a specific methodology to evaluate a system design, process, or service for possible ways in which failures (problems, errors, risks, concerns) can occur.” 33 A DMADV approach is used for a product At the end of its product life Product is not in existence That has been recalled The customer sees no added value in it

DMADV is design, product is being created 34 The roles and responsibilities of a Champion include all of the following EXCEPT: A Champion selects the Team Leader. A Champion reviews team progress. A Champion coordinates team logistics. A Champion assures the use of Six Sigma methods and tools.

The Process Owner is responsible for coordinating team logistics. 35 The benefits of a process map include all of the following EXCEPT: Serves as a training and orientation tool Helps identify when and where to collect data Helps determine sigma values Identifies non value added activities

The process flow map does not allow the user to determine sigma values 36 The roles and responsibilities of a Green Belt include all of the following EXCEPT: A Green Belt mentors Black Belts and Green Belts. A Green Belt is a part-time (25%) project leader or member and provides most of the functions of a Black Belt (Team Leader) for lower level project teams. A Green Belt analyzes data. Green Belts are the “work horses”of Six Sigma management.

The Master Black Belt is responsible for coordinating team logistics. 37 An early step in any project must be seeking the voice of the internal and external customers of a project. This statement is: False, because projects should only be concerned with external customers. True, because both internal and external customers can be impacted by the project. True, because a project team wants to maintain good will with all customers. False, because internal projects only impact internal customers.

Projects need to consider all stakeholders, including internal and external customers. 38

Which of the following methods is an effective tool to use when collecting customer data: Written surveys. Focus groups. Interviews by phone or in person. All of the above.

Written surveys can be sent to a randomly selected group of customers or potential customers. Focus groups are an attempt to improve the depth and accuracy of the responses. Interviews by phone or in person permit a higher response rate than written surveys; a skillful interviewer can record customer feelings that written surveys wouldn’t detect. 39 Which quality management tool displays connections between customer needs and various product features? Parameter (P) Diagram Quality Function Deployment Cause and effect Diagram Relationship Matrix

By definition 40 Which of the following quality terms is most closely associated with Quality Function Deployment (QFD)? House of Quality. SIPOC. Process flow diagram. Focus groups.

One of the methods used in Quality Function Deployment is the “house of quality.” The house of quality is a graphical display, which includes prioritized customer needs, design requirements, relationship of design to needs, customer rating of competitors, technical benchmarks, correlation of design requirements, technical evaluation, and performance targets. 41 Which of the following is NOT a key element of the define phase? Measure Process mapping Problem statement

Measure Is actually the next phase of DMAIC 42 Project scope can be defined by answering a series of questions. Which of the following questions would not yield relevant to project scope? What is the critical path of the project? What resources are available for the project? What are the obstacles and constraints of the project? What are the process boundaries of the project?

The critical path of the project is not known when the project scope is developed and is not relevant to developing a good project scope statement. 43

It is most important that key metrics for a Six Sigma project are aligned with: The overall cost and timing for the project The team responsibility matrix The key business and strategic objectives The project leaders previous goals and objectives

Unless the Six Sigma projects key metrics are not aligned with the business and strategic objectives of the organization, it will be difficult to get resources and support for the project. Alignment with project count and timing is important but not as important here. Alignment with the responsibility matrix, or the project leaders’ personal goals and objectives are not relevant in this context. 44 Features of the critical path method (CPM) include: I. The time and cost factors for each activity are considered. II. Activities with the lowest crash cost (per incremental time savings) are selected first. III. As an activity is crashed, it is possible for a new critical path to develop. IV. Each group of activities on the chart is an event. I and IV only I, II and IIII only III and IV only IV only

Choice IV refers to the PERT chart, which is event-oriented. The critical path method (CPM) is very similar to PERT, but CPM is activity oriented. Choices I, II, and III are activity-related features included in the critical path method. 45 Which of the following Six Sigma project tools was borrowed from movies and advertising? Pareto Chart. Storyboard. Run Chart. SIPOC Diagram.

The Storyboard is a series of graphical panels that tell the “story” of a Six Sigma project. This is the same tool used in movies and advertising, where drawings are used to map out a commercial or animated feature before it goes into production. The Storyboard may contain the other tools listed. 46 A/An______is a tool to identify, estimate, prioritize and reduce the risk of failure. FMEA QFD Boundary Diagram

• QFD is a tool to translate customer wants needs and desires to engineering/technical requirements • An Ishikawa diagram is a way to analyze cause and effects relationships • A Boundary diagram is a tool to help depict how elements of a system relate to other systems to which it comes in contact with either directly or in directly 47

The analysis of lessons learned, or what went well and what went wrong during a project would most likely take place during which of the following? Milestones reporting. Document archiving. Post mortem analysis. Project champion updates.

After the final report is completed. The next step of project information is the post mortem analysis. The analysis of what went well and what went wrong is used as a learning tool for future projects. 48 The objective of the define phase of a six sigma project is to define: The quality policy The customer, core business process involved and CTQ business issues The statistics work instructions The procedures manual for control charting

Hopefully A) quality policy C) Work instruct D) Procedures exist but when defining a six sigma project the core focus is on the customer the core process to be improved and the critical to quality issues 49 The definition that states, ‘total number of deficiencies divided by the total number of units’ represents the calculation for: DPMO RPN DPU DPO

•By definition of DPU, DPO and DPMO

•DPO = •DPMO = DPO x 1,000,000 50 Which of the following tools is used to identify, estimate, prioritize, and reduce the risk of failure in CTQs through the development of actions (process changes) and contingency plans based on Xs. Process Flow Diagram. Affinity Diagram. Failure Modes and Effects Analysis (FMEA). .

Team members select the Xs with the highest weighted averages and input them into a failure modes and effects analysis. 51 During project team meetings, the Team Leader is responsible for all of the following activities EXCEPT: Starts and ends the meeting on time Stays on the agenda Leads brainstorming sessions Monitors how much time the team spends on each agenda item

The Timekeeper is responsible for monitoring how much time the team spends on each agenda item. 52

In which phase of DMAIC do you define the Roles and Responsibilities of the Improvement Team? Analyze Define Measure Improve

Define 53 Multivoting is a variation of which of the following team tools? Brainstorming Force field analysis Nominal group techniques Consensus

Multivoting is a variation of the nominal group technique in which each team member has 100 points to allocate to the items on the list as that team member feels appropriate, assigning the largest number of points to the highest items. 54 Excessive conflict within a work team: I. Has a negative effect on team members and should be avoided II. Has a positive effect on creating alternate solutions III. Most often results in lose-lose situations I only I and III only II and III only III only

Excessive conflict within a team often has a negative effect on employees (answer I). This leaves only answers a and b as options. Conflict most often results in win-lose or lose-lose situations (answer III). Rarely will either a win- win or creative alternate solutions result. Only a few exceptional personalities thrive in an environment of conflict. 55 The fishbone diagram is also known as a: I. Ishikawa Diagram II. Scatter Diagram III. Process Flow Diagram IV. Causes and Effect Diagram I Only I, II and IV only I and IV only I, II, II and IV only

The chart was developed by Ishikawa and it looks like a fish’s backbone, thus it is also called fishbone. It helps to assign causes for listed effects. Dr. Deming tried to Americanize it by calling a Feather Diagram, but that never stuck. 56 SIPOC stands for: Supplier, Input, Process, Output, Customer Supplier, Internal, Process, Output, Customer Supplier, Input, Production, Output, Customer Supplier, Input, Production, Output, Control

Supplier, Input, Process, Output, Customer 57 An early step in any project must be seeking the voice of the internal and external customers of a project. This statement is: False, because projects should only be concerned with external customers. True, because both internal and external customers can be impacted by the project. True, because a project team wants to maintain good will with all customers. False, because internal projects only impact internal customers.

Projects need to consider all stakeholders, including internal and external customers. 58 To approximate the normal distribution using the , it is best to have a sample size that is: Large Small Skewed Positive

When a sample of several random measurements are averaged, distribution of such repeated sample averages tends to be normally distributed regardless of the distribution of measurements (Large) 59 An examples of ‘Attribute Data’ is: Height of each student in 1st grade Number of students with blue eyes in the 1st grade Location of car dealerships in a large city Outdoor temperature recorded at each hour of a day on December 25th

Number of students with blue eyes in the 1st grade represents attribute data. Attribute data are data that can be counted; in this case, a total number of students with blue eyes are a specific integer number –Answer A) is variable data –Answer C) is location data –Answer D) is variable data 60 The average of five raw data points is called a: Parameter Constraint Population

Descriptive statistics help pull useful information from raw data 61 Coding data frequently improves the of data entry due to: Inspectors trying to squeeze too many digits into small block on a form Reduced follow through and increased errors by clerks at keyboards Reduced sensitivity due to runoff of large sequences of digits All of the above None of the above

Coding reduces large numbers into small manageable numbers. 62

Which type of sampling requires giving every part an equal chance of being selected for the sample: Stratified Sequential Random Tightened

True is an equal opportunity. 63 What are the three measures of : I. II. III.Mean IV.Sum V.Difference I, II, and IV I, II and III III, IV and V II, III and IV

1.Median is the midpoint 2.The mean is the average 3.The mode is the most frequently occurring number in a data sheet 64 Constructed much like a tally column for creating a histogram, except that the last digit of the data value is recorded as data instead of a tally mark: Box-and-whisker plot Stem-and-leaf plot Scatter diagram Pareto chart

A stem-and-leaf plot of this data can be constructed by writing the first digits in the first column, then writing the second digits of all the remaining data numbers in that range to the right of the original digit. 65 The distribution that is used to model situations having only two possible outcomes, usually labeled as success or failure, is the: Poisson Binomial Normal Chi-square

Binomial distribution always has two possible outcomes. 66 What is the purpose of a GR&R: Identification of the variability of the measurement of the accuracy of the measurement system Identification of the variability between operators Identification of the accuracy of two different measurement systems

• Gage R&R (repeatability and reproducibly) studies address the variability of the measurement system. • Measurement System Analysis (MSA) assesses the statically properties of repeatability, reproducibly, bias, stability, and linearity. • Bias, stability and linearity studies address the accuracy of the measurement system. 67 When the natural process limits are compared with the specification range, which of the following possible courses of action may result: I.Do nothing II.Change the specifications III.Center the process IV.Reduce variability V. Accept the loss I Only III Only II, III and IV only I, II, III, IV and V

If the process limits fall well within the specifications: –Specifications may be set tighter –Adjustment when process spread is approximately the same as specifications spread –Work on largest variation offender –Management may be content with high loss rate 68 The statistic that is a capability index that takes the process location as well as the capability into account is the: Cp Cpk Pp Ppk

•Cp is a capability index that compares the to the maximum allowable variation as indicated by the tolerance. •Pp is the performance index that compares the process performance to the maximum allowable variation as indicated by the tolerance. •Ppk is the performance index that takes the process location as well as the performance into account. 69 The capability index that relates to distance between the process mean and the closest specifications limit is: Cp Cpk Cmk Cpm

Cpk is the lesser value of USL – X̄/6s or X̄ – LSL/6s 70 What is the Cpk for a process with specification limits of 48 and 30 and a process mean of 29 and sigma of 4? 1.58 0.08 -0.08 -1.58

Cpk = lesser of USL – Xbar/3s or Xbar – LSL/3s –Cpu48-29/3*4 = 1.58 –Cpl 29-30/3*4 = -0.08 71

Which of the following is NOT a process performance index: Pp Ppk Cpk Cpm

Cpk is a capability index 72 Many Six Sigma practitioners focus on determining short-term variability with an assumed adjustment of ______to compensate for drifts to get long-term variability. 1.00 Sigma 1.33 Sigma 1.50 Sigma 2.00 Sigma 73 Which index is used to calculate attribute capability? DPMO p Chart c Chart Cpm

The p and c are charts that show stability of a process. Cpm is a performance index for variables data. 74 The use of the multi-variable chart is useful for all of the following EXCEPT? within-sample variation sample-to-sample variation within batches of samples weighted average-to-standard weights batch-to-batch variation

"Multi-vari" charts are used in a variety of industries to analyze process data with nested (hierarchical) patterns of variation –within-sample variation (for example, position within wafer) –sample-to-sample variation within batches of samples (for example, wafer within lot) –batch-to-batch variation (for example, across lots) 75 If r = 0.97, as the independent variable b increase, one would expect the dependant variable to______increase decrease stay the same can’t tell

Regression analysis is a method of analysis that enables you to quantify the relationship between two or more variables (X) and (Y) by fitting a line or plane through all the points such that they are evenly distributed about the line or plane. 76

The producer risk is also known as______Consumer risk Alpha Beta Type II error

•A value of α= 0.05 that we inadvertently reject the null hypothesis 5% of the time when it is in fact true. This is also called the type I error. •The probability of rejecting the null hypothesis when it is in fact false is called the power of the test and is denoted by 1 -β. Its complement, the probability of accepting the null hypothesis when the is, in fact, true (type II error), is called and can only be computed for a specific alternative hypothesis.

77 A sample Z-test for population means concludes that the null hypotheses should not be rejected. This means that statistically the sample mean is ______the population mean. the same as different than larger than not related

By definition 78 All of the following are regarding the null hypotheses EXCEPT: It can be rejected It cannot be rejected It can be accepted It is never accepted

By Definition –hypothesis test are never “accepted” as you can never test all variables or conditions 79 What is typically considered the crossover point between the T and Z tests? Sample size of 30 When standard deviation is known Degrees of freedom are unknown To model rates such as defects per unit

•By Definition •Also T distribution tables d..f. =1-29; D.f.=n-1 80

The test relies upon which distribution to calculate the cumulative distribution function? T-distribution Binomial Chi-square Poisson

•These features (center, spread, , presence of outliers or presence of multiple modes) provide strong indications of the proper distributional model for the data. The probability plot or a goodness-of-fit test can be used to verify the distributional model. •The residual standard deviation is a goodness-of-fit measure. That is, the smaller the residual standard deviation, the closer is the fit to the data. •An attractive feature of the chi-square goodness-of-fit test is that it can be applied to any •univariate distribution for which you can calculate the cumulative distribution function. •The chi-square goodness-of-fit test is applied to binned data (i.e., data put into classes). 81 An experiment was run to evaluate the effects of hinge thickness and hardness on the force required to close a door. The following results were recorded.

The number of factors in this experiment is? 2 3 4 5

Definition of Factors: Factors are variables that are studied at different levels in a designed experiment. The two factors in this experiment are Hinge Thickness and Hinge Hardness. 82

An experiment was run to evaluate the effects of hinge thickness and hardness on the force required to close a door. The following results were recorded.

What is the effect of the Hinge Hardness? -1.1 +1.1 -3.3 +3.3

•The Effect is the difference (delta) between the High and Low Level Average Results for each factor. •For Hinge Hardness Levels: •The average High Level result for Hardness is (5.5 + 7.9) / 2 = 6.7 •The average Low Level result for Hardness is (5.7 + 9.8) / 2 = 7.8 •The difference in results for Hardness is 6.7 –7.8 = -1.1 •Answer B is the negative value of A, which is arrived at if the High Level Result is subtracted from the Low Level result for Hinge Hardness. •Answer C is the Effect for Hinge Thickness rather than Hinge Hardness. •Answer D is the negative value of C, which is arrived at if the High Level result is subtracted from the Low Level result for Hinge Thickness. 83 In the 1920’s, Dr. Walter A. Shewhart of Bell Telephone Laboratories developed a theory of Statistical Quality Control (SQC). He concluded that there were two components to variations that were displayed in all manufacturing processes. What are these components? X variables & R variables (& R charts) Cause issues and effects issues (C&E diagrams) Gage repeatability and gage reproducibility Random variation and intermittent variation

•Understand the history and theory of SPC •Answers A, B and C are all tools •Random variation is also called common or normal process variation. •Intermittent variation is also called special, assignable or nonrandom process variation. 84 Segregating data from different mold cavities in a production line is an example of: Red Bead Experimentation Process Control Plan Rational Subgrouping Factor Allocation

•“Generally, subgroups are selected in a way that makes each subgroup as homogeneous as possible. “-CQI Primer •“Traditionally, rational subgrouping issues involve the selection of samples that yield relatively homogeneous conditions within the subgroup …”Implementing Six Sigma •Add refer to basic definition of rational subgrouping. 85

Inspection data for number of imperfections in a windshield was taken, with 3 samples taken from every incoming lot, as shown in the table below. If the number of defects are charted what would be the Lower Control Limit?

7.14 2.56 0 -0.87

•This question evaluates the individual’s ability to calculate control Limits on a C Chart and knowledge that the LCL can never be lower than 0 (zero) on a C Chart. •The formula for calculating the Lower Control Limit on an C Chart is : •LCL= C Bar –3*(sqrt(CBar)) •C Bar = Total number of Defects / Number of Lots = (9+6+4+6+7+3+15) / 7 = 50 / 7 = 7.14 •Square Root of CBar= Square Root of 7.14 = 2.67 •LCL = CBar-3 * SQRT(CBar) = 7.14 –3*2.67 = -0.87 •However there can never be less defectives than 0. The LCL = 0. 86 In statistical process control, when a point falls outside of control limits, the probability is quite high that the process is experiencing ______. common cause variation student t variation a reduction of variables special cause variation 87 The 'F' distribution is used to test: the ratio of two the ratio of two mean the ratio of two standard deviations none of the above 88

The best source for developing a Control Plan would be which of the following? Poka-Yoke Control Chart House of Quality FMEA

•“The control plan is an extension of the control column of an FMEA. The FMEA is an important source for the identification of KPIVs that are included within a Control Plan”–see Implementing Six Sigma by Forrest Breyfogle. •Poka-yoke should be part of the Control Plan but it is only one of many possible controls in the Control Plan. •Use of Control Charts should be only one of the many possible controls in the Control Plan. •The House of Quality can be used to help identify possible KPIVs and KPOVs early in the Six Sigma process. However FMEA helps to identify the controls that were determined to be critical for obtaining or sustaining improvements based upon the actual and potential failure modes or risks of the process. 89