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Quality Tools for Six Sigma Six Sigma Quality: Concepts & Cases‐ Volume I STATISTICAL TOOLS IN SIX SIGMA DMAIC PROCESS WITH MINITAB® APPLICATIONS Chapter 5 Quality Tools for Six Sigma © 2010-12 Amar Sahay, Ph.D. 1 Chapter 5: Quality Tools for Six Sigma Chapter Outline Process Histograms Evaluating Process Capability Using Histogram Stem-and-leaf Plot Box Plot Run Chart Example 1: Constructing a Run Chart Example 2: A Run Chart with Subgroup Size Greater than 1 Example 3: A Run Chart with Subgroup Size Greater than 1 (Data across the Row) Example 4: Run Chart Showing a Stable Process, a Shift, and a Trend Pareto Chart Example 5: A Simple Pareto Chart Example 6:Pareto Chart with Cumulative Percentage Example 7:Pareto Chart with Cumulative Percentage when Data are in One Column Example 8:Pareto Chart By Variable Cause-and-Effect Diagram or Fishbone Diagram Example 9:Cause-and-Effect Diagram (1) Example 10: Cause-and-effect Diagram (2) Example 11: Creating other Types of Cause-and-effect Diagram Summary and Application of Plots Bivariate Data: Measuring and Describing Two Variables Scatter Plots Example 12: Scatterplots with Histogram, Box-plots and Dot plots Example 13: Scatterplot with Fitted Line or Curve Example 14: Scatterplot Showing an Inverse Relationship between X and Y Example 15: Scatterplot Showing a Nonlinear Relationship between X and Y Example 16: Scatterplot Showing a Nonlinear (Cubic) Relationship between X and Y Multi-Vari Chart and Other Plots Useful to Investigate Relationships Before Running Analysis of Variance -Example 17: A Multi-vari Chart for Two-factor Design -Main Effects Plot -Interaction Plot Example 18: Another Multi-vari Chart for a Two-factor Design -Multi-Vari plot -Box Plots -Main Effects Plot -Interaction Plot 2 Chapter 5: Quality Tools for Six Sigma Example 19: Mult-vari chart for a Three-factor Design -Multi-Vari Chart -Box Plots -Main Effects Plot Example 20: Multi-vari Chart for a Four-factor Design -Multi-Vari Chart -Box Plots -Main Effects and Interaction Plots Example 21: Determine a Machine-to-Machine, Time-to-Time variation Part-to-Part Variation in a Production Run using Multi-vari and Other Plots Symmetry Plot Summary and Applications This chapter explains the graphical techniques that have been applied as problem-solving tools in quality control. Many graphs and charts are helpful in detecting and solving quality problems. Some of the graphical techniques in this chapter are described in previous chapters. In this chapter we describe and analyze the graphs and charts as they relate to quality control. We also provide examples and specific situations in which these graphical techniques are used in detecting and solving quality problems. Some examples from the chapter are presented below. The book provides step­wise instructions with data files for each case. 3 Chapter 5: Quality Tools for Six Sigma Histograms In quality, histograms are useful in detecting process problems-including a shift in the process evaluating process capability (ability of the process to be within its specification limits) determining how well centered the process is or how close the data values are to the target value, and determining the process variation. Examples Histogram of Ring Dia: Run 2 4.95 5 5.05 18 16 14 12 10 8 Frequency 6 4 2 0 4.950 4.965 4.980 4.995 5.010 5.025 5.040 Ring Dia: Run 2 (a) Figure 5.1(a) Most values within specification, some assignable causes may be present Histogram of Ring Dia: Run 3 4.95 5 5.05 25 20 15 Frequency 10 5 0 4.950 4.965 4.980 4.995 5.010 5.025 5.040 Ring Dia: Run 3 (c) Figure 5.1(c) Process variation has reduced compared to (a): a shift to the right 4 Chapter 5: Quality Tools for Six Sigma Hi stogram of Ring Dia: Run 5 Hi stogram of Ring Dia: Run 6 4.95 5 5.05 4.95 5 5.05 25 20 20 15 15 10 Fr e que ncy10 Fr e que ncy 5 5 0 0 4.94 4.96 4.98 5.00 5.02 5.04 4.950 4.965 4.980 4.995 5.010 5.025 5.040 Ring Dia: Run 6 Ring Dia: Run 5 (e) (f) Figure 5.1(e) The process has shifted to the left; products out of specification (may be calibration problem) Figure 5.1(f) Process shift to the left; more variation compared to (e) Histogram of Ring Dia: Run 9 4.95 5 5.05 14 12 10 8 6 Frequency 4 2 0 4.953 4.966 4.979 4.992 5.005 5.018 5.031 5.044 Ring Dia: Run 9 (i) Figure 5.1 (i) Process stable and close to the target (desirable) The above histograms are useful in examining the possible problems and the causes behind them. Evaluating Process Capability using Histograms Histograms can also be used to assess the process capability (the ability of a process to be 5 Chapter 5: Quality Tools for Six Sigma within its specifications). The process capability can be determined once the process is stable ……. The next chapter provides the measures of process capability and their relationship to six sigma quality. Run Charts A run chart is used in Quality Control to analyze the data either in the development stage of a product or before the state of statistical control. A run chart can be used to determine if the process is running in a state of control or if special or assignable causes are influencing the process, thereby making the process out of control. : : Example 4: Run Chart Showing a Stable Process, a Shift, and a Trend A Run Chart Showing a Stable Process 3.5 3.0 2.5 Process 1 2.0 1.5 1 10 20 30 40 50 60 70 80 90 Observation Number of runs about median: 53 Number of runs up or down: 56 Expected number of runs: 46.00000 Expected number of runs: 59.66667 Longest run about median: 4 Longest run up or down: 5 Approx P-Value for Clustering: 0.93111 A pprox P-Value for Trends: 0.17721 A pprox P-Value for Mixtures: 0.06889 A ppro x P-Value fo r O scillatio n: 0.82279 A Run Chart Showing a Stable Process 6 Chapter 5: Quality Tools for Six Sigma A Run Chart Showing a Trend 10 9 8 7 6 Process 2 5 4 3 1 5 10 15 20 25 30 35 40 45 50 55 60 65 Observation Number of runs about median: 18 Number of runs up or down: 43 Expected number of runs: 33.96970 Expected number of runs: 43.66667 Longest run about median: 12 Longest run up or down: 4 Approx P-Value for Clustering: 0.00004 Approx P-Value for Trends: 0.42178 A pprox P-Value for Mixtures: 0.99996 A p p ro x P -Value fo r O scillatio n: 0.57822 Run Chart Showing a Trend A Run Chart Showing a Shift in the Process 10 9 8 7 6 Process 3 5 4 3 1 5 10 15 20 25 30 35 40 45 50 55 60 Observation Number of runs about median: 19 Number of runs up or dow n: 42 Expected number of runs: 32.96875 Expected number of runs: 42.33333 Longest run about median: 13 Longest run up or down: 4 A pprox P-Value for C lustering: 0.00021 A pprox P-Value for Trends: 0.46007 A pprox P-Value for Mixtures: 0.99979 A p p ro x P -Value fo r O scillatio n : 0.53993 A Run Chart Showing a Shift A run chart is a quick, easy, and economical way to detect process problems. In the initial stages of a process, or for a new process, run charts provide opportunities for improvement without the implementation of control charts. 7 Pareto A Pareto chart is very similar to a histogram or a frequency distribution of attribute data Chart Chapter where the bars are arranged by categories from cumulative percentage and count of the bars. This chart is widely used in Quality Control to analyze the defect data. Through this chart, th 5: identified quickly and easily. This helps to Quality percentage of defects. A Pareto chart does identifies the categories that oc Tools manufacturing applications. There are several variations of the Pareto for construct this chart. The data for the Six Sigma : Example 6: cur most frequently. Pareto charts are also used widely in non Pareto largest to smallest with a line that shows the focus ethe defects improvement that occur efforts most frequentlyon the largest can be Chart not identify the most important category; it chart can be entered in several ways. with chart. MINITAB provides several options to Cumulative Count Pareto Chart of Defects in Machined Parts 90 Pareto Failure Cause 80 70 60 Percentage 50 40 30 20 10 0 (Second Inc orrect Dimensions Count 12 Percent 27.8 18.2 13.2 10.9 8.3 7.0 5.6 5.0 Dam Chart of DefectCum % Data 27.8 with 46.0 No 59.3age 70.2d Pa 78.5rts 85.4 91.1 96.0 Ma chining Errors Option) 84 Internal Flaws 55 Meas urement Errors 40 33 25 21 17 15 M echanical Errors In-use Failures S urfa ce Finish Errors Cumulative Points Plotted D rawing Errors 8 100.04.0 Chapter 5: Quality Pareto Chart of Defects in Machined Parts Count 300 Tools 250 200 for Pareto Chart Failure C ause 150 Six 100 Sigma 50 Example 0 The data file Inc orre ct Dimensions Count the shifts they produced (columns C3 and C4).
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