1. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter 17 Introduction to Quality and Statistical Process Control

2. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-2 Chapter Goals After completing this chapter, you should be able to:  Use the seven basic tools of quality  Construct and interpret x-bar and R-charts  Construct and interpret p-charts  Construct and interpret c-charts

3. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-3 Chapter Overview Quality Management and Tools for Improvement Deming’s 14 Points Juran’s 10 Steps to Quality Improvement The Basic 7 Tools Philosophy of Quality Tools for Quality Improvement Control Charts X-bar/R-charts p-charts c-charts

4. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-4 Themes of Quality Management Primary focus is on process improvement Most variations in process are due to systems Teamwork is integral to quality management Customer satisfaction is a primary goal Organization transformation is necessary It is important to remove fear Higher quality costs less

5. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-5 1. Create a constancy of purpose toward improvement become more competitive, stay in business, and provide jobs 2. Adopt the new philosophy Better to improve now than to react to problems later 3. Stop depending on inspection to achieve quality -- build in quality from the start Inspection to find defects at the end of production is too late 4. Stop awarding contracts on the basis of low bids Better to build long-run purchaser/supplier relationships Deming’s 14 Points

6. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-6 5. Improve the system continuously to improve quality and thus constantly reduce costs 6. Institute training on the job Workers and managers must know the difference between common cause and special cause variation 7. Institute leadership Know the difference between leadership and supervision 8. Drive out fear so that everyone may work effectively. 9. Break down barriers between departments so that people can work as a team. (continued) Deming’s 14 Points

7. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-7 10. Eliminate slogans and targets for the workforce They can create adversarial relationships 11. Eliminate quotas and management by objectives 12. Remove barriers to pride of workmanship 13. Institute a vigorous program of education and self-improvement 14. Make the transformation everyone’s job (continued) Deming’s 14 Points

8. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-8 Juran’s 10 Steps to Quality Improvement 1. Build awareness of both the need for improvement and the opportunity for improvement 2. Set goals for improvement 3. Organize to meet the goals that have been set 4. Provide training 5. Implement projects aimed at solving problems

9. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-9 Juran’s 10 Steps to Quality Improvement 6. Report progress 7. Give recognition 8. Communicate the results 9. Keep score 10. Maintain momentum by building improvement into the company’s regular systems (continued)

10. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-10 The Deming Cycle The Deming Cycle The key is a continuous cycle of improvement Act Plan Do Study

11. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-11 The Basic 7 Tools 1.Process Flowcharts 2.Brainstorming 3.Fishbone Diagram 4.Histogram 5.Trend Charts 6.Scatter Plots 7.Statistical Process Control Charts

12. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-12 The Basic 7 Tools 1.Process Flowcharts 2.Brainstorming 3.Fishbone Diagram 4.Histogram 5.Trend Charts 6.Scatter Plots 7.Statistical Process Control Charts Map out the process to better visualize and understand opportunities for improvement (continued)

13. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-13 The Basic 7 Tools 1.Process Flowcharts 2.Brainstorming 3.Fishbone Diagram 4.Histogram 5.Trend Charts 6.Scatter Plots 7.Statistical Process Control Charts Cause 4 Cause 3 Cause 2Cause 1 Problem Fishbone (cause-and-effect) diagram: Sub-causes Show patterns of variation (continued)

14. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-14 The Basic 7 Tools 1.Process Flowcharts 2.Brainstorming 3.Fishbone Diagram 4.Histogram 5.Trend Charts 6.Scatter Plots 7.Statistical Process Control Charts time y x y Identify trend Examine relationships (continued)

15. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-15 The Basic 7 Tools 1.Process Flowcharts 2.Brainstorming 3.Fishbone Diagram 4.Histogram 5.Trend Charts 6.Scatter Plots 7.Statistical Process Control Charts X Examine the performance of a process over time time (continued)

16. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-16 Introduction to Control Charts Control Charts are used to monitor variation in a measured value from a process Exhibits trend Can make correction before process is out of control A process is a repeatable series of steps leading to a specific goal Inherent variation refers to process variation that exists naturally. This variation can be reduced but not eliminated

17. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-17 Process Variation Total Process Variation Common Cause Variation Special Cause Variation =+ Variation is natural; inherent in the world around us No two products or service experiences are exactly the same With a fine enough gauge, all things can be seen to differ

18. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-18 Sources of Variation Total Process Variation Common Cause Variation Special Cause Variation =+ People Machines Materials Methods Measurement Environment Variation is often due to differences in:

19. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-19 Common Cause Variation Total Process Variation Common Cause Variation Special Cause Variation =+ Common cause variation naturally occurring and expected the result of normal variation in materials, tools, machines, operators, and the environment

20. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-20 Special Cause Variation Total Process Variation Common Cause Variation Special Cause Variation =+ Special cause variation abnormal or unexpected variation has an assignable cause variation beyond what is considered inherent to the process

21. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-21 Statistical Process Control Charts Show when changes in data are due to: Special or assignable causes Fluctuations not inherent to a process Represents problems to be corrected Data outside control limits or trend Common causes or chance Inherent random variations Consist of numerous small causes of random variability

22. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-22 Process Average Control Chart Basics UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations UCL LCL +3σ - 3σ- 3σ Common Cause Variation: range of expected variability Special Cause Variation: Range of unexpected variability time

23. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-23 Process Average Process Variability UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations UCL LCL ±3σ → 99.7% of process values should be in this range time Special Cause of Variation: A measurement this far from the process average is very unlikely if only expected variation is present

24. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-24 Statistical Process Control Charts X-bar charts and R-charts c-charts Used for measured numeric data Used for proportions (attribute data) Used for number of attributes per sampling unit p-charts

25. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-25 x-bar chart and R-chart Used for measured numeric data from a process Start with at least 20 subgroups of observed values Subgroups usually contain 3 to 6 observations each

26. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-26 Steps to create an x-chart and an R-chart Calculate subgroup means and ranges Compute the average of the subgroup means and the average range value Prepare graphs of the subgroup means and ranges as a line chart

27. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-27 Steps to create an x-chart and an R-chart Compute the upper and lower control limits for the x-bar chart Compute the upper and lower control limits for the R-chart Use lines to show the control limits on the x-bar and R-charts (continued)

28. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-28 Example: x-chart Process measurements: Subgroup measures Subgroup number Individual measurements Mean, x Range, R 123…123… 15 12 17 … 17 16 21 … 15 9 18 … 11 15 20 … 14.5 13.0 19.0 … 674…674… Average subgroup mean = x Average subgroup range = R

29. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-29 Average of Subgroup Means and Ranges Average of subgroup means: where: x i = i th subgroup average k = number of subgroups Average of subgroup ranges: where: R i = i th subgroup range k = number of subgroups

30. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-30 Computing Control Limits The upper and lower control limits for an x-chart are generally defined as or UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations

31. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-31 Computing Control Limits Since control charts were developed before it was easy to calculate σ, the interval was formed using R instead The value A 2 R is used to estimate 3σ, where A 2 is from Appendix Q The upper and lower control limits are (continued) where A 2 = Shewhart factor for subgroup size n from appendix Q

32. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-32 Example: R-chart The upper and lower control limits for an R-chart are where: D 4 and D 3 are taken from the Shewhart table (appendix Q) for subgroup size = n

33. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-33 x-chart and R-chart UCL LCL time UCL LCL time R-chart x-chart

34. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-34 Using Control Charts Control Charts are used to check for process control H 0 : The process is in control i.e., variation is only due to common causes H A : The process is out of control i.e., special cause variation exists If the process is found to be out of control, steps should be taken to find and eliminate the special causes of variation

35. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-35 Process In Control Process in control: points are randomly distributed around the center line and all points are within the control limits UCL LCL time

36. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-36 Process Not in Control Out of control conditions: One or more points outside control limits Nine or more points in a row on one side of the center line Six or more points moving in the same direction 14 or more points alternating above and below the center line

37. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-37 Process Not in Control One or more points outside control limits UCL LCL Nine or more points in a row on one side of the center line UCL LCL Six or more points moving in the same direction UCL LCL 14 or more points alternating above and below the center line UCL LCL

38. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-38 Out-of-control Processes When the control chart indicates an out-of- control condition (a point outside the control limits or exhibiting trend, for example) Contains both common causes of variation and assignable causes of variation The assignable causes of variation must be identified If detrimental to the quality, assignable causes of variation must be removed If increases quality, assignable causes must be incorporated into the process design

39. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-39 p-Chart Control chart for proportions Is an attribute chart Shows proportion of nonconforming items Example -- Computer chips: Count the number of defective chips and divide by total chips inspected Chip is either defective or not defective Finding a defective chip can be classified a “success”

40. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-40 p-Chart Used with equal or unequal sample sizes (subgroups) over time Unequal sizes should not differ by more than ±25% from average sample sizes Easier to develop with equal sample sizes Should have np > 5 and n(1-p) > 5 (continued)

41. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-41 Creating a p-Chart Calculate subgroup proportions Compute the average of the subgroup proportions Prepare graphs of the subgroup proportions as a line chart Compute the upper and lower control limits Use lines to show the control limits on the p-chart

42. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-42 p-Chart Example Subgroup number Sample size Number of successes Proportion, p 123…123… 150 15 12 17 … 10.00 8.00 11.33 … Average subgroup proportion = p

43. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-43 Average of Subgroup Proportions The average of subgroup proportions = p where: p i = sample proportion for subgroup i k = number of subgroups of size n where: n i = number of items in sample i  n i = total number of items sampled in k samples If equal sample sizes:If unequal sample sizes:

44. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-44 Computing Control Limits The upper and lower control limits for an p-chart are or UCL = Average Proportion + 3 Standard Deviations LCL = Average Proportion – 3 Standard Deviations

45. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-45 Standard Deviation of Subgroup Proportions The estimate of the standard deviation for the subgroup proportions is If equal sample sizes:If unequal sample sizes: where: = mean subgroup proportion n = common sample size Generally, is computed separately for each different sample size

46. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-46 Computing Control Limits The upper and lower control limits for the p-chart are (continued) If sample sizes are equal, this becomes Proportions are never negative, so if the calculated lower control limit is negative, set LCL = 0

47. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-47 p-Chart Examples For equal sample sizes For unequal sample sizes UCL LCL UCL LCL pp is constant since n is the same for all subgroups varies for each subgroup since n i varies

48. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-48 c-Chart Control chart for number of nonconformities (occurrences) per sampling unit (an area of opportunity) Also a type of attribute chart Shows total number of nonconforming items per unit examples: number of flaws per pane of glass number of errors per page of code Assume that the size of each sampling unit remains constant

49. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-49 Mean and Standard Deviation for a c-Chart The mean for a c-chart is The standard deviation for a c-chart is where: x i = number of successes per sampling unit k = number of sampling units

50. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-50 c-Chart Control Limits The control limits for a c-chart are

51. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-51 Process Control Determine process control for p-chars and c-charts using the same rules as for x-bar and R-charts Out of control conditions: One or more points outside control limits Nine or more points in a row on one side of the center line Six or more points moving in the same direction 14 or more points alternating above and below the center line

52. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-52 c-Chart Example A weaving machine makes cloth in a standard width. Random samples of 10 meters of cloth are examined for flaws. Is the process in control? Sample number1234567 Flaws found2130510

53. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-53 Constructing the c-Chart The mean and standard deviation are: The control limits are: Note: LCL < 0 so set LCL = 0

54. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-54 The completed c-Chart The process is in control. Individual points are distributed around the center line without any pattern. Any improvement in the process must come from reduction in common-cause variation UCL = 5.642 LCL = 0 Sample number 1 2 3 4 5 6 7 c = 1.714 65432106543210

55. Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 17-55 Chapter Summary Reviewed the philosophy of quality management Demings 14 points Juran’s 10 steps Described the seven basic tools of quality Discussed the theory of control charts Common cause variation vs. special cause variation  Constructed and interpreted x-bar and R-charts  Constructed and interpreted p-charts  Constructed and interpreted c-charts