1. © 2002 Prentice-Hall, Inc.Chap 15-1 Statistics for Managers Using Microsoft Excel 3 rd Edition Chapter 15 Statistical Applications in Quality and Productivity Management

2. © 2002 Prentice-Hall, Inc. Chap 15-2 Chapter Topics Total quality management (TQM) Theory of process management (Deming’s fourteen points) The theory of control charts Common cause variation vs. Special cause variation Control charts for the proportion of nonconforming items

3. © 2002 Prentice-Hall, Inc. Chap 15-3 Chapter Topics Process variability The c chart Control charts for the mean and the range Process capability (continued)

4. © 2002 Prentice-Hall, Inc. Chap 15-4 Themes of Quality Management 1. Primary focus is on process improvement 2. Most variations in process are due to systems 3. Teamwork is integral to quality management 4. Customer satisfaction is a primary goal 5. Organization transformation is necessary 6. It is important to remove fear 7. Higher quality costs less

5. © 2002 Prentice-Hall, Inc. Chap 15-5 Deming’s 14 Points: Point 1 Plan Do Study Act Point 1. Create Constancy of Purpose The Shewhart-Deming Cycle Focuses on Constant Improvement

6. © 2002 Prentice-Hall, Inc. Chap 15-6 Deming’s 14 Points: Points 2 and 3 Point 2. Adopt a New Philosophy Better to be proactive and change before crisis occurs. Point 3. Cease Dependence on mass inspection achieve quality. Any inspection the purpose of which is to improve quality is too late.

7. © 2002 Prentice-Hall, Inc. Chap 15-7 Point 4. End the practice of awarding business on the basis of price tag alone Develop a long-term relationship between purchaser and supplier. Point 5. Improve constantly and forever Reinforce the importance of the Shewhart-Deming cycle. Deming’s 14 Points: Points 4 and 5

8. © 2002 Prentice-Hall, Inc. Chap 15-8 Deming’s 14 Points: Points 6 and 7 Point 6. Institute Training Especially important for managers to understand the difference between special causes and common causes. Point 7. Adopt and Institute Leadership Differentiate between leadership and supervision. Leadership is to improve the system and achieve greater consistency of performance.

9. © 2002 Prentice-Hall, Inc. Chap 15-9 8.Drive out fear 9.Break down barriers between staff areas 10.Eliminate slogans 11. Eliminate numerical quotas for workforce and numerical goals for management 12.Remove barriers to pride of workmanship Deming’s 14 Points: Points 8 to 12

10. © 2002 Prentice-Hall, Inc. Chap 15-10 Point 13. Encourage education and self improvement for everyone. Improved knowledge of people will improve assets of organization. Point 14. Take action to accomplish transformation. Continually strive toward improvement. Deming’s 14 Points: Points 13 and 14

11. © 2002 Prentice-Hall, Inc. Chap 15-11 Control Charts Monitors variation in data Exhibits trend -- make correction before process is out of control A process -- A repeatable series of steps leading to a specific goal

12. © 2002 Prentice-Hall, Inc. Chap 15-12 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 Chance or common causes Inherent random variations Consist of numerous small causes of random variability (continued)

13. © 2002 Prentice-Hall, Inc. Chap 15-13 Graph of sample data plotted over time Process Control Chart Special Cause Variation Common Cause Variation Process Average  Mean UCL LCL

14. © 2002 Prentice-Hall, Inc. Chap 15-14 Control Limits UCL = Process Average + 3 Standard Deviations LCL = Process Average - 3 Standard Deviations Process Average UCL LCL X + 3  - 3  TIME

15. © 2002 Prentice-Hall, Inc. Chap 15-15 Types of Error First Type: Belief that observed value represents special cause when in fact it is due to common cause Second Type: Treating special cause variation as if it is common cause variation

16. © 2002 Prentice-Hall, Inc. Chap 15-16 Comparing Control Chart Patterns XXX Common Cause Variation: No Points Outside Control Limits Special Cause Variation: 2 Points Outside Control Limits Downward Pattern: No Points Outside Control Limits but Trend Exists

17. © 2002 Prentice-Hall, Inc. Chap 15-17 When to Take Corrective Action Take corrective action when you observe points outside the control limits or when a trend has been detected Eight consecutive points above the center line (or eight below) Eight consecutive points that are increasing (decreasing)

18. © 2002 Prentice-Hall, Inc. Chap 15-18 Out-of-control Processes When the control chart indicates an out-of- control condition (a point outside the control limits or exhibiting trend) 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

19. © 2002 Prentice-Hall, Inc. Chap 15-19 In-control Process When the control chart does not indicate any out-of-control condition Contains only common causes of variation Sometimes said to be in a state of statistical control If the common causes of variation is small, then control chart can be used to monitor the process If the common causes of variation is too large, you need to alter the process

20. © 2002 Prentice-Hall, Inc. Chap 15-20 p Chart Control chart for proportions Is an attribute chart Shows proportion of nonconforming (success) items e.g.: Count the number defective chairs and divide by total chairs inspected Chair is either defective or not defective Used with equal or unequal sample sizes over time Unequal sizes should not differ by more than ±25% from average sample size

21. © 2002 Prentice-Hall, Inc. Chap 15-21 p Chart Control Limits Average Group Size Average Proportion of Nonconforming Items # Defective Items in Sample i Size of Sample i # of Samples

22. © 2002 Prentice-Hall, Inc. Chap 15-22 p Chart Example You’re manager of a 500-room hotel. You want to achieve the highest level of service. For seven days, you collect data on the readiness of 200 rooms. Is the process in control?

23. © 2002 Prentice-Hall, Inc. Chap 15-23 p Chart Hotel Data # Not Day# RoomsReadyProportion 1200160.080 2200 70.035 3200210.105 4200170.085 5200250.125 6200190.095 7200160.080

24. © 2002 Prentice-Hall, Inc. Chap 15-24 p Chart Control Limits Solution 16 + 7 +...+ 16

25. © 2002 Prentice-Hall, Inc. Chap 15-25 Mean p Chart Control Chart Solution UCL LCL 0.00 0.05 0.10 0.15 1234567 P Day Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.

26. © 2002 Prentice-Hall, Inc. Chap 15-26 p Chart in PHStat PHStat | control charts | p chart … Excel spreadsheet for the hotel room example

27. © 2002 Prentice-Hall, Inc. Chap 15-27 WorkerDay 1 Day 2 Day 3All Days A 9 (18%)11 (12%) 6 (12%) 26 (17.33%) B 12 (24%)12 (24%) 8 (16%) 32 (21.33%) C 13 (26%) 6 (12%) 12 (24%) 31(20.67%) D 7 (14%) 9 (18%) 8 (16%) 24 (16.0%) Totals 41 38 34 113 Understanding Process Variability: Red Bead Example Four Workers (A, B, C, D) spent three days to collect beads, at 50 beads per day. The expected number of red bead to be collected per day per worker is 10 or 20%.

28. © 2002 Prentice-Hall, Inc. Chap 15-28 AverageDay 1Day 2Day 3All Days X10.259.58.5 9.42 p20.5%19%17% 18.83% Understanding Process Variability: Example Calculations _

29. © 2002 Prentice-Hall, Inc. Chap 15-29 0 A 1 B 1 C 1 D 1 A 2 B 2 C 2 D 2 A 3 B 3 C 3 D 3 Understanding Process Variability: Example Control Chart.30.20.10 p UCL LCL _

30. © 2002 Prentice-Hall, Inc. Chap 15-30 Morals of the Example 1.Variation is an inherent part of any process. 2.The system is primarily responsible for worker performance. 3.Only management can change the system. 4.Some workers will always be above average, and some will be below.

31. © 2002 Prentice-Hall, Inc. Chap 15-31 The c Chart Control chart for number of nonconformities (occurrences) in a unit (an area of opportunity) Is an attribute chart Shows total number of nonconforming items in a unit e.g.: Count number of defective chairs manufactured per day Assume that the size of each subgroup unit remains constant

32. © 2002 Prentice-Hall, Inc. Chap 15-32 c Chart Control Limits Average Number of Occurrences # of Samples # of occurrences in sample i

33. © 2002 Prentice-Hall, Inc. Chap 15-33 c Chart: Example You’re manager of a 500-room hotel. You want to achieve the highest level of service. For seven days, you collect data on the readiness of 200 rooms. Is the process in control?

34. © 2002 Prentice-Hall, Inc. Chap 15-34 c Chart: Hotel Data # Not Day# RoomsReady 120016 2200 7 320021 420017 520025 620019 720016

35. © 2002 Prentice-Hall, Inc. Chap 15-35 c Chart: Control Limits Solution

36. © 2002 Prentice-Hall, Inc. Chap 15-36 c Chart: Control Chart Solution UCL LCL 0 10 20 30 1234567 c Day Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.

37. © 2002 Prentice-Hall, Inc. Chap 15-37 Variable Control Charts: R Chart Monitors variability in process Characteristic of interest is measured on numerical scale Is a variables control chart Shows sample range over time Difference between smallest and largest values in inspection sample e.g.: Amount of time required for luggage to be delivered to hotel room

38. © 2002 Prentice-Hall, Inc. Chap 15-38 R Chart Control Limits Sample Range at Time i or subgroup i # Samples From Table

39. © 2002 Prentice-Hall, Inc. Chap 15-39 R Chart Example You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?

40. © 2002 Prentice-Hall, Inc. Chap 15-40 R Chart and Mean Chart Hotel Data SampleSample DayAverageRange 15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

41. © 2002 Prentice-Hall, Inc. Chap 15-41 R Chart Control Limits Solution From Table E.11 (n = 5)

42. © 2002 Prentice-Hall, Inc. Chap 15-42 R Chart Control Chart Solution UCL 0 2 4 6 8 1234567 Minutes Day LCL R _

43. © 2002 Prentice-Hall, Inc. Chap 15-43 Variables Control Charts: Mean Chart (The Chart) Shows sample mean over time Compute mean of inspection sample over time e.g.: Average luggage delivery time in hotel Monitors process average Must be preceded by examination of the R chart to make sure that the process is in- control

44. © 2002 Prentice-Hall, Inc. Chap 15-44 Mean Chart Sample Range at Time i # Samples Sample Mean at Time i Computed From Table

45. © 2002 Prentice-Hall, Inc. Chap 15-45 Mean Chart Example You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For seven days, you collect data on five deliveries per day. Is the process in control?

46. © 2002 Prentice-Hall, Inc. Chap 15-46 R Chart and Mean Chart Hotel Data SampleSample DayAverageRange 15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

47. © 2002 Prentice-Hall, Inc. Chap 15-47 Mean Chart Control Limits Solution From Table E.9 (n = 5)

48. © 2002 Prentice-Hall, Inc. Chap 15-48 Mean Chart Control Chart Solution UCL LCL 0 2 4 6 8 1234567 Minutes Day X _ _

49. © 2002 Prentice-Hall, Inc. Chap 15-49 R Chart and Mean Chart in PHStat PHStat | control charts | R & Xbar charts … Excel spreadsheet for the hotel room example

50. © 2002 Prentice-Hall, Inc. Chap 15-50 Process Capability Process capability is the ability of a process to consistently meet specified customer-driven requirement Specification limits are set by management in response to customers’ expectations The upper specification limit (USL) is the largest value that can be obtained and still conform to customers’ expectations The lower specification limit (LSL) is the smallest value that is still conforming

51. © 2002 Prentice-Hall, Inc. Chap 15-51 Estimating Process Capability Must first have an in-control process Estimate the percentage of product or service within specification Assume the population of X values is approximately normally distributed with mean estimated by and standard deviation estimated by

52. © 2002 Prentice-Hall, Inc. Chap 15-52 Estimating Process Capability For a characteristic with an LSL and a USL Where Z is a standardized normal random variable (continued)

53. © 2002 Prentice-Hall, Inc. Chap 15-53 Estimating Process Capability For a characteristic with only a LSL Where Z is a standardized normal random variable (continued)

54. © 2002 Prentice-Hall, Inc. Chap 15-54 Estimating Process Capability For a characteristic with only a USL Where Z is a standardized normal random variable (continued)

55. © 2002 Prentice-Hall, Inc. Chap 15-55 You’re manager of a 500-room hotel. You have instituted a policy that 99% of all luggage deliveries must be completed within ten minutes or less. For seven days, you collect data on five deliveries per day. Is the process capable? Process Capability Example

56. © 2002 Prentice-Hall, Inc. Chap 15-56 Process Capability: Hotel Data SampleSample DayAverageRange 15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

57. © 2002 Prentice-Hall, Inc. Chap 15-57 Process Capability: Hotel Example Solution Therefore, we estimate that 99.38% of the luggage deliveries will be made within the ten minutes or less specification. The process is capable of meeting the 99% goal.

58. © 2002 Prentice-Hall, Inc. Chap 15-58 Capability Indices Aggregate measures of a process’s ability to meet specification limits. The larger (>1) the values, the more capable a process is of meeting requirements Measure of process potential performance C p >1 implies a process has the potential of having more than 99.73% of outcomes within specifications

59. © 2002 Prentice-Hall, Inc. Chap 15-59 Capability Indices Measures of actual process performance For one-sided specification limits CPL (CPU) >1 implies that the process mean is more than 3 standard deviation away from the lower (upper) specification limit (continued)

60. © 2002 Prentice-Hall, Inc. Chap 15-60 Capability Indices For two-sided specification limits C pk = 1 indicates that the process average is 3 standard deviation away from the closest specification limit. Larger C pk indicates larger capability of meeting the requirements (continued)

61. © 2002 Prentice-Hall, Inc. Chap 15-61 You’re manager of a 500- room hotel. You have instituted a policy that all luggage deliveries must be completed within ten minutes or less. For seven days, you collect data on five deliveries per day. Compute an appropriate capability index for the delivery process. Process Capability Example

62. © 2002 Prentice-Hall, Inc. Chap 15-62 Process Capability: Hotel Data SampleSample DayAverageRange 15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

63. © 2002 Prentice-Hall, Inc. Chap 15-63 Process Capability: Hotel Example Solution Since there is only the upper specification limit, we need to only compute CPU. The capability index for the luggage delivery process is.8337, which is less than 1. The upper specification limit is less than 3 standard deviation above the mean.

64. © 2002 Prentice-Hall, Inc. Chap 15-64 Chapter Summary Described total quality management (TQM) Addressed the theory of process management Deming’s fourteen points Discussed the theory of control charts Common cause variation vs. special cause variation

65. © 2002 Prentice-Hall, Inc. Chap 15-65 Chapter Summary Computed control charts for the proportion of nonconforming items Described process variability Described c chart Computed control charts for the mean and the range Discussed process capability (continued)