1. © 2004 Prentice-Hall, Inc. Basic Business Statistics (9 th Edition) Chapter 18 Statistical Applications in Quality and Productivity Management Chap 18-1

2. © 2004 Prentice-Hall, Inc. Chap 18-2 Chapter Topics Total Quality Management (TQM) Theory of Management (Deming’s Fourteen Points) Six Sigma ® Management Approach The Theory of Control Charts Common-cause variation versus special-cause variation Control Charts for the Proportion of Nonconforming Items

3. © 2004 Prentice-Hall, Inc. Chap 18-3 Chapter Topics Process Variability The c Chart Control Charts for the Mean and the Range Process Capability (continued)

4. © 2004 Prentice-Hall, Inc. Chap 18-4 Themes of Quality Management 1. Primary Focus on Process Improvement 2. Most Variation in Process Due to System 3. Teamwork is Integral to Quality Management 4. Customer Satisfaction is a Primary Goal 5. Organizational Transformation Necessary 6. Remove Fear 7. Higher Quality Costs Less

5. © 2004 Prentice-Hall, Inc. Chap 18-5 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. © 2004 Prentice-Hall, Inc. Chap 18-6 Point 2. Adopt New Philosophy Better to be proactive and change before crisis occurs. Point 3. Cease Dependence on Mass Inspection to Achieve Quality Any inspection whose purpose is to improve quality is too late. Deming’s 14 Points: Points 2 and 3

7. © 2004 Prentice-Hall, Inc. Chap 18-7 Point 4. End the Practice of Awarding Business on the Basis of Price Tag Alone Develop 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. © 2004 Prentice-Hall, Inc. Chap 18-8 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. © 2004 Prentice-Hall, Inc. Chap 18-9 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 12 300

10. © 2004 Prentice-Hall, Inc. Chap 18-10 Point 13. Encourage Education and Self-Improvement for Everyone Improved knowledge of people will improve the assets of the organization. Point 14. Take Action to Accomplish Transformation Continually strive toward improvement. Deming’s 14 Points: Points 13 and 14 Quality is important

11. © 2004 Prentice-Hall, Inc. Chap 18-11 Six Sigma ® Management A Managerial Approach Designed to Create Processes that Result in No More Than 3.4 Defects Per Million A Method for Breaking Processes into a Series of Steps in Order to Eliminate Defects and Produce Near Perfect Results Define: (1) Define: Define the problem along with costs, benefits and the impact on customers Measure (2) Measure: Develop operational definitions for each Critical-to-Quality characteristic and verify measurement procedure to achieve consistency over repeated measurements

12. © 2004 Prentice-Hall, Inc. Chap 18-12 Six Sigma ® Management Analyze (3) Analyze: Use control charts to monitor defects and determine the root causes of defects Improve (4) Improve: Study the importance of each process variable on the Critical-to-Quality characteristic to determine and maintain the best level for each variable in the long term Control (5) Control: Avoid potential problems that occur when a process is changed and maintain the gains that have been made in the long term (continued)

13. © 2004 Prentice-Hall, Inc. Chap 18-13 Control Charts Monitor Variation in Data Exhibit trend - make correction before process is out of control A Process - A Repeatable Series of Steps Leading to a Specific Goal

14. © 2004 Prentice-Hall, Inc. Chap 18-14 Control Charts Show When Changes in Data are Due to: Special or assignable causes Fluctuations not inherent to a process Represent 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)

15. © 2004 Prentice-Hall, Inc. Chap 18-15 Graph of sample data plotted over time Process Control Chart Special Cause Variation Common Cause Variation Process Average  Mean UCL LCL

16. © 2004 Prentice-Hall, Inc. Chap 18-16 Control Limits UCL = Process Average + 3 Standard Deviations LCL = Process Average - 3 Standard Deviations Process Average UCL LCL X + 3  - 3  TIME

17. © 2004 Prentice-Hall, Inc. Chap 18-17 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

18. © 2004 Prentice-Hall, Inc. Chap 18-18 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

19. © 2004 Prentice-Hall, Inc. Chap 18-19 When to Take Corrective Action Corrective Action Should Be Taken When Observing 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)

20. © 2004 Prentice-Hall, Inc. Chap 18-20 Out-of-Control Processes If 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 quality, assignable causes of variation must be removed If increases quality, assignable causes must be incorporated into the process design

21. © 2004 Prentice-Hall, Inc. Chap 18-21 In-Control Process If the Control Chart is Not Indicating Any Out- of-Control Condition, then Only common causes of variation exist It is sometimes said to be in a state of statistical control If the common-cause variation is small, then control chart can be used to monitor the process If the common-cause variation is too large, the process needs to be altered

22. © 2004 Prentice-Hall, Inc. Chap 18-22 p Chart Control Chart for Proportions attribute chart Is an attribute chart Shows Proportion of Nonconforming Items E.g., Count # of nonconforming chairs & divide by total chairs inspected Chair is either conforming or nonconforming Used with Equal or Unequal Sample Sizes Over Time Unequal sizes should not differ by more than ±25% from average sample size

23. © 2004 Prentice-Hall, Inc. Chap 18-23 p Chart Control Limits Average Group Size Average Proportion of Nonconforming Items # Defective Items in Sample i Size of Sample i # of Samples

24. © 2004 Prentice-Hall, Inc. Chap 18-24 p Chart Example You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?

25. © 2004 Prentice-Hall, Inc. Chap 18-25 p Chart Hotel Data # Not Day# RoomsReadyProportion 1200160.080 2200 70.035 3200210.105 4200170.085 5200250.125 6200190.095 7200160.080

26. © 2004 Prentice-Hall, Inc. Chap 18-26 p Chart Control Limits Solution 16 + 7 +...+ 16

27. © 2004 Prentice-Hall, Inc. Chap 18-27 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.

28. © 2004 Prentice-Hall, Inc. Chap 18-28 p Chart in PHStat PHStat | Control Charts | p Chart … Excel Spreadsheet for the Hotel Room Example

29. © 2004 Prentice-Hall, Inc. Chap 18-29 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) spend 3 days to collect beads, at 50 beads per day. The expected number of red beads to be collected per day per worker is 10 or 20%.

30. © 2004 Prentice-Hall, Inc. Chap 18-30 AverageDay 1Day 2Day 3All Days X10.259.58.5 9.42 p20.5%19%17% 18.83% Understanding Process Variability: Example Calculations _

31. © 2004 Prentice-Hall, Inc. Chap 18-31 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 _

32. © 2004 Prentice-Hall, Inc. Chap 18-32 Morals of the Example Variation is an inherent part of any process. The system is primarily responsible for worker performance. Only management can change the system. Some workers will always be above average, and some will be below.

33. © 2004 Prentice-Hall, Inc. Chap 18-33 The c Chart Control Chart for Number of Nonconformities (Occurrences) in a Unit (an Area of Opportunity) attribute chart Is an attribute chart Shows Total Number of Nonconforming Items in a Unit E.g., Count # of defective chairs manufactured per day Assume that the Size of Each Subgroup Unit Remains Constant

34. © 2004 Prentice-Hall, Inc. Chap 18-34 c Chart Control Limits Average Number of Occurrences # of Samples # of Occurrences in Sample i

35. © 2004 Prentice-Hall, Inc. Chap 18-35 c Chart: Example You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?

36. © 2004 Prentice-Hall, Inc. Chap 18-36 c Chart: Hotel Data # Not Day# RoomsReady 120016 2200 7 320021 420017 520025 620019 720016

37. © 2004 Prentice-Hall, Inc. Chap 18-37 c Chart: Control Limits Solution

38. © 2004 Prentice-Hall, Inc. Chap 18-38 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.

39. © 2004 Prentice-Hall, Inc. Chap 18-39 Variables Control Charts: R Chart Monitors Variability in Process Characteristic of interest is measured on numerical scale variables control chart Is a variables control chart Shows Sample Range Over Time Difference between smallest & largest values in inspection sample E.g., Amount of time required for luggage to be delivered to hotel room

40. © 2004 Prentice-Hall, Inc. Chap 18-40 R Chart Control Limits Sample Range at Time i or Sample i # Samples From Table

41. © 2004 Prentice-Hall, Inc. Chap 18-41 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?

42. © 2004 Prentice-Hall, Inc. Chap 18-42 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

43. © 2004 Prentice-Hall, Inc. Chap 18-43 R Chart Control Limits Solution From Table (n = 5)

44. © 2004 Prentice-Hall, Inc. Chap 18-44 R Chart Control Chart Solution UCL 0 2 4 6 8 1234567 Minutes Day LCL R _

45. © 2004 Prentice-Hall, Inc. Chap 18-45 Variables Control Charts: Mean Chart (The Chart) Shows Sample Means 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

46. © 2004 Prentice-Hall, Inc. Chap 18-46 Mean Chart Sample Range at Time i # Samples Sample Mean at Time i Computed From Table

47. © 2004 Prentice-Hall, Inc. Chap 18-47 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 7 days, you collect data on 5 deliveries per day. Is the process in control?

48. © 2004 Prentice-Hall, Inc. Chap 18-48 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

49. © 2004 Prentice-Hall, Inc. Chap 18-49 Mean Chart Control Limits Solution From Table E.9 (n = 5)

50. © 2004 Prentice-Hall, Inc. Chap 18-50 Mean Chart Control Chart Solution UCL LCL 0 2 4 6 8 1234567 Minutes Day X _ _

51. © 2004 Prentice-Hall, Inc. Chap 18-51 R Chart and Mean Chart in PHStat PHStat | Control Charts | R & Xbar Charts … Excel Spreadsheet for the Hotel Room Example

52. © 2004 Prentice-Hall, Inc. Chap 18-52 Process Capability Process Capability is the Ability of a Process to Consistently Meet Specified Customer-Driven Requirements Specification Limits are Set by Management in Response to Customer’s Expectations The Upper Specification Limit (USL) is the Largest Value that Can Be Obtained and Still Conform to Customer’s Expectation The Lower Specification Limit (LSL) is the Smallest Value that is Still Conforming

53. © 2004 Prentice-Hall, Inc. Chap 18-53 Estimating Process Capability Must Have an In-Control Process First 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

54. © 2004 Prentice-Hall, Inc. Chap 18-54 Estimating Process Capability For a Characteristic with an LSL and a USL where Z is a standardized normal random variable (continued)

55. © 2004 Prentice-Hall, Inc. Chap 18-55 Estimating Process Capability For a Characteristic with Only a LSL where Z is a standardized normal random variable (continued)

56. © 2004 Prentice-Hall, Inc. Chap 18-56 Estimating Process Capability For a Characteristic with Only a USL where Z is a standardized normal random variable (continued)

57. © 2004 Prentice-Hall, Inc. Chap 18-57 You’re manager of a 500- room hotel. You have instituted a policy that 99% of all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day. Is the process capable? Process Capability Example

58. © 2004 Prentice-Hall, Inc. Chap 18-58 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

59. © 2004 Prentice-Hall, Inc. Chap 18-59 Process Capability: Hotel Example Solution Therefore, we estimate that 99.38% of the luggage deliveries will be made within the 10 minutes or less specification. The process is capable of meeting the 99% goal.

60. © 2004 Prentice-Hall, Inc. Chap 18-60 Capability Indices Aggregate Measures of a Process’ 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 that a process has the potential of having more than 99.73% of outcomes within specifications

61. © 2004 Prentice-Hall, Inc. Chap 18-61 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 deviations away from the lower (upper) specification limit (continued)

62. © 2004 Prentice-Hall, Inc. Chap 18-62 Capability Indices For two-sided specification limits C pk = 1 indicates that the process average is 3 standard deviations away from the closest specification limit Larger C pk indicates larger capability of meeting the requirements (continued)

63. © 2004 Prentice-Hall, Inc. Chap 18-63 You’re manager of a 500- room hotel. You have instituted a policy that all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day. Compute an appropriate capability index for the delivery process. Process Capability Example

64. © 2004 Prentice-Hall, Inc. Chap 18-64 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

65. © 2004 Prentice-Hall, Inc. Chap 18-65 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 deviations above the mean.

66. © 2004 Prentice-Hall, Inc. Chap 18-66 Chapter Summary Described Total Quality Management (TQM) Addressed the Theory of Management Deming’s 14 Points Described the Six Sigma ® Management Approach Discussed the Theory of Control Charts Common-cause variation versus special-cause variation

67. © 2004 Prentice-Hall, Inc. Chap 18-67 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)