1. © 2003 Prentice-Hall, Inc. Quantitative Analysis Chapter 17 Statistical Quality Control Chap 17-1

2. © 2003 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. © 2003 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. © 2003 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. © 2003 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. © 2003 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. © 2003 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. © 2003 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. © 2003 Prentice-Hall, Inc. Chap 18-9 Points 8-12. Drive Out Fear Break Down Barriers between Staff Areas Eliminate Slogans Eliminate Numerical Quotas for Workforce and Numerical Goals for Management Remove Barriers to Pride of Workmanship Deming’s 14 Points: Points 8 to 12 300

10. © 2003 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. © 2003 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. © 2003 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. © 2003 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. © 2003 Prentice-Hall, Inc. Chap 18-14 Characteristics for which you focus on defects Classify products as either ‘good’ or ‘bad’, or count # defects e.g., radio works or not Categorical or discrete random variables Attributes Variables Quality Characteristics Characteristics that you measure, e.g., weight, length May be in whole or in fractional numbers Continuous random variables

15. © 2003 Prentice-Hall, Inc. Chap 18-15 Statistical technique used to ensure process is making product to standard All process are subject to variability Common (or Natural) causes: Random variations Special (or Assignable) causes: Correctable problems Machine wear, unskilled workers, poor material Objective: Identify assignable causes Uses process control charts Statistical Process Control (SPC)

16. © 2003 Prentice-Hall, Inc. Chap 18-16 Graph of sample data plotted over time Process Control Chart Special Cause Variation Common Cause Variation Process Average  Mean UCL LCL

17. © 2003 Prentice-Hall, Inc. Chap 18-17 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 Common causes (or Natural Causes) Inherent random variations Consist of numerous small causes of random variability (continued)

18. © 2003 Prentice-Hall, Inc. Chap 18-18 Control Limits UCL = Process Average + 3 Standard Deviations LCL = Process Average - 3 Standard Deviations Process Average UCL LCL X + 3  - 3  TIME

19. © 2003 Prentice-Hall, Inc. Chap 18-19 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

20. © 2003 Prentice-Hall, Inc. Chap 18-20 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

21. © 2003 Prentice-Hall, Inc. Chap 18-21 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

22. © 2003 Prentice-Hall, Inc. Chap 18-22 Control Chart Patterns: How to tell the Process is Out of Control Upper control chart limit Target Lower control chart limit Normal behavior.One point out above. Investigate for cause. One point out below. Investigate for cause.

23. © 2003 Prentice-Hall, Inc. Chap 18-23 Control Chart Patterns: How to tell the Process is Out of Control (Cont.) Upper control limit Target Lower control limit Run of 5 points below central line. Investigate for cause. Trends in either Direction. Investigate for cause of progressive change. Erratic behavior. Investigate.

24. © 2003 Prentice-Hall, Inc. Chap 18-24 Control Chart Patterns: How to tell the Process is Out of Control cont. Upper control chart limit Target Lower control chart limit Two points near upper control. Investigate for cause. Two points near lower control. Investigate for cause. Run of 5 points above central line. Investigate for cause.

25. © 2003 Prentice-Hall, Inc. Chap 18-25 Produce Good Provide Service Stop Process Yes No Assign. Causes? Take Sample Inspect Sample Find Out Why Create Control Chart Start Statistical Process Control Steps

26. © 2003 Prentice-Hall, Inc. Chap 18-26 4 Basic Types of Control Charts What is the difference between Variables and Attributes?

27. © 2003 Prentice-Hall, Inc. Chap 18-27 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

28. © 2003 Prentice-Hall, Inc. Chap 18-28 R Chart Control Limits Sample Range at Time i or Subgroup i # Samples From Table 17.2 Page 683

29. © 2003 Prentice-Hall, Inc. Chap 18-29 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?

30. © 2003 Prentice-Hall, Inc. Chap 18-30 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

31. © 2003 Prentice-Hall, Inc. Chap 18-31 R Chart Control Limits Solution From Table 17.2 page 683 (n = 5)

32. © 2003 Prentice-Hall, Inc. Chap 18-32 R Chart Control Chart Solution UCL 0 2 4 6 8 1234567 Minutes Day LCL R _

33. © 2003 Prentice-Hall, Inc. Chap 18-33 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

34. © 2003 Prentice-Hall, Inc. Chap 18-34 Mean Chart Sample Range at Time i # Samples Sample Mean at Time i Computed From Table 17.2 Page 683

35. © 2003 Prentice-Hall, Inc. Chap 18-35 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?

36. © 2003 Prentice-Hall, Inc. Chap 18-36 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

37. © 2003 Prentice-Hall, Inc. Chap 18-37 Mean Chart Control Limits Solution From Table 17.2 Page 683 (n = 5)

38. © 2003 Prentice-Hall, Inc. Chap 18-38 Mean Chart Control Chart Solution UCL LCL 0 2 4 6 8 1234567 Minutes Day X _ _

39. © 2003 Prentice-Hall, Inc. Chap 18-39 R Chart and Mean Chart in PHStat PHStat | Control Charts | R & Xbar Charts … Excel Spreadsheet for the Hotel Room Example

40. © 2003 Prentice-Hall, Inc. Chap 18-40 Examples 17.8 Monitor the performance of Refrigerators. Calculate Upper and Lower Control Limits for Average and Range. Overall average Temperature =46 o Fahrenheit Average Range is 2 o Fahrenheit Samples of 6 have been taken to get this data. (Samples Size, n= 6) 17.10 Monitor the Weight of Cereal in Boxes. Calculate Upper and Lower Control Limits for Average and Range. Overall average Weight = 17 grams Average Range is 0.5 grams Samples of 8 Boxes have been taken to get this data. (Samples Size, n= 8)

41. © 2003 Prentice-Hall, Inc. Chap 18-41 Do Example 17.5 Find UCL and LCL for Mean Chart and Range Chart. You need to Know: - 1. the Mean of the Sample Averages (Symbol__) 2.the Mean of the Range (Symbol ___) 3.the Sample Size (Symbol n)

42. © 2003 Prentice-Hall, Inc. Chap 18-42 Other Examples Do 17-12 for Homework

43. © 2003 Prentice-Hall, Inc. Chap 18-43 p Chart Control Chart for Proportions attribute chart Is an attribute chart Success Shows Proportion of Nonconforming (Success ) 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

44. © 2003 Prentice-Hall, Inc. Chap 18-44 p Chart Control Limits Average Group Size Average Proportion of Nonconforming Items # Defective Items in Sample i Size of Sample i # of Samples

45. © 2003 Prentice-Hall, Inc. Chap 18-45 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?

46. © 2003 Prentice-Hall, Inc. Chap 18-46 p Chart Hotel Data # Not Day# RoomsReadyProportion 1200160.080 2200 70.035 3200210.105 4200170.085 5200250.125 6200190.095 7200160.080

47. © 2003 Prentice-Hall, Inc. Chap 18-47 p Chart Control Limits Solution 16 + 7 +...+ 16

48. © 2003 Prentice-Hall, Inc. Chap 18-48 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.

49. © 2003 Prentice-Hall, Inc. Chap 18-49 p Chart in PHStat PHStat | Control Charts | p Chart … Excel Spreadsheet for the Hotel Room Example

50. © 2003 Prentice-Hall, Inc. Chap 18-50 Example The Delivery company wants to monitor its delivery service. Draw a p-chart. Does the process give an out of Control Signal? Control Chart Patterns: How to tell if the Process is Out of Control

51. © 2003 Prentice-Hall, Inc. Chap 18-51 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%.

52. © 2003 Prentice-Hall, Inc. Chap 18-52 AverageDay 1Day 2Day 3All Days X10.259.58.5 9.42 p20.5%19%17% 18.83% Understanding Process Variability: Example Calculations _

53. © 2003 Prentice-Hall, Inc. Chap 18-53 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 _

54. © 2003 Prentice-Hall, Inc. Chap 18-54 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.

55. © 2003 Prentice-Hall, Inc. Chap 18-55 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

56. © 2003 Prentice-Hall, Inc. Chap 18-56 c Chart Control Limits Average Number of Occurrences # of Samples # of Occurrences in Sample i

57. © 2003 Prentice-Hall, Inc. Chap 18-57 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?

58. © 2003 Prentice-Hall, Inc. Chap 18-58 c Chart: Hotel Data # Not Day# RoomsReady 120016 2200 7 320021 420017 520025 620019 720016

59. © 2003 Prentice-Hall, Inc. Chap 18-59 c Chart: Control Limits Solution

60. © 2003 Prentice-Hall, Inc. Chap 18-60 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.

61. © 2003 Prentice-Hall, Inc. Chap 18-61 Example 17.8 Number of small paint errors on each Ornaments. 1.Draw a c-chart. 2.Does the process give an out of Control Signal?

62. © 2003 Prentice-Hall, Inc. Chap 18-62 Example 17.8 (cont) The same exercise is repeated one week later. Number of small paint errors on each Ornaments are recorded as follows. 1.Draw a c-chart. 2.Does the process give an out of Control Signal? Control Chart Patterns: How to tell if the Process is Out of Control

63. © 2003 Prentice-Hall, Inc. Chap 18-63 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

64. © 2003 Prentice-Hall, Inc. Chap 18-64 Chapter Summary Computed Control Charts for the Mean and the Range Computed Control Charts for the Proportion of Nonconforming Items Described Process Variability Described c Chart (continued)