Business Statistics A First Course 3 rd Edition
Business Statistics: A First Course (3 rd Edition) Chapter 13 Statistical Applications in Quality and Productivity Management © 2003 Prentice-Hall, Inc. Chap 13 -1
Chapter Topics n n n Total Quality Management (TQM) Theory of Management (Deming’s Fourteen Points) Theory of Control Charts n n Common-cause variation versus special-cause variation Control Charts for the Proportion of Nonconforming Items © 2003 Prentice-Hall, Inc. 2
Chapter Topics (continued) n Process Variability n Control Charts for the Mean and the Range © 2003 Prentice-Hall, Inc. 3
Themes of Quality Management 1. 2. 3. 4. 5. 6. 7. Primary Focus on Process Improvement Most Variation in Process due to System Teamwork is Integral to Quality Management Customer Satisfaction is a Primary Goal Organization Transformation Necessary Remove Fear Higher Quality Costs Less © 2003 Prentice-Hall, Inc. 4
Deming’s 14 Points: Point 1. Create Constancy of Purpose Act Plan Study Do The Shewhart-Deming Cycle Focuses on Constant Improvement © 2003 Prentice-Hall, Inc. 5
Deming’s 14 Points: Points 2 and 3 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. © 2003 Prentice-Hall, Inc. 6
Deming’s 14 Points: Points 4 and 5 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. © 2003 Prentice-Hall, Inc. 7
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. © 2003 Prentice-Hall, Inc. 8
Deming’s 14 Points: Points 8 to 12 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 © 2003 Prentice-Hall, Inc. 300 9
Deming’s 14 Points: Points 13 and 14 Point 13. Encourage Education and Self-Improvement for Everyone is important Quality Improved knowledge of people will improve assets of organization. Point 14. Take Action to Accomplish Transformation Continually strive toward improvement. © 2003 Prentice-Hall, Inc. 10
Control Charts n Monitors Variation in Data n n Exhibits trend - make correction before process is out of control A Process -- A Repeatable Series of Steps Leading to A Specific Goal © 2003 Prentice-Hall, Inc. 11
Control Charts n (continued) Show when Changes in Data are Due to: n Special or assignable causes n n Fluctuations not inherent to a process Represents problems to be corrected Data outside control limits or trend Chance or common causes n n © 2003 Prentice-Hall, Inc. Inherent random variations Consist of numerous small causes of random variability 12
Process Control Chart Graph of sample data plotted over time Special Cause Variation UCL Mean LCL Process Average Common Cause Variation © 2003 Prentice-Hall, Inc. 13
Control Limits UCL = Process Average + 3 Standard Deviations LCL = Process Average - 3 Standard Deviations X UCL + 3 Process Average - 3 LCL TIME © 2003 Prentice-Hall, Inc. 14
Types of Error n First Type: n n Belief that observed value represents special cause when in fact it is due to common cause Second Type: n Treating special cause variation as if it is common cause variation © 2003 Prentice-Hall, Inc. 15
Comparing Control Chart Patterns X X Common Cause Variation: No Points Outside Control Limits © 2003 Prentice-Hall, Inc. X Special Cause Variation: 2 Points Outside Control Limits Downward Pattern: No Points Outside Control Limits but Trend Exists 16
When to Take Corrective Action n Corrective Action should be Taken when Observing Points Outside the Control Limits or when a Trend has been Detected n n Eight consecutive points above the center line (or eight below) Eight consecutive points that are increasing (or decreasing) © 2003 Prentice-Hall, Inc. 17
Out-of-control Processes n If the Control Chart Indicates an Out-of. Control Condition (a Point Outside the Control Limits or Exhibiting Trend), then n n Both common causes of variation and assignable causes of variation exist The assignable causes of variation must be identified n n © 2003 Prentice-Hall, Inc. If detrimental to the quality, assignable causes of variation must be removed If increases quality, assignable causes must be incorporated into the process design 18
In-control Process n If the Control Chart is not Indicating Any Outof-Control Condition, then n n Only common causes of variation exists It is sometimes said to be in a state of statistical control n n © 2003 Prentice-Hall, Inc. 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 19
p Chart n Control Chart for Proportions n n Is an attribute chart Shows Proportion of Nonconforming (success ) Items n e. g. , Count # of nonconforming chairs & divide by total chairs inspected n n Chair is either conforming or nonconforming Used with Equal or Unequal Sample Sizes Over Time n © 2003 Prentice-Hall, Inc. Unequal sizes should not differ by more than ± 25% from average sample size 20
p Chart Control Limits Average Group Size # of Samples © 2003 Prentice-Hall, Inc. Average Proportion of Nonconforming Items # Defective Items in Sample i Size of Sample i 21
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? © 2003 Prentice-Hall, Inc. 22
p Chart Hotel Data # Not Day # Rooms Ready 1 200 16 0. 080 2 200 7 0. 035 3 200 21 0. 105 4 200 17 0. 085 5 200 25 0. 125 6 200 19 0. 095 7 200 16 0. 080 © 2003 Prentice-Hall, Inc. Proportion 23
p Chart Control Limits Solution 16 + 7 +. . . + 16 © 2003 Prentice-Hall, Inc. 24
p Chart Control Chart Solution 0. 15 P UCL 0. 10 Mean 0. 05 LCL 0. 00 1 2 3 4 Day 5 6 7 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. © 2003 Prentice-Hall, Inc. 25
p Chart in PHStat n n PHStat | Control Charts | p Chart … Excel Spreadsheet for the Hotel Room Example © 2003 Prentice-Hall, Inc. 26
Understanding Process Variability: Red Bead Example Four Workers (A, B, C, D) spent 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%. Worker Day 1 Day 2 Day 3 All Days A 9 (18%) 11 (12%) 6 (12%) 26 (17. 33%) B 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 © 2003 Prentice-Hall, Inc. 41 38 34 113 27
Understanding Process Variability: Example Calculations Average Day 1 Day 2 Day 3 X 10. 25 9. 5 8. 5 9. 42 p 20. 5% 19% 17% 18. 83% _ © 2003 Prentice-Hall, Inc. All Days 28
Understanding Process Variability: Example Control Chart UCL. 30 _ p . 20. 10 LCL 0 A 1 © 2003 Prentice-Hall, Inc. B 1 C 1 D 1 A 2 B 2 C 2 D 2 A 3 B 3 C 3 D 3 29
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. © 2003 Prentice-Hall, Inc. 30
Variables Control Charts: R Chart n Monitors Variability in Process n n n Characteristic of interest is measured on numerical scale Is a variables control chart Shows Sample Range Over Time n n Difference between smallest & largest values in inspection sample e. g. , Amount of time required for luggage to be delivered to hotel room © 2003 Prentice-Hall, Inc. 31
R Chart Control Limits From Table E. 9 Sample Range at Time i or subgroup i # Samples © 2003 Prentice-Hall, Inc. 32
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? © 2003 Prentice-Hall, Inc. 33
R Chart and Mean Chart Hotel Data Sample Day Average Range 1 5. 32 3. 85 2 6. 59 4. 27 3 4. 88 3. 28 4 5. 70 2. 99 5 4. 07 3. 61 6 7. 34 5. 04 7 6. 79 4. 22 © 2003 Prentice-Hall, Inc. 34
R Chart Control Limits Solution From Table E. 9 (n = 5) © 2003 Prentice-Hall, Inc. 35
R Chart Control Chart Solution Minutes 8 6 4 2 0 1 2 © 2003 Prentice-Hall, Inc. UCL _ R LCL 3 4 Day 5 6 7 36
Variables Control Charts: Mean Chart (The Chart) n Shows Sample Means Over Time n n n Compute mean of inspection sample over time e. g. , Average luggage delivery time in hotel Monitors Process Average n Must be preceded by examination of the R chart to make sure that the process is in-control © 2003 Prentice-Hall, Inc. 37
Mean Chart Computed From Table E. 9 Sample Mean at Time i Sample Range at Time i # Samples © 2003 Prentice-Hall, Inc. 38
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? © 2003 Prentice-Hall, Inc. 39
R Chart and Mean Chart Hotel Data Sample Day Average Range 1 5. 32 3. 85 2 6. 59 4. 27 3 4. 88 3. 28 4 5. 70 2. 99 5 4. 07 3. 61 6 7. 34 5. 04 7 6. 79 4. 22 © 2003 Prentice-Hall, Inc. 40
Mean Chart Control Limits Solution From Table E. 9 (n = 5) © 2003 Prentice-Hall, Inc. 41
Mean Chart Control Chart Solution Minutes 8 6 4 2 0 1 2 © 2003 Prentice-Hall, Inc. UCL __ X LCL 3 4 Day 5 6 7 42
R Chart and Mean Chart in PHStat n n PHStat | Control Charts | R & Xbar Charts … Excel Spreadsheet for The Hotel Room Example © 2003 Prentice-Hall, Inc. 43
Chapter Summary n n Described Total Quality Management (TQM) Addressed the Theory of Management n n Deming’s fourteen points Discussed the Theory of Control Charts n Common-cause variation versus special-cause variation © 2003 Prentice-Hall, Inc. 44
Chapter Summary n n n (continued) Computed Control Charts for the Proportion of Nonconforming Items Described Process Variability Computed Control Charts for the Mean and the Range © 2003 Prentice-Hall, Inc. 45
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