© 2003 Prentice-Hall, Inc.Chap 13-1 Business Statistics: A First Course (3 rd Edition) Chapter 13 Statistical Applications in Quality and Productivity Management

© 2003 Prentice-Hall, Inc. Chap 13-2 Chapter Topics Total Quality Management (TQM) Theory of Management (Deming’s Fourteen Points) The Theory of Control Charts Common-cause variation versus special-cause variation Control Charts for the Proportion of Nonconforming Items

© 2003 Prentice-Hall, Inc. Chap 13-3 Chapter Topics Process Variability Control Charts for the Mean and the Range (continued)

© 2003 Prentice-Hall, Inc. Chap 13-4 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. Organization Transformation Necessary 6. Remove Fear 7. Higher Quality Costs Less

© 2003 Prentice-Hall, Inc. Chap 13-5 Deming’s 14 Points: Point 1: Plan Do Study Act Point 1. Create Constancy of Purpose The Shewhart-Deming Cycle Focuses on Constant Improvement

© 2003 Prentice-Hall, Inc. Chap 13-6 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. Chap 13-7 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

© 2003 Prentice-Hall, Inc. Chap 13-8 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.

© 2003 Prentice-Hall, Inc. Chap 13-9 Points 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

© 2003 Prentice-Hall, Inc. Chap 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 Quality is important

© 2003 Prentice-Hall, Inc. Chap 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

© 2003 Prentice-Hall, Inc. Chap 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)

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

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

© 2003 Prentice-Hall, Inc. Chap 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

© 2003 Prentice-Hall, Inc. Chap 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

© 2003 Prentice-Hall, Inc. Chap 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 (or decreasing)

© 2003 Prentice-Hall, Inc. Chap Out-of-control Processes If the Control Chart Indicates an Out-of- Control Condition (a Point Outside the Control Limits or Exhibiting Trend), then Both common causes of variation and assignable causes of variation exist 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

© 2003 Prentice-Hall, Inc. Chap In-control Process If the Control Chart is not Indicating Any Out- of-Control Condition, then Only common causes of variation exists 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

© 2003 Prentice-Hall, Inc. Chap 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

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

© 2003 Prentice-Hall, Inc. Chap 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. Chap p Chart Hotel Data # Not Day# RoomsReadyProportion

© 2003 Prentice-Hall, Inc. Chap p Chart Control Limits Solution

© 2003 Prentice-Hall, Inc. Chap Mean p Chart Control Chart Solution UCL LCL 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.

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

© 2003 Prentice-Hall, Inc. Chap 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 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%.

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

© 2003 Prentice-Hall, Inc. Chap 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 p UCL LCL _

© 2003 Prentice-Hall, Inc. Chap 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. Chap 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

© 2003 Prentice-Hall, Inc. Chap R Chart Control Limits Sample Range at Time i or subgroup i # Samples From Table E.9

© 2003 Prentice-Hall, Inc. Chap 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. Chap R Chart and Mean Chart Hotel Data SampleSample DayAverageRange

© 2003 Prentice-Hall, Inc. Chap R Chart Control Limits Solution From Table E.9 (n = 5)

© 2003 Prentice-Hall, Inc. Chap R Chart Control Chart Solution UCL Minutes Day LCL R _

© 2003 Prentice-Hall, Inc. Chap 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

© 2003 Prentice-Hall, Inc. Chap Mean Chart Sample Range at Time i # Samples Sample Mean at Time i Computed From Table E.9

© 2003 Prentice-Hall, Inc. Chap 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. Chap R Chart and Mean Chart Hotel Data SampleSample DayAverageRange

© 2003 Prentice-Hall, Inc. Chap Mean Chart Control Limits Solution From Table E.9 (n = 5)

© 2003 Prentice-Hall, Inc. Chap Mean Chart Control Chart Solution UCL LCL Minutes Day X _ _

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

© 2003 Prentice-Hall, Inc. Chap Chapter Summary Described Total Quality Management (TQM) Addressed the Theory of Management Deming’s fourteen points Discussed the Theory of Control Charts Common-cause variation versus special-cause variation

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