1. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter 17 Statistical Quality Control

2. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-2 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Learning Objectives Students will be able to Define the quality of a product or service. Develop four types of control charts Understand the basic theoretical underpinnings of statistical quality control; including the central limit theorem. Know if a process is in control or not.

3. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-3 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Module Outline M1.1 Introduction M1.2 Defining quality and TQM M1.3 Statistical Process Control M1.4 Control charts for Variables M1.5 Control Charts for Attributes

4. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-4 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Definitions of Quality Quality is the degree to which a specific product conforms to a design or specification Quality is more than making a good product Quality is fitness for use Quality is the degree of excellence at an acceptable price and the control of variability at an acceptable cost Quality of a product depends on how well it fits patterns of consumer preferences Even though quality cannot be defined, you know what it is

5. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-5 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 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

6. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Statistical technique used to ensure process is making product to standard All process are subject to variability Natural causes: Random variations Assignable causes: Correctable problems Machine wear, unskilled workers, poor material Objective: Identify assignable causes Uses process control charts Statistical Process Control (SPC)

7. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-7 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Control Chart Patterns 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.

8. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-8 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Control Chart Patterns 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.

9. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Control Chart Patterns 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.

10. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-10 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Population and Sampling Distributions - Fig. M1.2

11. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-11 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Sampling Distribution of Sample Means 99.7% of all x fall within ± 3  x 95.5% of all x fall within ± 2  x

12. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-12 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Process Control Charts

13. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-13 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Show changes in data pattern e.g., trends Make corrections before process is out of control Show causes of changes in data Assignable causes Data outside control limits or trend in data Natural causes Random variations around average Control Chart Purposes

14. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-14 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 X As sample size gets large enough (n>30)... sampling distribution becomes almost normal regardless of population distribution. Central Limit Theorem X Theoretical Basis of Control Charts

15. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-15 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Mean Central Limit Theorem Standard deviation Theoretical Basis of Control Charts

16. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-16 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Theoretical Basis of Control Charts Properties of normal distribution x

17. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-17 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Statistical Quality Control Process Control Acceptance Sampling Variables Charts Attributes Charts VariablesAttributes Types of Statistical Quality Control

18. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-18 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Control Chart Types Control Charts R Chart Variables Charts Attributes Charts X Chart P C Continuous Numerical Data Categorical or Discrete Numerical Data

19. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-19 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 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

20. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-20 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Steps to Follow Using Control Charts 1. Collect 20 - 25 samples of n = 4, or n = 5 from a stable process. Compute the mean and range of each sample. 2. Compute the overall means. Set appropriate control limits - usually at 99.7 level. Calculate preliminary upper and lower control limits. If process not stable, use desired mean instead of sample mean. 3. Graph the sample means and ranges on their respective control charts. Look to see if any fall outside acceptable limits.

21. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-21 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 4. Investigate points or patterns that indicate the process is out of control. Try to assign causes for the variation, then resume the process. 5. Collect additional samples. If necessary, re-validate the control limits using the new data. Steps – cont.

22. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-22 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Type of variables control chart Interval or ratio scaled numerical data Shows sample means over time Monitors process average Example: Weigh samples of coffee & compute means of samples; Plot  X Chart

23. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-23 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458  X Chart Control Limits Sample Range at Time i # of Samples Sample Mean at Time i From Table S4.1 Control Limits

24. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-24 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Factors for Computing Control Chart Limits

25. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-25 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Type of variables control chart Interval or ratio scaled numerical data Shows sample ranges over time Difference between smallest & largest values in inspection sample Monitors variability in process Example: Weigh samples of coffee & compute ranges of samples; Plot R-Chart

26. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-26 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 R Chart Control Limits Sample Range at Time i # Samples From Table S4.1

27. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-27 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Type of attributes control chart Nominally scaled categorical data e.g., good-bad Shows % of nonconforming items Example: Count # defective chairs & divide by total chairs inspected; Plot Chair is either defective or not defective p Chart

28. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-28 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 p Chart Control Limits # Defective Items in Sample i Size of sample i z = 2 for 95.5% limits; z = 3 for 99.7% limits

29. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-29 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Type of attributes control chart Discrete quantitative data Shows number of nonconformities (defects) in a unit Unit may be chair, steel sheet, car etc. Size of unit must be constant Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot c Chart

30. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17-30 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 ARCO’s p-Chart