1. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 1 Chapter 9 Statistical Thinking and Applications

2. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 2 Statistical Thinking All work occurs in a system of interconnected processes Variation exists in all processes Understanding and reducing variation are the keys to success

3. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 3 Sources of Variation in Production Processes Materials Tools OperatorsMethods Measurement Instruments Human Inspection Performance EnvironmentMachines INPUTSPROCESSOUTPUTS

4. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 4 Variation Many sources of uncontrollable variation exist (common causes) Special (assignable) causes of variation can be recognized and controlled Failure to understand these differences can increase variation in a system

5. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 5 Importance of Understanding Variation time PREDICTABLE ? UNPREDECTIBLE

6. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 6 Two Fundamental Management Mistakes 1.Treating as a special cause any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to common causes 2.Attributing to common causes any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to a special cause

7. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 7 Note to Instructors The following slides can be used to guide a class demonstration and discussion of the Deming Red Bead experiment using small bags of M&M’s® Chocolate Candies, from a suggestion I found on a TQ newsgroup several years ago. The good output (“red beads”) are the blue M&Ms, with the instructor playing the role of Dr. Deming.

8. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 8 We’re Going into Business!!! We have a new global customer and have to start up several factories. So I need teams of 5 to do the work: 1 production worker 2 inspectors 1 Chief Inspector 1 Recorder

9. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 9 Production Setup 1.Take the bag in your left hand. 2.Tear a 3/4” opening in the right corner. (only large enough for one piece at a time)

10. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 10 Production Process 1. Production worker produces 10 pieces and places them on the napkin. 2. Each inspector, independently, counts the blue ones, and passes to the Chief Inspector to verify. 3. If Chief Inspector agrees, s/he tells the recorder, who reports it to me.

11. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 11 Do it right the first time! Be a Quality Worker! Take Pride in Your Work!

12. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 12 Lessons Learned Quality is made at the top. Rigid procedures are not enough. People are not always the main source of variability. Numerical goals are often meaningless. Inspection is expensive and does not improve quality.

13. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 13 Statistical Methods Descriptive statistics Statistical inference Predictive statistics

14. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 14 Review of Key Concepts Random variables Probability distributions Populations and samples Point estimates Sampling distributions Standard error of the mean

15. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 15 Important Probability Distributions Discrete –Binomial –Poisson Continuous –Normal –Exponential

16. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 16 Central Limit Theorem If simple random samples of size n are taken from any population, the probability distribution of sample means will be approximately normal as n becomes large.

17. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 17 Sampling Methods Simple random sampling Stratified sampling Systematic sampling Cluster sampling Judgment sampling

18. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 18 Sampling Error Sampling error (statistical error) Nonsampling error (systematic error) Factors to consider: –Sample size –Appropriate sample design

19. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 19 Design of Experiments A test or series of tests to compare two or more methods to determine which is better, or to determine levels of controllable factors to optimize the yield of a process or minimize the variability of a response variable. Factorial experiment –Analysis of all combinations of factor levels to understand main effects and interactions

20. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 20 Excel Descriptive Statistics Tool Tools…Data Analysis… Descriptive Statistics

21. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 21

22. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 22 Excel Histogram Tool Tools…Data Analysis…Histogram

23. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 23

24. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 24 Process Capability The range over which the natural variation of a process occurs as determined by the system of common causes Measured by the proportion of output that can be produced within design specifications

25. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 25 Types of Capability Studies Peak performance study - how a process performs under ideal conditions Process characterization study - how a process performs under actual operating conditions Component variability study - relative contribution of different sources of variation (e.g., process factors, measurement system)

26. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 26 Process Capability Study 1.Choose a representative machine or process 2.Define the process conditions 3.Select a representative operator 4.Provide the right materials 5.Specify the gauging or measurement method 6.Record the measurements 7.Construct a histogram and compute descriptive statistics: mean and standard deviation 8.Compare results with specified tolerances

27. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 27 Process Capability specification natural variation (a)(b) natural variation (c)(d)

28. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 28 Process Capability Index C p = UTL - LTL 6  C pl, C pu } UTL -  3  C pl =  - LTL 3  C pk = min{ C pu =

29. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 29 PROCESS_CAPABILITY.XLS