1. Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Statistical Process Control Operations Management - 5 th Edition Chapter 4 Roberta Russell & Bernard W. Taylor, III

2. Copyright 2006 John Wiley & Sons, Inc.4-2 Lecture Outline  Introduction  Sources of process variation  The inspection process  Control Charts  Control Charts for Attributes  Control Charts for Variables  Control Chart Patterns  Process Capability

3. Copyright 2006 John Wiley & Sons, Inc.4-3 Statistical Quality Control Acceptance sampling Process Control AttributesVariables Statistical Quality Control for Acceptance Sampling and for Process Control. AttributesVariables

4. Copyright 2006 John Wiley & Sons, Inc.4-4 Ch 4 - 2 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Quality Control Approaches  Statistical process control (SPC) Monitors production process to prevent poor quality Monitors production process to prevent poor quality  Acceptance sampling Inspects random sample of product to determine if a lot is acceptable Inspects random sample of product to determine if a lot is acceptable

5. Copyright 2006 John Wiley & Sons, Inc.4-5 Process Variation

6. Copyright 2006 John Wiley & Sons, Inc.4-6 Types of Variations  Common Cause  Random  Chronic  Small  System problems  Mgt controllable  Process improvement  Process capability  Special Cause  Situational  Sporadic  Large  Local problems  Locally controllable  Process control  Process stability

7. Copyright 2006 John Wiley & Sons, Inc.4-7 Variation from Common Causes

8. Copyright 2006 John Wiley & Sons, Inc.4-8 Variation from Special Causes

9. Copyright 2006 John Wiley & Sons, Inc.4-9 The Inspection Process  Quality measures Attribute vs. variables Attribute vs. variables  Sampling vs. screening

10. Copyright 2006 John Wiley & Sons, Inc.4-10 Quality Measures  Attribute a product characteristic that can be evaluated with a discrete response a product characteristic that can be evaluated with a discrete response good – bad; yes - no good – bad; yes - no  Variable a product characteristic that is continuous and can be measured a product characteristic that is continuous and can be measured weight - length weight - length

11. Copyright 2006 John Wiley & Sons, Inc.4-11 Sampling vs. Screening  Sampling When you inspect a subset of the population When you inspect a subset of the population  Screening When you inspect the whole population When you inspect the whole population  The costs consideration

12. Copyright 2006 John Wiley & Sons, Inc.4-12 Control Charts  A graph that establishes control limits of a process  Control limits upper and lower bands of a control chart upper and lower bands of a control chart  Theoretical foundation of control charts  Types of charts Attributes Attributes p-chart p-chart c-chart c-chart Variables Variables range (R-chart) range (R-chart) mean (x bar – chart) mean (x bar – chart)

13. Copyright 2006 John Wiley & Sons, Inc.4-13 Process Control Chart 12345678910 Sample number Uppercontrollimit Processaverage Lowercontrollimit Out of control

14. Copyright 2006 John Wiley & Sons, Inc.4-14 Normal Distribution  =0 1111 2222 3333 -1  -2  -3  95% 99.74%

15. Copyright 2006 John Wiley & Sons, Inc.4-15 A Process Is in Control If … 1.… no sample points outside limits 2.… most points near process average 3.… about equal number of points above and below centerline 4.… points appear randomly distributed

16. Copyright 2006 John Wiley & Sons, Inc.4-16 Control Charts for Variables  Mean chart ( x -Chart )  uses average of a sample  Range chart ( R-Chart )  uses amount of dispersion in a sample

17. Copyright 2006 John Wiley & Sons, Inc.4-17 Using x- bar and R-Charts Together  Process average and process variability must be in control.  It is possible for samples to have very narrow ranges, but their averages is beyond control limits.  It is possible for sample averages to be in control, but ranges might be very large.

18. Copyright 2006 John Wiley & Sons, Inc.4-18 Control Charts for Attributes  p-charts  uses portion defective in a sample  c-charts  uses number of defects in an item

19. Copyright 2006 John Wiley & Sons, Inc.4-19 p-Chart UCL = p + z  p LCL = p - z  p z=number of standard deviations from process average p=sample proportion defective; an estimate of process average  p = standard deviation of sample proportion p =p =p =p = p(1 - p) n

20. Copyright 2006 John Wiley & Sons, Inc.4-20 c-Chart UCL = c + z  c LCL = c - z  c where c = number of defects per sample  c = c

21. Copyright 2006 John Wiley & Sons, Inc.4-21 Control Chart Patterns UCL LCL Sample observations consistently above the center line LCL UCL Sample observations consistently below the center line

22. Copyright 2006 John Wiley & Sons, Inc.4-22 Control Chart Patterns (cont.) LCL UCL Sample observations consistently increasing UCL LCL Sample observations consistently decreasing

23. Copyright 2006 John Wiley & Sons, Inc.4-23 Zones for Pattern Tests UCL LCL Zone A Zone B Zone C Zone B Zone A Process average 3 sigma = x + A 2 R = 3 sigma = x - A 2 R = 2 sigma = x + (A 2 R) = 2323 2 sigma = x - (A 2 R) = 2323 1 sigma = x + (A 2 R) = 1313 1 sigma = x - (A 2 R) = 1313 x = Sample number |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | 10 | 11 | 12 | 13

24. Copyright 2006 John Wiley & Sons, Inc.4-24 Control Chart Patterns  8 consecutive points on one side of the center line  8 consecutive points up or down across zones  14 points alternating up or down  2 out of 3 consecutive points in zone A but still inside the control limits  4 out of 5 consecutive points in zone A or B

25. Copyright 2006 John Wiley & Sons, Inc.4-25 Sample Size  Attribute charts require larger sample sizes  50 to 100 parts in a sample  Variable charts require smaller samples  2 to 10 parts in a sample

26. Copyright 2006 John Wiley & Sons, Inc.4-26 Process Capability  Tolerances design specifications reflecting product requirements design specifications reflecting product requirements  Process capability range of natural variability in a process what we measure with control charts range of natural variability in a process what we measure with control charts

27. Copyright 2006 John Wiley & Sons, Inc.4-27 Process Capability (b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time. Design Specifications Process (a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time. Design Specifications Process

28. Copyright 2006 John Wiley & Sons, Inc.4-28 Process Capability (cont.) (c) Design specifications greater than natural variation; process is capable of always conforming to specifications. Design Specifications Process (d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification. Design Specifications Process

29. Copyright 2006 John Wiley & Sons, Inc.4-29 Process Capability Measures Process Capability Ratio Cp==Cp== tolerance range process range upper specification limit - lower specification limit 6 

30. Copyright 2006 John Wiley & Sons, Inc.4-30 Process Capability Measures Process Capability Index C pk = minimum x - lower specification limit 3  = upper specification limit - x 3  =,