Chapter 9A

1. Chapter 9A Process Capability and SPC

2. Learning Objectives • Explain what statistical quality control is. • Calculate the capability of a process. • Understand how processes are monitored with control charts. • Recognize acceptance sampling concepts.

3. Types of Situations where SPC can be Applied • How many paint defects are there in the finish of a car? • How long does it take to execute market orders? • How well are we able to maintain the dimensional tolerance on our ball bearing assembly? • How long do customers wait to be served from our drive-through window? LO 1

4. What Is Quality? • How do you define quality? • Durability, reliability, long warrantee • Fitness for use, degree of conformance • Maintainability • Measures of quality • Grade—measurable characteristics, finish • Consistency—good or bad, predictability • Conformance—degree product meets specifications • Consistency versus conformance

5. Basic Forms of Variation • Assignable variation: caused by factors that can be clearly identified and possibly managed • Example: a poorly trained employee that creates variation in finished product output • Common variation: variation that is inherent in the production process • Example: a molding process that always leaves “burrs” or flaws on a molded item LO 1

6. Variations Around Us • When variation is reduced, quality is improved • However, it is impossible to have zero variation • Engineers assign acceptable limits for variation • The limits are know as the upper and lower specification limits • Also known as upper and lower tolerance limits LO 1

7. Taguchi’s View of Variation • Traditional view is that quality within the range is good and that the cost of quality outside this range is constant • Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs • Society loses (pays) for poor quality • Design products/processes impervious to variations • Use experimental/robust design • Shoot for target not conformance to specifications LO 1

8. Process Capability • Taguchi argues that tolerance is not a yes/no decision, but a continuous function • Other experts argue that the process should be so good the probability of generating a defect should be very low LO 2

9. Process Capability • Process (control) limits • Calculated from data gathered from the process • It is natural tolerance limits • Defined by ±3σ (standard deviation) • Used to determine if process is in statistical control • Tolerance (specification) limits • Often determined externally, e.g., by customer • Process may be in control but not within specification • How do the limits relate to one another?

10. Process Capability LO 2

11. Process Capability • Case 1: Cp > 1 • USL-LSL > 6 sigma • Process quality higher than customer’s • Situation desired • Defacto standard is 1.33+ LSL USL LNTL UNTL

12. Process Capability • Case 2: Cp = 1 • USL-LSL = 6 sigma • Approximately 0.27% defectives will be made • Process is unstable LSL USL LNTL UNTL

13. Process Capability • Case 3: Cp < 1 • USL-LSL < 6 sigma • Situation undesirable • Process is yield sensitive • Could produce large number of defectives LNTL UNTL USL LSL

14. Process Capability Index, • Most widely used capability measure • Measures design versus specification relative to the nominal value • Based on worst case situation • Defacto value is 1 and processes with this score is capable • Scores > 1 indicates 6-sigma subsumed by the inspection limits • Scores less than 1 will result in an incapable process

15. Capability Index (Cpk) • Capability index (Cpk) shows how well parts being produced fit into design limit specifications • Also useful to calculate probabilities LO 2

16. Example: Capability • Data • Designed for an average of 60 psi • Lower limit of 55 psi, upper limit of 65 psi • Sample mean of 61 psi, standard deviation of 2 psi • Calculate Cpk LO 2

17. What does a Cpk of 0.6667 mean? • An index that shows how well the units being produced fit within the specification limits. • This is a process that will produce a relatively high number of defects. • Many companies look for a Cpk of 1.3 or better… 6-Sigma companies want 2.0!

18. Example: Probabilities LO 2

19. Process Control Procedures • Attribute (Go or no-go information) • Defectives refers to the acceptability of product across a range of characteristics. • Defects refers to the number of defects per unit which may be higher than the number of defectives. • p-chart application • Variable (Continuous) • Usually measured by the mean and the standard deviation. • X-bar and R chart applications LO 3

20. Control Chart Evidence for Investigation LO 3

21. Process Control with Attribute Measurement: Using ρ Charts • Created for good/bad attributes • Use simple statistics to create the control limits LO 3

22. Example: Control Chart Design LO 3

23. Example: Calculations LO 3

24. Process Control with Attribute Measurements: Using c Charts • With ρ charts, each item was either good or bad • With a c chart, each item can have multiple defects LO 3

25. Example: Lumber Yard • Lumber yard expects four knotholes per eight foot board LO 3

26. Process Control with Variable Measurements: Using x and R Charts • In variable sampling, we measure actual values rather than sampling attributes • Generally want small sample size • Quicker • Cheaper • Samples of 4-5 are typical • Want 25 or so samples to set up chart LO 3

27. How to Construct x Charts if Standard Deviation Known LO 3

28. How to Construct x and R Charts LO 3

29. Example: The Data LO 3

30. Example: Calculations and Chart LO 3

31. Acceptance Sampling • Acceptance sampling is sampling to accept or reject the immediate lot of product at hand • Does not always “Determine quality level” • Results subject to sampling error • Purposes • Make decision about (sentence) a product • Otherwise, ensures quality is within predetermined level LO 4

32. Acceptance Sampling • Advantages • Economy • Less handling damage • Fewer inspectors • Upgrading of the inspection job • Applicability to destructive testing • Entire lot rejection (motivation for improvement) • Disadvantages • Risks of accepting “bad” lots (consumer’s risk) and rejecting “good” lots (producer’s risk) • Added planning and documentation • Sample provides less information than 100-percent inspection

33. Single Sampling Plan • Defined by n and c • n is sample size—how many to sample at a time • c is the acceptance number—the maximum number of defective items that can be found in the sample before the lot is rejected • Values for n and c are determined by the interaction of four factors • AQL or acceptable quality level • α • LTPD or lot tolerance percent defective • β LO 4

34. Risk • Acceptable quality level (AQL) • Maximum acceptable percentage of defectives defined by producer • The  (producer’s risk) • The probability of rejecting a good lot • Lot tolerance percent defective (LTPD) • Percentage of defectives that defines consumer’s rejection point • The  (consumer’s risk) • The probability of accepting a bad lot LO 4

35. Standard Table of Sampling Plans • MIL-STD-105D • For attribute sampling plans • Needs to know: • The lot size N • The inspection level (I, II, III) • The AQL • Type of sampling (single, double, multiple) • Type of inspection (normal, tightened, reduced) • Find a code letter then read plan from Table

36. Standard Table of Sampling Plans: Single Sampling Plan Example: If N=2000 and AQL=0.65% find the normal, tightened, and reduced single sampling plan using inspection level II. Example: If N=20,000 and AQL=1.5% find the normal, tightened, and reduced double sampling plan using inspection level I.