Chapter 13

1. Chapter 13

2. Myths and Legends Myth: “Acceptance sampling assures good quality.” Truth: Acceptance sampling provides confidence that p (the population fraction defective) is stable over a long period of time and across many lots. The fundamental goal of acceptance sampling is to reduce the amount of inspection needed to verify that lots of material have some predetermined level of quality. Truth: Acceptance sampling allows for some predetermined level of non-conformances

3. Not as popular today • Modern production philosophies like small batch sizes and statistical process control by variables data are making acceptance by attributes increasingly less effective. • To achieve the high levels of quality that are being achieved in a free market through competition, it is getting increasingly difficult for acceptance sampling to meet its goal with reasonable sample sizes.

4. Two schools of thoughts • Part acceptance (old school) • Acceptable Quality Limits (AQL) • Incoming inspection • Process control (new school) • Control charts • Capability studies • Both ways have been used to decrease consumer risk of receiving non-conforming product from suppliers

5. Sampling Dilemma • Very good at accepting very good lots and rejecting very bad lots – but what about in-between?

6. How does this effect the zero defect mentality? • In the past AQL’s of 1% were reasonable and process capability was accepted at Cpk=1 • Now we need much lower AQL’s and Cpk much greater than 1 What happens to sampling?

7. What’s being done? • Vendor certification • Companies need to prove themselves worthy • Supplied data • Auditing • No receiving inspection • Required SPC • Cpk>1.5 usually 2 • Ever hear of PPAP, APQP, FMEA, AS9102? If you haven’t its coming. • Prove control and capability - then sample

8. Simple Example • The home company tells us they put about 13% RED M&Ms in their mix. • We have a lot (one bag) of delivered M&Ms. We are randomly going to sample a bag and we will only accept the lot if the sample has 13% or less red in it. • What is the probability of accepting a sampled lot?

9. What can we learn from this? • How does this correspond to “Sampling Dilemma”? • What problems does this activity cause? How does it add cost? • What if we increase the sample size?

10. Type I and Type II error • Type 1 (producer’s risk, alpha ) – The probability that a hypothesis that is actually true will be rejected • The chance that a good lot will be rejected • Type 2 (consumer’s risk, beta ) – The probability that a hypothesis that is actually false will be accepted • The chance that a bad lot will be accepted

11. Sample size compared to risk What happens to: producer’s risk consumer’s risk as you increase your sample size? Why? What do we do?

12. Operational Characteristic Curves • Commonly referred to as OC Curves • Quantifies the producer’s and consumer’s risk • Identified by the sample size (n) and the maximum acceptance number (c) • Constructed from the Poisson probability distribution • No perfect sampling plan exist, there will always be some risk

13. Poisson probability distribution • Characterized by • Only two independent outcomes • the average number of occurrences per time period (pn=) • used for rare events when n is large and p is small • Good to approximate the binomial distribution • Constructed by • using a Poisson probability table Figure 13.2 • equation – the probability of exactly c defectives in a sample of n (pn=)

14. How to construct an OC Curve • Choose p values between 0 and .09 • Multiply each p value by n and place it on the table • Make a percent column for p and mark it 100p • Using Figure 13.2, start at the pn value on the x-axis and go straight up to the c= line. Then move straight across to the y-axis. Read the probability of acceptance. • Record the Pa value on the table

15. Example • n=150c=3

16. Acceptable Quality Level • AQL • Defined as • The maximum percent defective that is allowed as a process average • The level of quality of a submitted lot that has a 95% chance of being accepted • 1-AQL is the producer’s risk • Not the quality level that is being produced or accepted • Not always the quality goal • In our exercise, it is .9% • How does sample size effect AQL? • See figure 13.7

17. Indifference / RejectableQuality Level • IQL • The quality level that will be accepted 50% of the time. • In our exercise, it is 2.5% • How does sample size effect IQL? • See figure 13.7 • RQL • The level of quality that will be accepted only 10% of the time • This is the consumer’s risk • In our exercise, it is 4.5% • How does sample size effect RQL? • See figure 13.7

18. Average Outgoing Quality Limit • AOQL • The maximum Average Outgoing Quality • Found on the Average Outgoing Quality (AOQ) curve

19. Average Outgoing Quality Curve • Shows the result of the incoming inspection and sorting of rejected lots • Outgoing quality is the quality level expected from the process of inspection • Assumptions • The lots size and incoming quality level is relatively consistent • All the lots that pass go to production • All rejected lots are 100% inspected, non-conforming units are replaced with conforming units

20. How to construct an AOQ Curve • Create a table that includes; • a column for incoming percent defective (100p) • percent accepted from the OC curve(Pa), • percentage rejected and fully sorted (1-Pa) • and defects outgoing (Pa*100p) • Fill in the table • Graph the defects outgoing • Identify the AOQL 100p 1-Pa Pa * 100p

21. Example • n=150c=3

22. Inspection Plans • Variable • Mil-Std-414 • ANSI/ASQ-Z1.9-1993 • Attribute • Mil-Std-105D • ANSI/ASQ-Z1.4-1993 • Dodge-Romig Tables • Purpose • Establishes sampling plans and procedures • Used as a reference to standardize sampling • To drive conformity on the switching procedures between the use a normal, tightened or reduced sampling plan

23. How to use • Typically you are given a set of criteria to use by your customer • You will need to know the following: • Inspection level • Lot size • Single, double or multiple inspection • Normal, reduced or tightened • AQL

24. Procedure for using sample plans • Determine inspection level and lot size • Find inspection plan code letter • Determine if plan is single, double or multiple inspection • Determine if plan is normal, tightened or reduced • Find the correct plan chart • Based on code letter, determine sample size needed • Inspect samples • Find the appropriate AQL column • Find the cell that connects the code letter row to the AQL column • Find acceptance and reject numbers • If your sample has non-conformances equal to or less than the Ac number, accept the lot • If your sample has non-conformances equal to or greater than the Re number, reject the lot Use Table 13.10-13.14

25. Example • Your customer requires you to use MIL-STD-105D, single sampling, normal inspection level II with an AQL of 1%. • The shipment that arrived had a lot quantity of 2000. You found the sample size and determined there are 3 non-conformances in the lot. • Do you accept or reject the lot? • What about a double inspection? Why do a double inspection?

26. The Deming Inspection Criterion • As batch sizes get smaller, the effective number of parts requiring inspection gets bigger (approaches 100%) • You can see this in the sampling tables • As quality gets better, bigger and bigger samples are needed to detect a shift in the process average • Deming suggests a better (I think) answer: • Control the process with SPC. • If it’s capable and in control, don’t inspect any more than needed to keep it that way. • If it’s not capable and in control, 100% inspect.