Acceptance Sampling McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

You should be able to: 1. Explain the purpose of acceptance sampling 2. Contrast acceptance sampling and process control 3. Compare and contrast single- and multiple-sampling plans 4. Determine the average outgoing quality of inspected lots Instructor Slides 10S-2

Acceptance sampling A form of inspection applied to lots or batches of items before or after a process, to judge conformance with predetermined standards May be applied to both attribute and variable inspection Instructor Slides 10S-3

The purpose of acceptance sampling is to decide whether a lot satisfies predetermined standards Lots that satisfy these standards are passed or accepted Rejected lots may be subjected to 100 percent inspection In the case of purchased goods, they may be returned for credit or replacement Instructor Slides 10S-4

Acceptance sampling is most useful when at least one of the following conditions exists: 1. A large number of items must be processed in a short time 2. The cost consequences of passing defectives are low 3. Destruction testing is required 4. Fatigue or boredom caused by inspecting large numbers of items leads to inspection errors Instructor Slides 10S-5

Sampling plans: Plans that specify lot size, sample size, number of samples, and acceptance/rejection criteria Single-sampling plan Double-sampling plan Multiple-sampling plan Instructor Slides 10S-6

Single-sampling plan One random sample is drawn from each lot Every item in the sample is inspected and classified as “good” or “defective” If any sample contains more than a specified number of defectives, c, the lot is rejected Instructor Slides 10S-7

Double-Sampling Plan Allows the opportunity to take a second sample if the results of the initial sample are inconclusive Two values are specified for the number of defective items A lower level, c 1 An upper level, c 2 If the number of defectives in the first sample is ≤ c 1 the lot is accepted and sampling is terminated > c 2 the lot is rejected and sampling is terminated Between c 1 and c 2 a second sample is collected The number of defectives in both samples is compared to a third value, c 3 If the combined number of defectives does not exceed this value, the lot is accepted; otherwise, it is rejected Instructor Slides 10S-8

Multiple-sampling plan Similar to a double-sampling plan except more than two samples may be required A sampling plan will specify each sample size and two limits for each sample The limit values increase with the number of samples If, for any sample, the cumulative number of defectives found exceeds the upper limit specified, the lot is rejected If for any sample the cumulative number of defectives found is less than or equal to the lower limit, the lot is accepted. If the number of defectives found is between the two limits, another sample is taken The process continues until the lot is accepted or rejected Instructor Slides 10S-9

Sampling plan choice is dictated by cost and time required for inspection Two primary considerations: Number of samples needed Total number of observations required Instructor Slides 10S-10

Single-sampling plan requires only one sample; however, the sample size is large compared to the total number of observations taken under double- or multiple-sampling plans Single-sampling plans preferred when the cost of collecting a sample is high relative to the cost of analyzing the observations When cost of analyzing observations is high (e.g., destructive testing), double- or multiple-sampling plans are more desirable Instructor Slides 10S-11

An important sampling plan characteristic is how it discriminates between high and low quality OC curves describe a sampling plan’s ability to discriminate OC curve Probability curve that shows the probabilities of accepting lots with various fractions defective Instructor Slides 10S-12

A typical OC Curve for Proportions Instructor Slides 10S-13

No sampling plan perfectly discriminates between good and bad quality The degree to which a sampling plan discriminates is a function of the graph’s OC curve Steeper OC curves are more discriminating Instructor Slides 10S-14

Instructor Slides 10S-15

To perfectly discriminate, theoretically, between “good” and “bad” quality would require 100% inspection. 100% inspection is impractical Costly and time-consuming Destructive testing Instructor Slides 10S-16

Given the impracticality of 100% inspection, buyers are willing to live with a small number of defectives if the cost of doing so is low Usually, in the range of 1% - 2% defective Instructor Slides 10S-17

Acceptable quality Level (AQL) The percentage level of defects at which consumers are willing to accept lots as “good” Lot tolerance percent defective (LTPD) The upper limit on the percentage of defects that a consumer is willing to accept Instructor Slides 10S-18

Customers want quality equal to or better than the AQL, and are willing to accept some lots with quality as poor as the LTPD, but they prefer not to accept any lots with a defective percentage that exceeds the LTPD Instructor Slides 10S-19

Consumer’s risk, β The probability that a lot containing defects exceeding LTPD will be accepted Manufacturer’s risk, α The probability that a lot containing the acceptable quality level will be rejected Instructor Slides 10S-20

Many sampling plans are developed to have a Producer’s risk of 5 percent Consumer’s risk of 10 percent Standard references are widely available to obtain sample sizes and acceptance criteria for sampling plans Government MIL-STD tables Instructor Slides 10S-21

The AQL indicates good lots, and the LTPD indicates bad lots Instructor Slides 10S-22

When sample size is small relative to lot size, it is reasonable to use the binomial distribution to obtain the probabilities that a lot will be accepted for various lot qualities n/N<5 percent When n > 20 and p <.05, the Poisson distribution is useful in constructing OC curves for proportions In effect, the Poisson distribution is used to approximate the binomial Instructor Slides 10S-23

Suppose you want to develop an OC curve for a situation in which n = 10 N = 2,000 items Lot is accepted if no more than c = 1 defective is found Instructor Slides 10S-24

Fraction Defective, p nx c= 1  Instructor Slides 10S-25

OC Curve for n = 10, c = 1 Instructor Slides 10S-26

An interesting feature of acceptance sampling is that the level of inspection automatically adjusts to the quality of the lots being inspected, assuming rejected lots are subjected to 100 percent inspection Good lots have a high probability and bad lots a low probability of being accepted. If the lots inspected are mostly good, few will end up going through 100 percent inspection. The poorer the quality of the lots, the greater the number of lots that will come under close scrutiny Instructor Slides 10S-27

Average outgoing quality Average of rejected lots (100 percent inspection) and accepted lots (a sample of items inspected) Instructor Slides 10S-28

In practice, the last term of the AOQ formula is close to 1.0 Eliminate this term, so Construct the AOQ curve for this situation N = 500, n = 10, and c = 1 p p ac AOQ Instructor Slides 10S-29

Approximate AOQ =.082 Instructor Slides 10S-30

A manager can determine the worst possible outgoing quality The manager can determine the amount of inspection that will be needed by obtaining an estimate of the incoming quality Information can be used to establish the relationship between inspection cost and the incoming fraction defective Underscores the benefit of process improvement over weeding out defectives via inspection Instructor Slides 10S-31