Acceptance sampling

• A predetermined number of units from each lot is inspected by attributes. If the number of nonconforming units is less than the prescribed minimum, the lot is accepted; if not the lot is rejected as being below standard.

• Sampling Plan: Lot size N = 9000 Sample size n = 300 Acceptance Number c = 2

Where Sampling Plan is used?

• Test is destructive.• Cost of 100% inspection is high.• When there are many similar units to be inspected.• When information such as Xbar and R, p or c-charts

and Cpk are not available.• When automated inspection is not available.• Provides a strong motivation to improve quality

because an entire batch may be rejected.

Advantage of acceptance sampling

• Place responsibility on the appropriate place.• More economical.• Upgrade the inspection job monotonous piece

by piece decisions to lot-by-lot decisions.• Good for destructive testing.• If entire lots are not accepted: stronger

motivation for improvement.

Disadvantage of acceptance sampling

• Risk of rejecting a “good” lot (producer’s risk) or accepting a “poor” lots (consumer’s risk)

• More time and effort is devoted to planning and documentation.

• Less information is provided about the product, although there is usually enough.

• There is no assurance given that the entire lot conforms to specifications.

Types of Sampling Plan

• Single sampling• Double sampling• Multiple sampling

Operating Characteristics (OC) curve

• It plots the probability of accepting the lot versus proportion nonconforming of the lot.

• In judging a particular sampling plan, it is desirable to know the probability that a lot submitted with certain percent nonconforming 100P0 will be accepted. The OC curve will provide this information.

Example of drawing OC curve

Sampling Plan: N = 3000, n = 89, c =2.Steps:1. Assume P0 value.2. Calculate nP0 value.3. From Table C, Poisson Table in appendix

(page 515) attain probability of acceptance Pa value for c and nP0 values.

Acceptable Quality Level (AQL)

• Numerical definition of a good lot associated with producer’s risk. “Maximum percentage or proportion nonconforming items or number of nonconformities in a lot or batch that can be considered satisfactory as a process average”. It refers to the process avaerage, which if kept stable at this value, would result in accepting majority of the lots.

Example of Acceptable Quality Level (AQL)

• Producer’s risk is 5% for AQL of 0.02 means batches that are 2% nonconforming are considered to be good and prefer to reject such batches no more than 5% of the time.

Limited Quality Level (LQL)

• Numerical definition of a poor lot, associated with “consumer’s risk”. “The percentage or proportion of nonconforming items or number of nonconformities in a lot or batch for which the consumer wishes the probability of acceptance to be a specified low.”

Example of Limited Quality Level (LQL)

If the consumer risk is 10% for an LQL of 0.08, this means that batches that are 8% nonconforming are poor and the consumers prefer to accept these batches no more than 10% of the time.

Inspection Level

MIL-STD-105E provides for 7 inspection levels:• 4 special levels- S-1, S-2, S-3 and S-4. Limited in

applications. Small samples are necessary and large risks must be tolerated.

• 3 general levels – Level I, Level II and Level III.Progressing through S1 through Level III, the sample size and hence ability to discriminate between good and bad lots, increases. Level II is norm. Level I provides half as much as inspection; and level III provides about twice the amount of level II.

Inspection Scheme

• Normal• Tightened• Reduced

Three Components

• Sampling Plan states the lot size, sample size and the acceptance criteria. It determines the fate of the lot.

• Sampling scheme is a combination of sampling plan with switching rules from Normal to Reduced to Tightened or discontinue. A scheme is indexed by lot size and AQL. A set of rules specifies the type of inspection to be used.

• Sampling system is a collection of sampling schemes. It provides rules for the selection of an appropriate sampling plan. Example: ANSI/ASQ Z1.4-2003, modifications of MIL-STD-105E .

Implementation

• Determine the lot size.• Determine the inspection level (usually level II).• Enter the table and find sample size code letter.• Determine the AQL.• Determine the type of sampling plan.• Enter the appropriate table to find the sampling

plan.• Start with normal inspection and change to

tightened or reduced based on switching rules.

How to decide the AQL value?

• AQL is the most important part of the standard.

• The value is designated in the contract by the responsible authority.

• Degree of severity of

• AQL – 0.10% or less for critical• 1% for major • 2-4% for minor nonconformities