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6. Process or Product Monitoring and Control

6.2. Test Product for Acceptability: Lot Acceptance Sampling

6.2.1. What is Acceptance Sampling?Contributions of

Dodge and Romig to acceptance

sampling

Acceptance sampling is an important field of statistical quality

control that was popularized by Dodge and Romig and originallyapplied by the U.S. military to the testing of bullets during World

War II. If every bullet was tested in advance, no bullets would beleft to ship. If, on the other hand, none were tested, malfunctions

might occur in the field of battle, with potentially disastrous

results. Definintion of Lot

AcceptanceSampling

Dodge reasoned that a sample should be picked at random from

the lot, and on the basis of information that was yielded by the

sample, a decision should be made regarding the disposition of the lot. In general, the decision is either to accept or reject the lot.

This process is called Lot Acceptance Sampling or just

Acceptance Sampling ."Attributes" (i.e.,

defect counting)will be assumed

Acceptance sampling is "the middle of the road" approach between no inspection and 100% inspection. There are two major

classifications of acceptance plans: by attributes ("go, no-go")

and by variables. The attribute case is the most common for acceptance sampling, and will be assumed for the rest of this

section. Important point A point to remember is that the main purpose of acceptance

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sampling is to decide whether or not the lot is likely to be

acceptable, not to estimate the quality of the lot.Scenarios leading

to acceptance

sampling

Acceptance sampling is employed when one or several of thefollowing hold:

•

Testing is destructive• The cost of 100% inspection is very high

• 100% inspection takes too long

A lot acceptance sampling plan (LASP) is asampling scheme and a set of rules for

making decisions. The decision, based oncounting the number of defectives in a

sample, can be to accept the lot, reject the

lot, or even, for multiple or sequentialsampling schemes, to take another sample

and then repeat the decision process.Types of acceptance plans to choose from LASPs fall into the following

categories:

• Single sampling plans:. Onesample of items is selected at

random from a lot and thedisposition of the lot is

determined from the resulting

information. These plans areusually denoted as (n,c) plans

for a sample size n, where the

lot is rejected if there are more

than c defectives. These are the

most common (and easiest)

plans to use although not themost efficient in terms of

average number of samples

needed.

• Double sampling plans: After the first sample is tested, there

are three possibilities:

1. Accept the lot



2. Reject the lot

3. No decision

If the outcome is (3), and asecond sample is taken, the

procedure is to combine theresults of both samples and

make a final decision based onthat information.

• Multiple sampling plans: This

is an extension of the double

sampling plans where morethan two samples are needed to

reach a conclusion. The

advantage of multiple sampling

is smaller sample sizes.• Sequential sampling plans: .

This is the ultimate extension of multiple sampling where items

are selected from a lot one at a

time and after inspection of each item a decision is made to

accept or reject the lot or select

another unit.

• Skip lot sampling plans:. Skip

lot sampling means that only afraction of the submitted lots

are inspected. Definitions of basic Acceptance Sampling

termsDeriving a plan, within one of thecategories listed above, is discussed in

the pages that follow. All derivations

depend on the properties you want the plan to have. These are described using

the following terms:

• Acceptable Quality Level

(AQL): The AQL is a percentdefective that is the base line

requirement for the quality of

the producer's product. The producer would like to design a

sampling plan such that there is

a high probability of accepting

a lot that has a defect level less



than or equal to the AQL.

• Lot Tolerance Percent

Defective (LTPD): The LTPDis a designated high defect level

that would be unacceptable tothe consumer. The consumer

would like the sampling plan tohave a low probability of

accepting a lot with a defect

level as high as the LTPD.

• Type I Error (Producer's

Risk): This is the probability,

for a given (n,c) sampling plan,of rejecting a lot that has a

defect level equal to the AQL.

The producer suffers when thisoccurs, because a lot withacceptable quality was rejected.

The symbol is commonly

used for the Type I error andtypical values for range from

0.2 to 0.01.

• Type II Error (Consumer's

Risk): This is the probability,

for a given (n,c) sampling plan,

of accepting a lot with a defect

level equal to the LTPD. Theconsumer suffers when this

occurs, because a lot with

unacceptable quality was

accepted. The symbol is

commonly used for the Type II

error and typical values rangefrom 0.2 to 0.01.

• Operating Characteristic (OC)

Curve: This curve plots the

probability of accepting the lot

(Y-axis) versus the lot fractionor percent defectives (X-axis).The OC curve is the primary

tool for displaying and

investigating the properties of a LASP .

• Average Outgoing Quality

(AOQ): A common procedure,



when sampling and testing is

non-destructive, is to 100%

inspect rejected lots and replaceall defectives with good units.

In this case, all rejected lots are

made perfect and the onlydefects left are those in lots that

were accepted. AOQ's refer to

the long term defect level for this combined LASP and 100%

inspection of rejected lots

process. If all lots come in with

a defect level of exactly p, andthe OC curve for the chosen

(n,c) LASP indicates a

probability pa of accepting such

a lot, over the long run the AOQ can easily be shown to be:

where N is the lot size.

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