# Acceptance sampling

ACCEPTANCE SAMPLING

There are two types of risks involved while taking decisions of acceptance or rejection on the basis of sample inspection.

Â· A bad lot may be accepted because the sample drawn from it was good.
Â· A good lot be rejected because the sample drawn from it was bad.

Types of Acceptance Sampling

Acceptance sampling is of two types:

1. Attribute acceptance sampling:

Here decision regarding acceptance or rejection is based on a number of defective found in a sample. A sample is taken from a lot and good items and defective items are separated. Then the number of defective items is compared with the allowable limit stated in a sampling plan. If the number of defective items is less than the allowable limit, the lot is accepted, otherwise rejected. This type of sampling is used widely, because of its simplicity.

2. Variable acceptance sampling:

Here decision regarding acceptance or rejection is based on â€˜averageâ€™ (mean) and â€˜spreadâ€™ of a number of individual measurements specifying the quality characteristics of a sample. Here a sample is taken, quality characteristics of each unit are measured, and average is worked out. The average value worked out is compared with the allowable value stated in a sampling plan, to decide whether to accept or reject a lot. A sampling system for inspection by variables is ISO 3951 which is based on MILD-STD-414. It is classified by AQL.

Types of Sampling Plan

Sampling plan may be of three types. It may be

1. a single sampling plan
2. a double sampling plan
3. Multiple (continuous) sampling plan

Single sampling plan: In such a type of plan, decision to accept or reject a lot is taken on the basis of the results of the first sample. Here, generally a large sample is used. When the lots are extremely good or bad or contain high proportion of good or bad items, decision can be taken on the basis of even a small sample. A large sample unnecessarily increases the cost of inspection in such a case.

Each of the sample items (n) is either acceptable or defective. Such a sampling plan is known as sampling by attributes.

In single sampling plan, one sample is drawn randomly from the lot, and acceptance/rejection decisions are taken on the basis of inspection of this sample.

Consider the following data:

Lot size (N) = 18,000

Sample size (n) = 600

Acceptance Number (C) =14

Here a sample of 600 units is drawn randomly from a lot of 18000 units. These 600 units are inspected and if fourteen (14) or less are defective in the sample, the lot is accepted. If fifteen (15) or more defectives are found in the sample, the lot is rejected.

Double sampling plan:

Sometimes it becomes difficult to decide, on the basis of first sample, whether a lot is good or bad. This happens in case of borderline cases. Number of defectives may be very close to the upper control limit. Under such circumstances, it becomes necessary to inspect another sample. A second sample, therefore, is drawn, inspected, added to the first sample and then on the basis of the combined result, decision regarding acceptance or rejection of the lot is taken. This is called double sampling plan, because here two samples are taken to arrive at the decision. The following procedure is followed under this plan:

1. Take first sample. Find out the number of defectives in that sample. Compare the number with two acceptance numbers C1 and C2.

2. If the number of defectives is less than C1, accept the lot and if it is more than C2, reject the lot.

3. If the number of defectives is between C1 and C2, take a second sample. Find out the number of defectives in the combined sample. Compare the number with two acceptance numbers C1 and C2.

4. If the number of defectives is less than C2, accept the lot and it if exceeds C2, reject the lot.

Let us consider the following example:

Lot size (N) = 18000

Sample size â€“ First sample (n1) = 120

Acceptance number â€“ first sample (c1) =2

Rejection number â€“ First sample (r1) =10

Sample size â€“ Second sample = 300

Acceptance number for both samples (c2) = 12

Rejection number for both samples (r2) = 14

If (n1) is the initial sample of 120 from a lot of 18000 (N) chosen for inspection, we can take any of the following judgments.

Â· If there are 2 or less defectives, the lot is accepted.
Â· It there are 10 or more defectives, the lot is rejected.
Â· If these are 3, 4, 5, 6, 7, 8, or 9 defectives, no decision is taken, and a second sample is drawn.

A second sample of 300 (n2) is drawn from the lot, and is inspected, and one of the following judgments is made:

Â· If there are 12 or less defectives (C2) in the combined sample, the lot is accepted. This number is obtained (12 or less) by 4 in the first sample and 8 or less in the second sample, by 6 in the first sample and 6 or less in the second sample, by 8 in the first sample and 4 or less in the second sample.

Â· If there are 14 or more defectives (r2) in both the samples, the lot is rejected. This number (14 or more) is obtained by 4 in the first sample and 10 or more in the second sample, by 6 in the first and 8 or more in the second sample or by 8 in the first sample and 6 or more in the second sample.

Acceptance sampling is a direct part of routine inspection activity in an engineering industry and form an important activity of Operations Management. The quality inspection plans are designed by the quality experts of the industry incorporating statistical methods. In this article we have incorporated one particular plan.