24 May 2011

Acceptance Sampling for Quality Control

When applying acceptance sampling as your approach to quality, a small batch of components are measured or observed and a decision to scrap or accept is made. This approach is dependent on statistical sampling techniques that use the data collected on a small number of samples to be extrapolated to predict the likelihood of large numbers of products meeting the design specification.

The decision to accept or reject is based on the idea that a certain number of defective items can be tolerated.

When is Acceptance Sampling Effective.

To consider when acceptance sampling is going to be effective it is necessary to look at 2 possible extremes.

If the cost of 100% inspection > the cost of all defective components, it is cheaper not to inspect.

If the cost of 100% inspection < cost of the customer finding 1 defect, it is cheaper to inspect 100%.

When the cost of inspection lies between these 2 extremes, acceptance sampling is said to become effective. This does however conveniently omit to take into account the possible damage to reputation, legal liability and potential loss of business as a result of the customer receiving defective goods. In other words the qualitative aspects of doing business are ignored in favour of the quantative aspects.

Ref. Edwards & Endean (1990)

How Does Acceptance Sampling Work

Acceptance sampling is formed around probability theories from which it can be predicted what percentage of a lot of components will be acceptable given the results from the observations made on a sample batch from that lot.

Batches whose samples show fewer than a specified number of defectives are going to be accepted, so the probability of finding fewer than that number of defectives in the sample needs to be known. This is determined by the sum of probabilities up to that for the number of defectives specified.

For example: -

If we want to find the probability of finding 1 defective component in a lot of 20 given 3 samples then the equation is

P = 1/20 = 0.95, so the probability of finding fewer than 1 defective in a sample of 3 is

0.95x0.95x0.95 =0.8574

This means that rejecting samples which have at least one defective could result in nearly 15% of all acceptable batches being rejected.

However what we want to know is what would be the risk of allowing batches with more than the permissible number of bad components to get through at either threshold of acceptance/rejection.

To find out requires calculating all relevant values of p, the fraction of defective components in the batch.

Rather than calculate this information every time, there are appropriate national and international standards available that provide the information in the form of extensive tables that detail the size of samples and the levels of defectives to accept or reject in order to provide the desired probabilities of detecting bad batches of products.

There is a finite probability of passing unacceptable batches and rejecting acceptable ones. Inspection procedures are arranged to minimise this risk to either manufacturer or customer.

Ref. Edwards & Endean (1990).

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