# Acceptance Sampling By Variable

**Acceptance sampling by variable**

Acceptance sampling can be carried out by measuring a variable rather than classifying an item as conforming or non-conforming. Variables such as thickness, strength or weight might be measured. A typical plan would be to take a sample of size n and reject the batch if the mean measurement, x , is less than k. This would be appropriate for, say, the strength of a batch of climbing ropes where a large value is desirable. If the variable was, say, percentage of impurity in raw material,where a small value was desirable, the plan would be of the form - take a sample of size n and reject the batch if the mean measurement, x , is greater than k.

Usually it is easier and quicker to classify an item as conforming or non-conforming than to make an exact measurement. However, the information gained from an exact measurement is greater and so smaller sample sizes are required. A decision as to whether to use attributes or variables will depend on the particular circumstances of each case.

**Operating characteristic**

A component for use in the manufacture of office machinery will fail to function if the temperature becomes too high. A batch of these components has a mean failure temperature of 95.6˚C. The standard deviation is 2.4˚C. The company receiving this batch operates the following acceptance sampling scheme - test a

sample of size 16 and reject the batch if the mean failure temperature is less than 95.0˚C. It is reasonable to assume normal distribution since we are concerned with the mean of a reasonably large sample. The batch will be accepted if the sample mean exceeds 95.0˚C.

The probability of the batch being accepted is 0.841.

The operating characteristic can be constructed by carrying out this calculation for batches with different means (assuming the standard deviation remains at 2.4˚C). The calculations can be put in a table as shown on the next page. (Be careful to use the correct tail of the normal distribution, this will depend on the sign of z and will change when this changes).