## Sampling Inspection

Unless there are unusual requirements for extreme quality, as when death can result from a defective part, most customers will accept a certain amount of defects. The reason for this is stated in the law of diminishing returns. As the desire to locate each and every defect is satisfied, it becomes more and more costly to find them. One hundred percent inspections are expensive and require much time and effort. In 100 percent inspections there is also the problem of the inspection itself causing damage to some of the parts. This entire concept is based on the fact that the customer is willing to accept a small number of defective parts rather than pay the high cost of trying to locate each and every defect.

This policy of allowing a few unacceptable parts must be considered carefully. The ultimate use of the parts must be considered. In particular, it is important that the part that is defective not create danger to life. There can be no value placed on a human life, and many court cases have awarded large settlements against companies that attempted to do so.

For this reason, statistical sampling was developed. Without going into the statistical details that support sampling inspection, it can be described. Sampling inspection plans have been worked out and are available to quality managers to determine the parameters desired and to set up an inspection plan that will fit the type of work that they are doing.

In a sampling inspection, the sample size to be taken and inspected from a given lot size is determined. A sample size of fifteen parts may be taken from a lot of parts. Again, according to precalculated procedures, the fifteen-piece sample can contain no more than three unacceptable parts. If fewer than three parts in the sample are unacceptable, the lot passes, and if more than three parts are unacceptable, then the lot is rejected.

Acceptable Quality Level (AQL)

The rationale behind this technique is that if the acceptable quality level (AQL) was 3 percent and a sample of fifteen parts was taken from a lot of a thousand parts, there would be a very small chance that some of the bad parts would show up in the sample. If more than three parts were to show up in the sample, it could be said that the whole lot had more bad parts than the 3 percent allowed by the AQL.

Because discovering all of the defective parts can be a very costly process, most customers and suppliers agree that a certain level of defects is to be allowed in the normal process. As long as this acceptable quality level is maintained, the lot of parts is acceptable to the customer. The AQL says that a lot that has fewer than 3 percent bad parts in it is acceptable.

When we perform sampling inspections, there is a risk that the sample will give misleading information. There are four possible outcomes to this inspection process. The possibilities are:

1. The lot is good, and the sample inspection says that it is good. This is what we want.

2. The lot is good, and the sample inspection says that it is not good. This is not what we want.

3. The lot is bad, and the sample inspection says that it is good. This is not what we want.

4. The lot is bad, and the sample inspection says that it is bad. This is what we want.

If the sampling inspection accepts a lot that is good or rejects a lot that is bad, then the inspection process is working. If the sampling process accepts a lot that is really bad, this means that a lot that is really unacceptable is shipped as a good lot to the customer. This is called ''buyer's risk'' (see Figure 4-3). If the sampling process rejects a lot that is really good, this means that a lot that is really acceptable is rejected. This is called ''seller's risk.''