Binomial Experiments

We will consider acceptance samples as binomial experiments where the number of successes is the number of nonconforming items in the sample. Notice that an acceptance sample is usually drawn without replacement, so the draws are not independent. In practice, however, lots of a product are very large, and the sample size is small enough relative to the lot size that the independence issue is not a problem. The population of items in the lot is so large relative to the sample size that the probability of drawing a nonconforming item is roughly the same for each item selected, even though the sample of items is drawn without replacement. Then, the selection of items can be considered independent, and the binomial distribution can be used to model the situation.

For this activity, we will assume that the above description is the case for us as well— that the acceptance samples we are considering are drawn from lots of products that are sufficiently large for us to consider our selections to be independent and to assume that the probability of drawing a nonconforming item is the same for each item selected for the sample.

Thus, we will consider acceptance samples drawn from lots of a product as binomial experiments, where the number of successes is the number of nonconforming items in the sample and a lot of products has a fixed proportion of nonconforming items.

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