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Using the plan ( N, n, c) = (500, 25, 0), a lot with a relatively good quality level of 0.01 will still have about a chance of 0.23 being rejected.

Here the probability of acceptance is calculated using the Hypergeometric distribution. The following figure shows the OC curves for plans with N = 1000, n = 50, c = 0 and N = 500, n = 25, c = 0. Thus the probability of acceptance can be approximated by When the ratio is small, the Hypergeometric distribution can be approximated well by the Binomial distribution. Note that Np is an integer in this formula. The number X of defectives found in a sample will follow a Hypergeometric distribution, so the probability of lot acceptance is Suppose that the sampling plan is ( N, n, c) and the quality level of the lot is p. There are two ways to calculate the probability of lot acceptance. The risks associated with a sampling plan can be read from the operating characteristic (OC) curve, which is a graph showing the probability P a of lot acceptance for different lot quality levels. This type of risk is called the consumer’s risk. However, because of sampling, there is a possibility that the number of defectives found in the sample does not exceed c, which will lead to the decision that a bad quality level lot is accepted. That is, the probability P a of lot acceptance should be low for bad quality level lots. We want to reject such lots most of the time.

The second type of risk is that a lot with a bad quality level is accepted.

This type of risk is called the producer’s risk. However, because of sampling, there is a possibility that the number of defectives found in the sample exceeds c, which will lead to the decision that a good quality level lot is rejected. That is, the probability P a of lot acceptance should be high for good quality level lots. We want to accept such lots most of the time.

The first type of risk is that a lot with a good quality level is rejected.

However, unless the quality level p is 100%, a lot with a high percent defective, say 30%, will still have a chance of being accepted.ĭespite its wide applicability, there are two types of risk associated with each attribute sampling plan. It is worth noting that, if a lot has a quality level of p = 0%, then it will be accepted no matter what sampling plan ( N, n, c) is chosen. If p = 0%, all units in the lot are good, whereas if p = 100%, all units are defective. For instance, a quality level of p = 10% means that there are 10% defective units in the lot. The quality level of a lot is usually expressed as percentage defective or fraction defective. If this number does not exceed the pre-determined c, the lot is accepted otherwise the lot is rejected.

You then determine the number of defective components in the sample. You select a random sample of n units from the incoming lot of size N. The operation of an attribute sampling plan is simple. For example, in the context of manufacturing, it can be used to make sure that the quality of incoming parts satisfies certain requirements before they are assembled, that the quality of semi-finished products is acceptable before they are passed to the next manufacturing stage, or that the quality of finished products satisfies the customer’s specifications before they are shipped.Įach attribute sampling plan has three parameters ( N, n, c) - lot size, sample size, and acceptance number, respectively. One of the most widely used quality control tools is the attribute acceptance sampling plan, which can be applied in a variety of ways. Published February, 2003, under the longer title, "A Graphical Method for Designing Attribute Acceptance Sampling Plans" © 2002, Steve H. Ng is a Lecturer in the Department of Information and Communications Technology of the Hong Kong Institute of Vocational Education.

You need to have Excel installed on your computer to explore the interactive parts of this article, but the entire article can be read without Excel. The second concept is how the Spin Button can be used to design an attribute sampling plan that satisfies certain consumer’s and producer’s risks. The Spin Button can show visually that the exact probability of lot acceptance determined by the Hypergeometric distribution can be approximated by the Binomial distribution. The first concept is calculating the probability of lot acceptance, from which the operating characteristic curve of an attribute sampling plan can be drawn. In this article, I discuss a simple but useful feature of Excel called the Spin Button, and I use it to illustrate two concepts associated with attribute acceptance sampling plans.