Acceptance Sampling

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Disadvantages of 100% Inspection

1) Inspection costs are extremely high,

2) Inspection/testing is sometimes destructive,

3) When lot/batch sizes are extremely high, Inspection takes and excessive amount of time,

4) When process capability is extremely high, 100% inspection is a waste of time and resources.

Acceptance Sampling overcomes all of these disadvantages!

What is Acceptance Sampling

Acceptance sampling is a form of statistical quality control. It refers to the process of randomly inspecting a certain number of items from a lot or batch in order to decide whether to accept or reject the entire batch. 

What makes acceptance sampling different from statistical process control is that acceptance sampling is performed either before or after the process, rather than during the process. 

Acceptance sampling before the process involves sampling materials received from a supplier, such as metal castings that will be used in a machine shop. 

Sampling after the process involves sampling finished items that are to be shipped either to a customer or to a distribution center. Examples include randomly testing a certain number of computers from a batch to make sure they meet operational requirements, and randomly inspecting HDTV's to make sure that they are not defective.

The goal of acceptance sampling is to determine the criteria for acceptance or rejection based on the size of the lot, the size of the sample, and the level of confidence we wish to attain. Acceptance sampling can be used for both attribute and variable measures, though it is most commonly used for attributes.

Sampling Plans

Sampling plans became popular during WWII as a result of the military receiving excessive defective munitions from suppliers. Statisticians developed the plans which are based upon statistical probabilities. Once developed the plans were quickly implemented.

The plans precisely specify the parameters of the sampling process and the acceptance/rejection criteria. The variables specified include the size of the lot (N), the size of the sample inspected from the lot (n), the number of defects above which a lot is rejected (c), and the number of samples that will be taken.

Attributes Sample Size Table

Using Lot Size and Inspection Level determine the appropriate Code Letter

Using the Code Letter and Acceptable Quality Level determine the Sample Size

Types of Acceptance Sampling Plans

There are different types of sampling plans. Some call for single sampling, in which a random sample is drawn from every lot. Each item in the sample is examined and is labeled as either “good” or “bad.” Depending on the number of defects or “bad” items found, the entire lot is either accepted or rejected.

Another type of acceptance sampling is called double sampling. This provides an opportunity to sample the lot a second time if the results of the first sample are inconclusive.

In double sampling we first sample a lot of goods according to preset criteria for definite acceptance or rejection. However, if the results fall in the middle range, they are considered inconclusive and a second sample is taken.

In addition to single and double-sampling plans, there are multiple sampling plans. Multiple sampling plans are similar to double sampling plans except that criteria are set for more than two samples. 

What Sampling Plan To I Choose?

The decision as to which sampling plan to select has a great deal to do with the cost involved in sampling, the time consumed by sampling, and the cost of passing on a defective item. In general, if the cost of collecting and inspecting a sample is relatively high, single sampling is preferred.

Operating Characteristic Curves

Different sampling plans have different capabilities for discriminating between good and bad lots. At one extreme is 100 percent inspection, which has perfect discriminating power.

However, as the size of the sample inspected decreases, so does the chance of accepting a defective lot.We can show the discriminating power of a sampling plan on a graph by means of an operating characteristic (OC) curve.

This curve shows the probability or chance of accepting a lot given various proportions of defects in the lot.

Regardless of which sampling plan you select, the plan is not perfect. That is, there is still a chance of accepting lots that are “bad” and rejecting “good” lots.

The steeper the OC curve, the better our sampling plan is for discriminating between “good” and “bad.” In the picture below you can see that the steeper the slope of the curve, the more discriminating is the sampling plan

OC Curves

operating characteristic curve

OC Curves show the probability or chance of accepting a lot. 

For sampling plan to be used effectively there is a small percentage of defects that that the consumer should be willing to accept. This should be clearly defined the contract. This is called the Acceptable Quality Level (AQL) and is generally in the order of 0.5 to 1 percent.

However, sometimes the percentage of defects that passes through is higher than the AQL. Consumers will usually tolerate a few more defects, but at some point the number of defects reaches a threshold level beyond which consumers will not tolerate them.

This threshold level is called the Lot Tolerance Percent Defective (LTPD). The LTPD is the upper limit of the percentage of defective items consumers are willing to tolerate.

Acceptance Sampling Risks

When you make accept or reject decisions using Statistical Quality Control based plans there are risks.

Consumer’s Risk is the chance or probability that a lot will be accepted that contains a greater number of defects than the LTPD limit. This is the probability of making a Type II error—that is, accepting a lot that is truly “bad.” 

Consumer’s risk or Type II error is denoted by beta (B). The relationships among AQL, LTPD, and are shown in the figure below.

Producer’s Risk is the chance or probability that a lot containing an acceptable quality level will be rejected. This is the probability of making a Type I error—that is, rejecting a lot that is “good.” 

It is denoted by alpha (a). Producer’s risk is also shown in in the figure below.

Learn more about alpha and beta risks here.

OC Curve Showing Risks

oc curve producers and consumers risk

OC Curve Producers and Consumers Risk

You can determine from an OC curve what the consumer’s and producer’s risks are. These values should not be left to chance. Rather, sampling plans are usually designed to meet specific levels of consumer’s and producer’s risk.

For example, one common combination is to have a consumer’s risk of 10 percent and a producer’s risk of 5 percent. Many other combinations are possible.

Learn more here.

From Acceptance Sampling to Statistical Quality Control

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