          What is it: Acceptance sampling is a process that helps to determine whether to accept or reject the sample being observed. Acceptance sampling is a statistical quality control technique, where a random sample is taken from a lot, and upon the results of the sample taken the lot will either be rejected or accepted. A lot is defined as a quantity of product accumulated under uniform conditions. For example, one shift's production from a machine could be considered as a lot. Acceptance sampling, unlike SPC, involves "end-of-line" inspection.

There are two types of sampling methods:

• Attributes sampling
• Variables sampling

There are also two types of reject classification errors:

• Producers errors (Type 1)- rejecting acceptable parts. For item type 1 errors, AQL (Acceptable Quality Levels) is used, which is described as Number of defect percentage allowed in a lot which can still be considered accepted.
• Consumer errors (Type 2) - consumer obtaining defective parts. For item type 2 errors, LTPD (Lot Tolerance Percent Defective) is used, which is the amount of defects that will come with a lot of goods.

Why use it: Acceptance sampling is a compromise between not doing any  inspection at all and 100% inspection. The scheme by which representative samples will be selected from a population and tested  to determine whether the lot is acceptable or not is known as an  acceptance plan or sampling plan. There are two major classifications of acceptance plans: based on attributes ("go, no-go") and based on variables.

Where to use it:

• At any point in production
• The output of one stage is the input of the next

When to use it: When product testing is

• Destructive
• Expensive
• Time Consuming
• Items are delicate

How to use it: Sampling plans can be single, double or multiple.  A single sampling plan for attributes consists of a sample of size n and an acceptance number c.  The procedure operates as follows: select n items at random from the lot. If the number of defectives in the sample set is less than c, the lot is accepted. Otherwise, the lot is rejected. In order to measure the performance of an acceptance or sampling plan,  the Operating Characteristic  (OC) curve is used. This curve plots the probability of accepting the lot (Y-axis) versus the lot fraction or percent defectives.

Attribute sampling is usually based on Poisson statistics, where sample size and acceptance number (maximum number of BAD units in the sample) are specified. This generates an Operating Characteristic (OC) that is a plot of the probability of lot acceptance (or confidence level) vs. percent defective in the total lot from which the sample was randomly selected.

The AQL of a sampling plan is a level of quality routinely accepted by the sampling plan. It is generally defined as that level of quality (percent defective, defects per hundred units, etc.) that the sampling plan will accept 95% of the time. This means lots at or better than the AQL are accepted at least 95% of the time. The AQL can be determined using the OC curve by finding that quality level on the bottom axis that corresponds to a probability of acceptance of 0.95 (95%) on the left axis. Associated with the AQL is a confidence statement one can make. If the lot fails the sampling plan, one can state with 95% confidence that the quality level (defective rate, etc.) exceeds the AQL. In other words, failing the sampling plan demonstrates that the AQL has been exceeded.

The LTPD of a sampling plan is a level of quality routinely rejected by the sampling plan. It is generally defined as that level of quality (percent defective, defects per hundred units, etc.) that the sampling plan will accept 10% of the time. This means lots at or worse than the LTPD are accepted at most 10% of the time. In other words, they are rejected at least 90% of the time. The LTPD can be determined using the OC curve by finding that quality level on the bottom axis that corresponds to a probability of acceptance of 0.10 (10%) on the left axis. Associated with the LTPD is a confidence statement one can make. If the lot passes the sampling plan, one can state with 90% confidence that the quality level (defective rate, etc.) is below the LTPD. In other words, passing the sampling plan demonstrates that the LTPD has been meet.

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