Acceptance sampling is performed on goods that already exist to determine what percentage of products conforms to specifications. These products may be items received from another company and evaluated by the receiving department, or they may be components that have passed through a processing step and are evaluated by company personnel either in production or later in the warehousing function.
A single sampling plan is defined by n and c, where n is the number of units in the sample and c is the acceptance number. The size of n may vary from one up to all the items in the lot, denoted as N, from which it is drawn. The acceptance number c denotes the maximum number of defective items that can be found in the sample before the lot is rejected. Values for n and c are determined by the interaction of four factors that quantity the objectives of the product’s producer and its consumer. The objective of the producer is to ensure that the sampling plan has a low probability of rejecting good lots. Lots are defined as high quality if they contain no more than a specified level of defectives, termed the Acceptable Quality Level (AQL). The objective of the consumer is to ensure that the sampling plan has a low probability of accepting bad lots. Lots are defined as low quality if the percentage of defectives is greater than a specified amount, termed Lot Tolerance Percent Defective (LTPD). The probability associated with rejecting a high quality lot is denoted by the Greek letter alpha (α) and is termed the producer’s risk. The probability associated with accepting a low quality lot is denoted by the letter beta (β) and is termed the consumer’s risk. The selection of particular values for AQL, α LTPD, and β is an economic decision based on a cost trade-off or, more typically, on company policy or contractual requirements.
