A METHOD OF SAMPLING INSPECTION 619 



inspection procedure, such as single sampling, double sampling, 

 multiple sampling, etc., which allow the examination of only one 

 sample, of two samples, or of more than two samples before a pre- 

 scribed disposition of the entire lot is made. For each of these general 

 methods, different combinations of sample sizes and acceptance 

 criteria can be found which will satisfy the first requirement. We now 

 prescribe that any lot which fails to pass the sampling requirements 

 shall be completely inspected. Under this condition, one of the above 

 mentioned combinations will give a lesser amount of inspection than 

 the rest. Since a major cost item is that associated with the amount 

 of inspection, we will carry through in detail the problem of finding 

 the combination which will result in the minimum amount of in- 

 spection for one simple general method of inspection. 



Single Sampling Method of Inspection 



Attention is now directed to what is termed the Single Sampling 

 method of inspection, which involves the following procedure: 



(a) Inspect a sample. 



{b) If the acceptance number for the sample is not exceeded, accept 



the lot. 

 (c) If the acceptance number is exceeded, inspect the remainder of 



the lot. 



The term "Acceptance Number" is introduced to designate the 

 allowable number of defects in the sample. 



For this procedure, the first requirement reduces the problem to 

 one which can be solved readily by determining probabilities associated 

 with sampling from a finite lot containing the tolerance number of 

 defects. For any sample size, there is a definite probability of finding 

 no defects, of finding exactly one defect, exactly two defects, etc. 

 If, under the above conditions, the acceptance number were 1, for 

 example, there is one value of sample size such that the probability 

 of finding one or less defects is equal to the value of the Consumer's 

 Risk specified. Since a lot will be accepted if the observed number 

 of defects does not exceed the acceptance number, the probability 

 of finding one or less defects in a sample selected from a lot of tolerance 

 quality is the risk of accepting any lot of tolerance quality submitted 

 to the inspector. It follows that the risk of accepting a lot of worse- 

 than-tolerance quality is less than the Consumer's Risk just defined. 

 If the producer gets into trouble and begins to submit lots of un- 

 satisfactory quality, the consumer has the assurance that his chance 

 of getting them will not exceed this figure. In fact, the worse the 

 quality, the less will be their chance of passing without a detailed 



