626 BELL SYSTEM TECHNICAL JOURNAL 



inspected, such as the degree of control exerted by the producing 

 agencies, or the protective measures which precede or follow the 

 inspection step in question. For any Consumer's Risk value, sets of 

 charts similar to Figs. 2, 3, and 4 may be constructed. 



Other Methods of Inspection 



The above detailed discussion has been limited to one simple 

 method of inspection. Single Sampling, in order to show how certain 

 concepts and principles may be applied with the aid of sampling 

 theory. The same principles are readily extended to a plan of double 

 sampling or of multiple sampling in which cases a second sample may 

 be examined if the first fails or a third, fourth, etc. examined if the 

 preceding samples fail, before resorting to a detailed inspection of 

 the remainder of a lot. As a matter of fact, for given values of 

 tolerance and risk, the minimum average amount of inspection per 

 lot will be somewhat less for plans which permit the examination of 

 more than one sample before detailing, but when consideration is 

 given to the costs associated with interruption of work, extraction of 

 additional random samples, inconveniences or difficulties in handling 

 the routine called for, etc., it has not been found economical in general 

 to examine more than two samples from any lot. 



It may be well to point out that other basically different require- 

 ments may be chosen for setting up economical sampling inspection 

 plans. For example a satisfactory method has been devised to meet 

 the following requirements: 



(1) A limiting value to the average per cent defective after in- 



spection. 



(2) A minimum amount of inspection for product of process average 



quality. 



This method has been found of value in continuous production where 



the inspection is intended to serve as a partial screen for defective 



units. It differs from that described above in that it provides a 



fixed limit to the average quality of product after inspection rather 



than a limit to the quality of each individual lot. 



The solution of such problems, which employ probability theory 



as an aid, always demands a concise statement of the conditions and 



the specification of numerical requirements which the inspection must 



satisfy. 



MATHEMATICAL APPENDIX 



The problem considered is to minimize the average number of 

 pieces inspected per lot in Single Sampling Inspection. The method 

 and equations developed below may be extended to problems involving 



