16 BELL SYSTEM TECHNICAL JOURNAL 



sampling frequently throw the advantage to single sampling. Among the 

 added costs are those associated with interruption of work, extra handling 

 of product, etc. incidental to the selection of an independent second sample. 

 Aside from these considerations, it is common to find a psychological prefer- 

 ence for double sampling. This appears to be associated with the tendency 

 to look with favor on any plan that permits a "second chance" to make 

 good, particularly when an initial failure is of a marginal character. 



Given a specific problem of replacing 100% screening inspection by a 

 sampling inspection, the first step is to decide on the type of protection 

 desired, to select the desired limit of per cent defective — lot tolerance or 

 AOQL value — for that t3^e of protection, and to choose between single and 

 double sampling. This results in the selection of one of the appended 

 tables. The second step is to determine whether the quality of product is 

 good enough to warrant the introduction of sampling. The economies of 

 sampling will be realized, of course, only insofar as the per cent defective in 

 submitted product is such that the acceptance criteria of the selected sam- 

 pling plan will be met. A statistical analysis of past inspection results 

 should first be made, therefore, in order to determine existing levels and 

 fluctuations in the per cent defective for the characteristic or the group of 

 characteristics under consideration. This provides information with 

 respect to the degree of control of quality as well as the usual level of per 

 cent defective to be expected under existing conditions. From this and 

 other information is to be determined a value for the "process average" 

 per cent defective that should be used in applying the selected sampling 

 table, if sampling is to be introduced. 



The determination of the process average per cent defective is an engi- 

 neering problem, essentially one of prediction, in which use is made of all 

 available information — knowledge of manufacturing conditions past and 

 anticipated, judgment as to what periods of the past, if any, may be taken 

 as representative of the future, results of analyses showing uniformity and 

 level of per cent defective for such past periods, etc. The application of 

 "control chart" analysis '^ to past data is especially recommended.* If 



* The following procedure has been used with general success. Tabulate the observed 

 values of fraction defective, p, for at least 25 immediately preceding lots (or groups of 

 lots, say by days or weeks, if p is very small), excluding lots that are nonrepresentative 

 for known reasons, and apply the control chart test to the observed values of p. If the 

 data show statistical control, and if there are grounds for believing that future manu- 

 facturing conditions will be essentially the same as those of the past, use the average of 

 the observed values of p as the process average value, p. If lack of statistical control 

 is shown, replace values of p that are beyond ±3ff control hmitsi- ^ by values correspond- 

 ing to ±2(7 control hmits (where cr = Vp (1 — p)/n). Compute a corrected average 

 value of p, in which the individually corrected values are used in place of the correspond- 

 ing observed values. Unless other conflicting evidence predominates, use this corrected 

 value as a tentative process average value, until such time as a revision appears war- 

 ranted on the basis of new evidence. 



