SAMPLING INSPECTION TABLES 21 



To find: Values of n and c that will minimize /, the average number of pieces 



inspected per lot for product of process average {p) quality. 

 The average number of pieces inspected per lot (/) for product of p quality 

 is given by 



/ = « + (-V - n) (1 - Pa), (8) 



where Pa is given by equation (5). Substituting the approximation of equation 

 (5') gives 



( m=c \ 



1 - Z ^-.p» ) 

 m=0 / 



(80 



/ is a specific value of / and is obtained from equation (8') by using p = p. 

 The value of c that makes / a minimum may be read from the chart of Fig. 2 



P 

 of the previous paper,^ which uses coordinates of M = ptN and k = ~ and is 



Pt 



based on Pc = 0.10. The corresponding sample size n may be read from Fig. 3 



of the previous paper^ (based on equation (2')), from Fig. 6 if appropriate, or by 



direct computation from equation (2), (2'), or (2"), using Pc = 0.10. 



Double Sampling 



Given: Lot size (iV), lot tolerance fraction defective (pt), Consumer's Risk 



(Pc = 0.10), process average fraction defective (p). 

 To find: Values of «i, 112, ci, C2 that will minimize /. 



The average number of pieces inspected per lot (/) for product of p quality 

 is given by 



1 - Z) ^-■P"! ) + (^ - «1 - «2)(1 - Pa), 



TO=0 / 



(9) 



where Pa is determined from equation (6')- 



7 is a specific value of / and is obtained from equation (9) by using p = p. 

 As outlined on page 11, the pair of values of ci and C2 that makes / a minimum 

 is determined by trial and error, conditioned by the choice that the Consumer's 

 Risk of 0.10 be divided between the first and second samples so that the "initial 

 risk" for the first sample is 0.06. Figure 7 gives such pairs of ci, C2 values, cor- 



P 

 responding to values M = piN and k = - . 



Pt 

 For the selected apportionment of Consumer's Risk, the sample sizes «i and 

 112 may be determined approximately from the following equations, which are 

 based on equation (1'), 



m=ci / \M-m /„.\m 



o.o6."gc:(.-'^)''""('^)" 



(10) 



) 



Figure 8 based on these equations gives ptn\ and pi(ni + «2) values associated with 

 c\ and C2 for a given value of M = piN , and thus provides the desired values of 

 «i and ti2. 



