28 BELL SYSTEM TECHNICAL JOURNAL 



k values. Corresponding to if = 21 , k = 0.074, read 

 Ci = 0, C2 = 2. Hence the first choice was not the best. 



Step 3 — Similar to Step 1. Consult work chart, Fig. 10. 

 For ci = 0, C2 = 2, corresponding to pL = 0.01, read 

 Pt = Ml. 



Step '?— Similar to Step 2. M = ptN = .047 (500) = 



P 

 23.5; k = — = 0.085. Consult Fig. 7 and corresponding 

 pi 



to M = 23.5, k = 0.085, read ci = 0, C2 = 2. This agrees 



with the choice in Step 3 and gives desired solution. 



Step 5 — To determine «i and ?Z2 for Ci = 0, C2 = 2. On 

 Fig. 8, corresponding to M = 23.5, for ci = 0, read pmi 

 = 2.67 and for C2 = 2, read pt («i + n^) = 5.60. Since 

 per Step 3, pt = .047, m = 57, m + «2 = 119 and H2 = 62. 



Sampling Plan, ni = 57, n^ = 62, Ci = 0, C2 =2. (Round- 

 ing these values of n to the nearest 5 in accordance with the 

 practice used in preparing the tables, gives «i = 55, 

 ni + fV2 = 120, «2 = 65, the values shown in Table DA-1 

 for N = 401-500, p = 0.21-0.40%.) 



Nature and Magnitude of Errors 



Each sampling plan (combination of n and c values for single sampling, and of 

 ni, iH, ci and ci values for double sampling) in the tables constitutes a solution 

 for a range of process average values and a range of lot sizes. The following 

 paragraphs give information regarding the magnitude of errors, associated with 

 these solutions, that may be present because of the following two factors: 



(1) Approximate equations and curves derived therefrom were used in place of 

 exact equations over most areas of the tables, in order to minimize computa- 

 tive effort. 



(2) The sample sizes, «i and ni + tii, listed in the tables represent computed 

 values rounded to the nearest unit for n = 50 or less, rounded to the nearest 

 5 for 50 < « < 1000, and rounded to the nearest 10 for n > 1000. 



Effect of Approximations — The percentage error in the Consumer's Risk value 

 of 0.10, corresponding to lot tolerance values listed in the tables, attributable to 

 the use of approximate equations and curves derived therefrom, is on the 

 average about 3% and should not exceed 7%. The percentage error in the AOQL 

 values, listed in the tables, attributable to the use of approximate relations 

 involving the Poisson exponential rather than the binomial distribution, is on 

 the average about 4% and should not exceed 12%. In a large number of ex- 

 ploratory checks for both single and double sampling, it was found in every instance 

 that the Consumer's Risk and the AOQL values derived from approximate 

 equations were larger than the corresponding exact values. The largest error ob- 

 served in the Consumer's Risk for single sampling occurred when, instead of 0.10, 

 the exact relation gave a value of 0.0937. Similarly the largest error in the AOQL 

 occurred in single sampling when, instead of 0.0883, the exact relation gave a value 

 of 0.0786. The observed errors in double sampling were of the same order of 

 magnitude. 



