Downloaded from https://www.everyspec.com nomial Probability Distribution" in available. Whenever n : 0.IN and k 20 and p' :5 per- *o cent, use is made of the Poisson distribution, which may be used as a distribution in its own - . . ... . right, or as a good approximation of the bi- - nomnial. T io Using the Poisson distribution, the probability -- - of acceptance is given by jg - - Pa e- 1 ' 5 t. e-15 1 . 5 + e'"1".51 2 /. i + e-1.51.53/6 + e-.151.54/24 fiL.T.P.O 1s0 This is much easier to calculate. Also, tables of probabilities of accentance for various values I of np' are to be found in any standard text on quality control.
(The tables use p' as the frac- p 1 tion defective.) oL4 - - _s -I 0 6 C is Ito0 PENCI#T OCPFCTVE It should be noted that the hypergeometric and Flure 5-1. Typical Operatowg Characteristic binomial probabilities are based on a fixed lot (OC) curve size, while use of the Poisson distribution as- sumes an infinite lot size. Since in most ap- purely arbitrary. Plans outlined in MIL-STD- plications in Ordnance the actual size of the lot 105A are based on acceptance of AQL product is indeterminate at the time the sampling plan of quality from 88 percent to 99 percent of the is developed, the Poisson is nearly always used.
time, with corresponding producer's risks of For further study, reference is made to "Sta- 12 percent and 1 percent. tistical Quality Control" by Grantor "Engineer- ing Statistics and Quality Control" by Burr. On the other hand, the Lot Tolerance Percent Defective (LTPD) is the quality, expressed in The 0 curve is a plot of percent defective ver- terms of percent defective, that is considered sus probability of acceptance for a egiven sample unacceptable and which will be rejected most of i the time. The consumer's risk (iP) is the prob- Sof n size and acceptance numbor of c defectives.
tetm.Tecnue' ik()i h rb Thus, for any given percent defective (normal- ability of accepting material LTPD quality. In Tpractice, 8 usually is given a value of 0.1, or ly the abscissa), the probability that a lot of 10 percent, but other values may be given if this quality will be accepted may be found. Fig- cosiered desirabe. ure 5-1 is a plot of a typical OC curve. The discriminatory power of a plan cannot be Terms frequently used to indicate the charac- determined merely by knowing the AQI,.
The teristics of a plan, or used as an index to a proximity of the AQI, and LTPD of a plan in- series of plans, can best be indicated by ref- dicates its ability to distinguish between good erence to the OC curve. The term used most and bad quality. This is reflected by a steep often is Acceptance Quality Level (AQL). The OC curve. A tight AQL may not offer sufficient AQL represents that quality, expressed in terms protection if the LTPD is poor. of percent defective, which is considered ac- ceptable and which will be accepted most of the 5-6. The Average Outgoing Quality (AOQ) is the time.
The probability of not accepting material average quality of a succession of lots which of this level of quality is called the producer's have been accepted. If the rejected lots are risk (a). In standard practice it is customary not resubmitted for inspection, then, disre- to base the AQL on a probability el acceptance garding the removal of defectives found in the of 95 percent, with a producer's risk of rejec- samples, the average quality of the lots ac- tion of 5 percent. However, these figures are cepted is the same as the quality of the lots 3 I