A double sampling plan for tablet acceptance is presented and analyzed. T h e answers to three fundamental questions are presented: (a) H o w will the plan operate with respect to batches of tablets which vary i n quality from batch to batch? (b) What will be the quality of tablets passed into stock by the plan? ( c ) H o w much inspection o n the average will the plan require?
N THE PRODUCTION of coated aspirin tablets intended t o be used for sustained-release action, lot sizes of 500 tablets were produced. A double sampling plan was selected (nl = 50, n2 = 100, CI = 0, c? = 2). T h e authors were interested in analyzing t h e ability of this plan with respect to the three fundamental features listed below.
How will the plan operate with respect to batches of tablets which vary in quality from batch t o batch? (b) What will be the quality of tablets passed into stock by the plan?
(c) How much inspection on the average will the plan require?
The first question is answered b y the operating characteristic (OC) curve for the plan. The second question is answered b y t h e average outgoing quality (AOQ) curve for the plan and the third question by t h e average sample number (ASN) curve and the total amount of inspection (TAI) curve for the plan. This paper is intended to show how to construct, by approximate methods, these curves for our double sampling plan.
Pa(
,002) = ,905 + .090( ,819 + ,164) + .005( ,819) = ,998 Po( .005) = ,779 + .195( ,607 + .303) + .024( ,607) = ,971 Po( ,006) = ,741 + .222( .549 + ,329) + .033(. 549) = ,954 Po( .01) = .607 + .303( .368 + ,368) + .076( ,368) = ,858 Pa( .02) = ,368 + .368(. 135 + .271) + .184(. 135) = .542 Po( .03) = ,223 + .335( ,050 + ,149) + .251( ,050) = ,302 Po( .04) = ,135 f .271( ,018 + .074) + .271( ,018) = .165 Po( ,048) = ,091 -I-.218(.008 + ,040) + .261(.008) = ,103 Pa( .05) = .082 + .205( .007 + ,034) + .257( ,007) = ,092 Pa( .06) = .050 + .149(.002 + .015) + .224( ,002) = ,053 Pa(.07) = ,030 + .106(.001 + ,006) + .185(.001) = ,031 Po( .08) = ,018 + .074( .OOO + .003) + .