Inspection Errors for Attributes in Quality Control

Every book should have a motivation and a goal. We would like to share with our readers some reasons which have led us to allot a considerable part of our time and effort to the production of this monograph. We believe this book to originate from two 'godfathers'. The first took the form of the following, apparently straightforward, problem posed to us in 1979 by Horton L. Sorkin (at that time in the Department of Accounting, University of Maryland at College Park). 'There are N accounts, D with mistakes and N - D mistake-free. The probability that an accountant detects that an account is erroneous is p ( < 1). The accountant checks n ( < N) accounts, chosen at random. What is the probability that he will find Z of them to be erroneous?' This simple question, which H. L. Sorkin had solved a few years earlier in his PhD dissertation, leads to a compound distribution which had not (to our knowledge) been discussed heretofore in the statistical literature. Our interest was aroused by this, and we carried out a further literature search, and found that, although inspection error had indeed appeared in quality control literature during the previous twenty years or so, distributional aspects had been, by and large, neglected.