Methods of Deferred Sentencing in Testing the Fraction Defective of a Continuous Output

When the output of a continuous process is subjected to a routine test, in which it is observed whether the articles sampled are satisfactory or defective, a clustering of defectives (i.e. the occurrence of several defectives in rapid succession) may be taken as an indication that quality has deteriorated. In Part I inspection schemes of this kind are considered and compared with sequential sampling methods applied to the product after it has been divided into bulks of a suitable size. In Part II it is shown how the operating characteristic of a deferred sentencing scheme can be calculated.

These schemes are, we believe, the only inspection procedures available at present that relate specifically to a continuous output and apply when the inspection test is destructive. They are non‐rectifying.

Mathematically, we are concerned with, among other problems, the frequency of clusters of random points on a line of infinite length.

Most of the work on which this paper is based was carried out by the authors in the Ministry of Supply Advisory Service on Statistical Method (S.R. 17), and their thanks are due to the Director‐General of Scientific Research (Defence) for permission to publish it. Part I and the first section of Part II are by F. J. Anscombe, and the remainder of Part II by H. J. Godwin and R. L. Plackett, as indicated by author's initials.