Estimation of Batch Quality

A CERTAIN number of defectives, c, is observed in a sample of n articles drawn at random from a large batch. Nothing else is known about the batch. What inferences can be drawn as to the true but unknown proportion Q of defectives in the lot? In his book An Engineers' Manual of Statistical Methods, Col. L. E. Simon gives several charts which help to answer this question. The basic assumption made is that before sampling one “lot‐fraction‐defective” is as likely as another. The charts are based on the incomplete ?‐function ratio. They make no assumption of homogeneity. From these charts the accompanying alignment charts have been constructed. The degree of accuracy is not, of course, as high as in Simon's charts, but it is thought that it will be high enough for practical purposes.