Motivation for the use of discrete distributions in quality assurance

摘要

By considering a finite population ofNitems andSdefects, and observing the way defects should be distributed among the items we provide an interesting motivation to the bionomial, negative binomial (geometric) and Poisson distributions for the number of defects in a sample from a production line. The idea is to find out, from physical considerations about the production process, which configurations of defects in items are equally likely. A uniform distribution is assessed on the space generated by these configurations. Then, a distribution for a finite, and subsequently for an infinite population of items is derived.