Imperfect Inspection in a Multistage Production Process

The probabilistic behavior of good and defective in-process units in a multistage production process is explored, under the assumption of imperfect inspection. For binomial processing and inspection, the joint distribution of the two state variables at each stage is shown to be the product of two nonindependent binomial distributions. Initial simplifying assumptions about inspection policy, processing losses, and additional information are relaxed, and the modified forms of the resultant joint binomial distributions are presented.