On the probability distribution of total quality under sublot inspection and process restoration

A lot of N items is produced on a randomly degrading facility. The lot is split into inspection sublots for detection of faulty items, and the process is returned to as-new condition after each sublot. For exponentially distributed failure time the mean, variance and probability distribution of the total number of good items are considered. Stochastic optimality properties are developed for the equal-sublots policy in both the exponential and general failure time cases.