A binomial approximation of lot yield under Markov modulated Bernoulli item yield

摘要

The existing literature that models item-by-item production yield as a Bernoulli process assumes that the intraperiod likelihood of producing an acceptable item is stationary. We investigate the stochastic process that results from relaxing this assumption to account for system deterioration during each production run. More specifically, we consider a Bernoulli yield model with a non-stationary parameter that depends on the deterioration level of the system, which evolves according to a discrete-time Markov chain. For tractability reasons, we construct a simple binomial approximation of the non-stationary process, and compare the two yield distributions both analytically and numerically. Our results suggest that the approximation performs well, even when the deterioration occurs relatively fast, which serves to validate existing (and future) decision models that impose the stationarity assumption.