Statistical inference for two Markov binomial models with applications

Disturbance models, involved in Engineering Process Control (EPC) and Statistical Process Control (SPC), take into consideration an additional parameter, the probability of a jump in the process parameter in any time period. Corrective actions are necessary to bring the process back on target. In a tuning procedure, one can deal with permanent corrective actions (settings), or with provisional ones (adjustments). Tuning r machines can be modeled through some binomial Markov chains, with the transition matrix depending on the probability that a disturbance occurs. Using two such models, we construct consistent estimators for the probability that a disturbance occurs at any period of time.