Optimal number of production corrections before maintenance of imperfect production processes

This investigation considers imperfect production processes that require production correction and maintenance. The two states of the production process are the type I state (out-of-control state) and the type II state (in-control state). At the beginning of production of each renewal cycle, the state of the process is assumed not always to be restored to “in-control”. The type I state involves adjustment of the production mechanism, whereas the type II state does not. Production correction is either imperfect; worsening a production system, or perfect, returning it to the initial conditions. After N+1 type I states, the operating system must be maintained and returned to the initial condition. The mean cost per good item until the first successive N+1 type I states is determined. The existence of a unique and finite optimal N for an imperfect process under certain reasonable conditions is shown. Finally, a numerical example is presented.