Optimal number of production corrections before maintenance of imperfect production processes

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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.