Optimal production correction and maintenance policy for imperfect process

This study considers imperfect production processes that require production correction and maintenance. Two states of the production process are performed, namely: the type I state (out-of-control state) and the type II state (in-control state). At the beginning of the production of the each renewal cycle, the state of the process is assumed not always to be restored to “in-control”. The type I state involves the 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 “in-control”. After N + 1 type I states, the operating system must be maintained and returned to the beginning condition. The mean loss cost due to reproduction through production correction per the total expected cost until the N + 1 type I states are entered successively is determined. The existence of a unique and finite optimal N for an imperfect process under certain reasonable conditions is shown. A numerical example is presented.