To determine the optimal production run length in an imperfect production system,
Tseng [3] developed an on-line preventive maintenance (PM) mechanism that reduces the
number of nonconforming outputs of a production run length. The PM mechanism obtains
the optimal production run length by minimizing the total cost per unit time, which includes
the costs of setup, inventory holding, process maintenance and nonconforming products. The
optimal number of PM events for a given production run length was further studied by Kim
et al. [4] to establish an efficient procedure for determining the optimal production run
length. Note that both Tseng [3] and Kim et al. [4] are an extension of the study by Lee and
Rosenblatt [5], where the elapsed time until the process shifts from an in-control state to
an out-of-control state is assumed to be an exponential distribution. They found that when
the elapsed time for the process to stay in an in-control state was large, an approximate