Overview

Failures of units are roughly classified into two failure modes: catastrophic failure in which a unit fails suddenly and completely, and degraded failure in which a unit fails gradually with time by its performance deterioration. In the former, failures during actual operation might sometimes be costly or dangerous. It is an important problem to determine when to replace or preventively maintain a unit before failure. In the latter, maintenance costs of a unit increase with its age, and inversely, its performance suffers some deterioration. In this case, it is also required to measure some performance parameters and to determine when to replace or preventively maintain a unit before it has been degraded into failure state.

In this chapter, we consider the replacement of a single unit with catastrophic failure mode, where its failure is very serious, and sometimes may incur a heavy loss. Some electronic and electric parts or equipment are typical examples. We introduce a high cost incurred for failure during operation and a low cost incurred for replacement before failure. The replacements after failure and before failure are called corrective replacement and preventive replacement, respectively. It is assumed that the distribution of failure time of a unit is known a priori by investigating its life data, and the planning horizon is infinite. It is also assumed that an operating unit is supplied with unlimited spare units. In Section 9.4 we discuss the optimization problem of maximizing the mean time to failure in the case...