Availability and cost functions for periodically inspected preventively maintained units

Unavailability and cost rate functions are developed for components whose failures can occur randomly but they are detected only by periodic testing or inspections. If a failure occurs between consecutive inspections, the unit remains failed until the next inspection. Components are renewed by preventive maintenance periodically, or by repair or replacement after a failure, whichever occurs first (age-replacement). The model takes into account finite repair and maintenance durations as well as costs due to testing, repair, maintenance and lost production or accidents. For normally operating units the time-related penalty is loss of production. For standby safety equipment it is the expected cost of an accident that can happen when the component is down due to a dormant failure, repair or maintenance. The objective of maintenance optimization is to minimize the total cost rate by proper selection of two intervals, one for inspections and one for replacements. General conditions and techniques are developed for solving optimal test and maintenance intervals, with and without constraints on the production loss or accident rate. Insights are gained into how the optimal intervals depend on various cost parameters and reliability characteristics.