Inspection Policies When Duration of Checkings is Non-Negligible

Inspection policy models deal with stochastically failing systems, in which failure is detected by inspection only. Previous authors assume that the time required for checking is zero, while the current study deals with preparedness models when duration of checking is non-negligible. Costs are introduced for checking, unknown lost time and repairing (or replacing) the failed system. Furthermore, uncertainty probabilities associated with inspections are introduced. Optimal checking policies are calculated for three different objective functions: expected loss per cycle, per time unit and per unit of good time. The models are solved by differentiation and by dynamic programming. Numerical results indicate that the optimal policy for IFR distributions is characterized by decreasing checking time intervals, with a marked difference only between the first and second intervals.