A Variational Approach to Inspection Programs of Equipment Subject to Random Failure

摘要

A method for determining optimal inspection schedules of equipment is discussed, in which failures of equipment are detected only by inspection. The inspection density function, which generates inspection schedules, is employed in a minimization problem. Two types of objective are considered: the expected cost per cycle, and the expected cost per unit time. An optimal inspection density function is derived by the variational method. The proposed method can generate optimal inspection schedules when failure distributions of equipment are completely unknown. Optimal inspection density functions and optimal sequences of inspection times are obtained explicitly for some cases that failure distributions are completely unknown.