Economically optimal inspection policy with geometric adaptation

A process is considered whose quality deteriorates according to a constant failure intensity λ. As, in practice, it can be difficult to estimate the true value of λ, the purpose of this paper is to present a strategy that can be applied without knowing λ. In order to maximise profit per item, perfect inspections and renewals are performed. The length of inspection interval is described by a geometric sequence and changes in time, depending on perceived assignable causes. Optimal adaptive control plans provide nearly the same profit per item as in the case when λ is known.