Technically optimal inspection policy with arithmetical adaption

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 which can be applied without knowing λ. In order to maximize the number of conforming items per time unit perfect inspections and renewals are performed. The length of the inspection interval is described by an arithmetical sequence and changes by the time depending on perceived assignable causes. Optimal adaptive control plans provide nearly the same performance as in the case when λ is known.