Systems with different lifetime distributions, associated with increasing, decreasing, constant, and bathtub-shaped hazard rates, are examined in this paper. It is assumed that a failure is only detected if systems are inspected. New approximate solutions for the inspection period and for the expected duration of hidden faults are presented, on the basis of the assumption that only periodic and perfect inspections are carried out. By minimizing total expected cost per unit of time, on the basis of numerical results and a range of comparisons, the conclusion is drawn that these new approximate solutions are extremely useful and simple to put into practice.

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Purpose -The purpose of this paper is to investigate a new sampling methodology previously proposed for systems with a known lifetime distribution: the Predetermined Sampling Intervals (PSI) method. Design/methodology/approach -The methodology is defined on basis of system hazard cumulative rate, and is compared with other approaches, particularly those whose parameters may change in real time, taking into account current sample information. Findings -For different lifetime distributions, the results obtained for adjusted average time to signal (AATS) using a control chart for the sample mean are presented and analysed. They demonstrate the high degree of statistical performance of this sampling procedure, particularly when used in systems with an increasing failure rate distribution. Practical implications -This PSI method is important from a quality and reliability management point of view. Originality/value -This methodology involves a process by which sampling instants are obtained at the beginning of the process to be controlled. Also this new approach allows for statistical comparison with other sampling schemes, which is a novel feature.