Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 34506, 11 pages

New approximate solutions per unit of time for periodically checked systems with different lifetime distributions

J. Rodrigues Dias

Department of Mathematics, University of Évora, Évora 7000, Portugal

Received 26 October 2005; Revised 19 September 2006; Accepted 24 September 2006

Copyright © 2006 J. Rodrigues Dias. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.