zbMATH — the first resource for mathematics

Inspection policies: Comparisons and modifications. (English) Zbl 0667.90040
We discuss: (1) Comparisons between optimum and nearly optimum inspection policies: (2) Inspection policies for modified inspection models.
In Section 2, we numerically compare the optimum inspection policy by R. E. Barlow, L. C. Hunter and F. Proschan [J. SIAM 11, 1078- 1095 (1964; Zbl 0116.361)] and R. E. Barlow and F. Proschan [Mathematical theory of reliability (1965; Zbl 0132.393)] with the nearly optimum ones by the author [IEEE Trans. Reliab. R-33, 277-279 (1984; Zbl 0552.90034)], A. Munford and A. Shahani [Oper. Res. Quart. 23, 373-379 (1972; Zbl 0238.90023)] and T. Nakagawa and K. Yasui [J. Oper. Res. Soc. 31, 851-853 (1980; Zbl 0448.90023)], assuming a gamma lifetime distribution.
In Section 3, we treat a modified inspection model taking account of two kinds of imperfect inspection probabilities, obtain the structure of the optimum inspection policy, and discuss the optimum policy minimizing the total expected cost up to the detection of the failure. The numerical examples are presented.
In Section 4, we consider another modified inspection model with imperfect inspection probability and checking time. We obtain the nearly optimum inspectin policy which minimizes the nearly total expected cost up to the detection of the failure.

90B25 Reliability, availability, maintenance, inspection in operations research
Full Text: DOI EuDML