New results for the Brown-Proschan model of imperfect repair

Optimal Preparedness Maintenance of Multi-Unit Systems With Imperfect Maintenance and Economic Dependence

“…It makes each PM a weighted average of perfect PM and minimal PM with weight p [Pham and Wang (1996)]. Details on this treatment method for imperfect maintenance can be found in Bhattacharjee (1987), Brown and Proschan (1983), Fontenot and Proschan (1984), Makis and Jardine (1992). Note that PM of subsystem 0 together with another subsystem between jT's is assumed to be perfect where j = 1,2,3,... .…”

“…Let x be the age of subsystem 0 since last replacement of subsystem 0. This paper investigates the following opportunistic preparedness maintenance policy, modified from the preparedness maintenance model developed by Radner and Jorgenson (1963), based on the above (B-P) shut-off rule by Barlow and Proschan (1975) and Khalil (1985), and the concept of imperfect maintenance [Bhattacharjee (1987), Brown and Proschan (1983), Fontenot and Proschan (1984), Makis and Jardine (1992), Nakagawa (1987), Pham and Wang (1996), Sheu et al (1995), Zheng (1995)] and opportunistic maintenance: maintenance cost is still C 0 i and total maintenance time is woi-This process continues until subsystem 0 gets a perfect maintenance.…”

“…In this paper, imperfect PM is treated in a way that after PM a system is "good as new" with probability p (perfect PM) and is "bad as old" with probability q = 1 -p (minimal PM, 0 < p < 1) [Bhattacharjee (1987), Brown and Proschan (1983), Fontenot and Proschan (1984), Makis and Jardine (1992), Nakagawa (1987), Pham and Wang (1996), Sheu et al (1995), Zheng (1995)]. Note that PM becomes a perfect one when p = 1 and a minimal one when p = 0.…”

“…It usually becomes "younger" than at the time just prior to the tune-up and enters some state between "good as new" and "bad as old". In the recent literature, this kind of maintenance is often called imperfect maintenance [Bhattacharjee (1987), Brown and Proschan (1983), Fontenot and Proschan (1984), Makis and Jardine (1992), Nakagawa (1987), Pham and Wang (1996), Sheu et al (1995), Zheng (1995)]. Generally, imperfect maintenance means any maintenance which makes a system "younger", and results in an improved system operating condition.…”

Multivariate conditional hazard rates and the MIFRA and MIFR properties

“…It is easy to verify (see, e.g., Bhattacharjee (1984» that in the univariate case (n = 1) the stochastic inequality (6.2) holds for all a E (0, 1) if and only if T} is IFRA. A similar result holds also in the general (n~2) case.…”