Optimal number of minimal repairs before replacement of a system subject to shocks

Sheu, Shey‐Huei; Griffith, William S.

doi:10.1002/(sici)1520-6750(199604)43:3<319::aid-nav1>3.0.co;2-c

Cited by 92 publications

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“…A more realistic so called imperfect PM model assumes that the system lies somewhere between "as good as new" and its pre-maintenance condition after a PM. The imperfect PM model is more appropriate in studying a system with more general PM activities (more than just replacements) and has been considered by Nakagawa (1979), Sheu and Griffith (1996), Levitin and Lisnianski (2000), and Sheu and Chen (2004). Usually, the PM effect is measured by the updated reduced effective age as shown in Malik (1979), Nakagawa (1980Nakagawa ( , 1988, and Sheu and Chang (2010).…”

Section: Introductionmentioning

confidence: 99%

Optimal preventive maintenance and repair policies for multi-state systems

Sheu

Chang

Chen

et al. 2015

Reliability Engineering & System Safety

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Section: Introductionmentioning

confidence: 99%

Optimal preventive maintenance and repair policies for multi-state systems

Sheu

Chang

Chen

et al. 2015

Reliability Engineering & System Safety

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“…Further, Boland and Proschan (1983) considered periodic replacement of a system and offered sufficient conditions for the existence of an optimal finite period, assuming that the shock process is a non-homogeneous Poisson process and the cost structure does not depend on time. These previous policies have been investigated and extended, such as Nakagawa and Kowada (1983), Nguyen and Murthy (1984), Block et al (1985Block et al ( , 1988, Berg et al (1986), Ait Kadi and Cléroux (1988), Sheu et al (1995), Sheu and Griffith (1996), Sheu (1996Sheu ( , 1998Sheu ( , 1999, Wang and Pham (1999), Chien and Sheu (2006), and Sheu and Chang (2009), among others. Barlow and Hunter (1960) proposed a minimal repair model which restores the system to the functioning state once it fails, but does not improve the overall health condition of the system.…”

Section: Introductionmentioning

confidence: 99%

Optimal age-replacement time with minimal repair based on cumulative repair-cost limit for a system subject to shocks

2011

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An operating system is subject to random shocks that arrive according to a nonhomogeneous Poisson process and cause the system failed. System failures experience to be divided into two categories: a type-I failure (minor), rectified by a minimal repair; or a type-II failure (catastrophic) that calls for a replacement. An age-replacement model is studied by considering both a cumulative repair-cost limit and a system's entire repair-cost history. Under such a policy, the system is replaced at age T , or at the k-th type-I failure at which the accumulated repair cost exceeds the pre-determined limit, or at any type-II failure, whichever occurs first. The object of this article is to study analytically the minimum-cost replacement policy for showing its existence, uniqueness, and the structural properties. The proposed model provides a general framework for analyzing the maintenance policies, and presents several numerical examples for illustration purposes.Ann Oper Res (2011) 186:317-329 S k Arrival instant of the kth shock for k = 1, 2, 3, . . . W i Minimal repair cost due to the ith type-I failure for i = 1, 2, 3, . . . G(w) cdf (cumulative distribution function) of the r.v. (random variable) W i c w Mean cost of W i ; c w = E[W i ] Z j Accumulated repair cost until the j th type-I failure; Z jcdf of the r.v. Z j ; the j -fold Stieltjes convolution of the distribution G with itself M Number of shocks proceeding the first type-II failurē P k , p k sf (survival function), pmf (probability mass function) of M; P k = P (M > k) = Pr{first k shocks are type-I failures}, where the domain ofP k is {0, 1, 2, . . .} and 1 =P 0 ≥P 1 ≥P 2 ≥ · · ·;Pr{a type-I failure when shock k arrives} =P k /P k−1 θ k Pr{a type-II failure when shock k arrives} = 1 − q k T Replacement age of an operating system L Total repair-cost limit B(T ; L, {P k }) s-expected cost rate for an infinite time spanCost of a planned replacement c 1Cost of an unplanned replacement Y Waiting time until the first unplanned replacement (kth type-I failure at which the accumulated repair cost exceeds the pre-determined limit L or first type-II failure) when T = ∞ h(t), H (t) pdf (probability density function), cdf of the r.v. Ȳ H (t) sf of Y , which is 1 − H (t) r H (t) Failure (hazard) rate of Y ; r H (t) = h(t)/H (t) U i Length of successive replacement cycle for i = 1, 2, . . . V iOperational cost over U i D(t) s-expected cost of the operating system over [0, t]

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“…Further, Makabe and Morimura (1963a, 1963b proposed the new replacement model where a system is replaced at n-th failure, and discussed the optimum policy. This model has been generalized by Morimura (1970), Park (1979bPark ( , 1987, Nakagawa (1981Nakagawa ( , 1983, Nakagawa and Kowada (1983), Sheu (1992), Sheu and Griffith (1996), Sheu et al (1995), and .…”

Section: Introductionmentioning

confidence: 99%

Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy

2010

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In this paper, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a system's entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behavior of the assumed system, reflecting the costs of both storing a spare and of system downtime. The optimal age for preventive replacement minimizing that cost rate is derived, its existence and uniqueness is shown, and structural properties are presented. Various special cases are included, and a numerical example is given for illustration. Because the framework and analysis are general, the proposed model extends several existing results.Keywords Preventive replacement policy · Cumulative repair-cost limit · Minimal repair · Random lead time · Spare Notations X Time to failure of a new system f (·)Probability density function (pdf) of the random variable (r.v.) X F (·)Cumulative distribution function (Cdf) of the r.v. X F (·)Survival function (Sf) of the r.v. X, which is 1 − F (·) r(t) f (t)/F (t): failure (hazard) rate function of the r.v. X (t) t 0 r(u)du: cumulative hazard function of the r.v. X X L Lead-time of a new system for replacement l(·), L(·)Pdf, Cdf of the r.v. X L

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Optimal number of minimal repairs before replacement of a system subject to shocks

Cited by 92 publications

References 0 publications

Optimal preventive maintenance and repair policies for multi-state systems

Optimal preventive maintenance and repair policies for multi-state systems

Optimal age-replacement time with minimal repair based on cumulative repair-cost limit for a system subject to shocks

Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy

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