Extended optimal age-replacement policy with minimal repair of a system subject to shocks

Chien, Yu‐Hung; Sheu, Shey‐Huei

doi:10.1016/j.ejor.2005.01.032

Cited by 75 publications

(23 citation statements)

References 20 publications

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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: 96%

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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Section: Introductionmentioning

confidence: 96%

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

2011

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“…For the time-based policies, the decision rule mostly focuses on the lifetime models and more precisely on the expected lifetime distribution of the system; see for instance Kumar and Westberg (1997), Chien and Sheu (2006), Chang, Sheu, and Chen (2013), Wang and Pham (1999), Yeh, Chang, and Lo (2011), You, Li, andMeng (2011), Sheu, Chen, Chang, andZhang (2013) and Chang, Sheu, Chen, and Zhang (2011).…”

Section: Introductionmentioning

confidence: 99%

Condition-based maintenance policies for a combined wear and shock deterioration model with covariates

Zhu¹,

Fouladirad²,

Bérenguer³

2015

Computers & Industrial Engineering

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“…The choice of these two possible actions (minimal repair or replacement) depends on the age of that unit. Their systematic study of the age-replacement policy is further developed and extended in Berg [3], Berg and Epstein [4], Ingram and Scheaffer [15], Osaki and Nakagawa [19], Sheu et al [27], Sheu [24], Sheu and Chien [25], Chien and Sheu [13], and Chien et al [14], among others. Another well-known preventive maintenance (PM) policy is the classical block-replacement policy, where an operating system is replaced by a new one at times kT (k ¼ 1; 2; 3; .…”

Section: Introductionmentioning

confidence: 99%

Extended optimal age-replacement policy with minimal repair of a system subject to shocks

Cited by 75 publications

References 20 publications

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

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

Condition-based maintenance policies for a combined wear and shock deterioration model with covariates

A general age-replacement model with minimal repair under renewing free-replacement warranty

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