New failure and minimal repair processes for repairable systems in a random environment

Hwan, Ji; Finkelstein, Maxim

doi:10.1002/asmb.2331

Cited by 5 publications

(6 citation statements)

References 26 publications

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“…Therefore, in order to compute the 𝜒 2 l in Equation ( 8) we were left with the effective multinomial sizes m (1) + = 52 − 4 = 48, m (2) + = 33, and m (3) + = 22. For the three time periods considered we observed counts m (1) = (8,17,12,11), m (2) = (5,11,16), and m (3) = (11,11), resulting in estimates of the probabilities under order restriction of p(1) . = (0.167, 0.278, 0.278, 0.278), p(2) .…”

Section: Different Truncation Timesmentioning

confidence: 99%

“…10 For criticism to the usual MR concept, see, for instance, Cha and Finkelstein. 11,12 More recently, however, it has been realized that the assumptions of MR or PR may be too strong for many practical situations. This led to the introduction of imperfect repair (IR) models, whereby one or more additional parameters account for the effect of repair actions over the future reliability of the system.…”

Section: Introductionmentioning

confidence: 99%

“…For examples of these approaches, see, among others, Barlow and Hunter, 1 Phelps, 2 Barlow and Proschan, 3 Zhao and Xie, 4 Sen and Khattree, 5 Park et al, 6 Wang, 7 Oliveira et al, 8 Dauxois and Maalouf 9 or the book by Rigdon and Basu 10 . For criticism to the usual MR concept, see, for instance, Cha and Finkelstein 11,12 …”

Section: Introductionmentioning

confidence: 99%

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Nonparametric significance tests for imperfect repair

Gilardoni

Colosimo

Toledo

et al. 2022

Appl Stoch Models Bus & Ind

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Given the failure history for K ≥ 2 independent and identical repairable systems, a nonparametric procedure is presented to test the null hypothesis of minimal repair (MR) against the alternative of imperfect repair. The main idea is that, under non-harmful (harmful) repair, systems that failed later (earlier) are more reliable than those that have failed (later). This fact allows one, at any moment in time, to rank the systems from more to less reliable and, hence, to define a vector that counts how many times the system ranked r failed. When all the systems are time-truncated at the same time T, it is shown that, under the null hypothesis of MR, the vector of counts follows a multinomial distribution with class probabilities p r = K −1 for r = 1, … , K. The test proceeds by computing a chi-bar squared test statistic similar to the one used to test one-sided alternatives in the multinomial setup, which allows us to compute p-values using either asymptotic theory or a straightforward Monte Carlo simulation using the null multinomial distribution. Extension to the case of different truncation times is also discussed. The procedure is applied to two real datasets regarding equipment used in the mining industry. K E Y W O R D Sas-bad-as-old, as-good-as-new, chi-bar squared, minimal repair, repairable systems

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Section: Different Truncation Timesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonparametric significance tests for imperfect repair

Gilardoni

Colosimo

Toledo

et al. 2022

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

show abstract

“…Al-Chalabi (2022) developed a cost minimization model to optimize the lifetime of a drill rig used in Tara underground mine in Ireland, such that the model can be used to estimate the economic replacement time of fixable instrument applied in the mining and other production industries. Cha and Finkelstein (2019) proposed a novel sort of fix-up known as conditional statistical minimal repair, and their methodology extends to the corresponding minimal repair procedures for systems operating in a random environment. Chang and Chen (2018) discussed that effective replacement policies should be collaborative once data are gathered from time of operation, mission lengths, fix-up, and maintenance triggering approaches.…”

Section: Introductionmentioning

confidence: 99%

Assessment of Some Proposed Replacement Models Involving Moderate Fix-Up

Waziri

Yakasai

2022

JCCE

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Among all reasonable dynamic replacement strategies, the age replacement strategy is the best. Furthermore, when compared to optimal replacement time of the other alternative formations, the optimal replacement time of system with series formation is shorter. For such reason, this paper compared the optimal replacement times obtained under the standard age replacement policy (SARP) with optimal replacement times obtained under some proposed two replacement policies (policy A and policy B) for some four multicomponent systems. Two numerical examples are provided for simple illustrations of the replacement policies under SARP, policy A and policy B, so as to select and apply the best replacement policy with respect to a particular system in making a projected precautionary replacement maintenance action of the system.

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“…Based on that, the authors concluded that service at maintenance and repair organization (MRO) should be as short and as cost-effective as possible. Some interesting results regarding the minimal repair rate are given in [10,11]. Actually, according to [12], repair data are often used to predict the repair time or maintainability performance of an item.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Integral Characteristics of Repair Process under Maintenance Contracts

Kontrec¹,

Vujaković²,

Tošić³

et al. 2021

Symmetry

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The repair rate is a very important parameter for system maintainability and can be defined as a frequency of successfully performed repair actions on a failed component per unit of time. This paper analyzes the integral characteristics of a stochastic repair rate for corresponding values of availability in a system operating under maintenance contracts. The probability density function (PDF) of the repair rate has been studied extensively and it was concluded that it is not a symmetric function so its mean value does not correspond to its maximum. Based on that, the equation for the envelope line of the PDF maximums of the repair rate has been provided. Namely, instead of repair rate PDF equations, we can use envelope line parameters for certain calculations, which are expressed in a simpler mathematical form. That will reduce time required for calculations and prediction and enhance reactions in failure events. Further, for the analytical and numerical evaluation of a system performance, the annual repair rate PDFs are analyzed, such as particular solutions of corresponding differential equation, while the existence of a singular solution is considered and analyzed under different conditions. Moreover, we derived optimal values of availability for which the PDF maximums have been obtained. Finally, in order to generalize the behavior of the repair process, a partial differential equation, as a function of the repair rate process and availability parameter, has been formed.

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New failure and minimal repair processes for repairable systems in a random environment

Cited by 5 publications

References 26 publications

Nonparametric significance tests for imperfect repair

Nonparametric significance tests for imperfect repair

Assessment of Some Proposed Replacement Models Involving Moderate Fix-Up

Mathematical Modeling of Integral Characteristics of Repair Process under Maintenance Contracts

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