A general repair, proportional-hazards, framework to model complex repairable systems

Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers

“…R ji ðtjt 0 Þdt for j\i n. With (5), (6) and (8) in place, there is still one barrier in evaluating SF and MRL, effectively, where the explicit analytical expressions are needed.…”

“…We sample X 1 ; X 2 by the Monte Carlo technique and calculate the SF and MRL by (6) and (8).The convergence condition is that the coefficient of variation is less than 0.05. For a new component t 0 ¼ 0; t ¼ t 0 þ 5; for an old component, we presume…”

“…The baseline function offers the basis for hazard rate and the link function quantifies the covariate effect. Sample covariates such as those pertaining to the lifecycle data [7], operation mode [8], vibration [9] and dissolved gas [10], which could be time-dependent, are considered according to the actual system situations. PHM offers advantages when applied to explanatory techniques [11].…”

REPAIR EFFICIENCY ESTIMATION IN THE ARI1 IMPERFECT REPAIR MODEL

“…For the BrownProschan model, Lim [15] has studied estimation with the EM-algorithm, Langseth and Lindqvist [13] have estimated parameters on real data set with maximum likelihood, and Lim, Lu and Park [14] have used Bayesian estimation. For virtual age models some studies on maximum likelihood estimators have been published: Shin, Lim and Lie [19], Yun and Choung [21], Kaminskiy and Krivtsov [9], Yanez, Joglar and Modarres [20], Gasmi, Love and Kahle [8], Doyen and Gaudoin [6]. But all these studies only proposed numerical results.…”

A Data-Driven Approach to Selecting Imperfect Maintenance Models

“…The most relevant efforts among the existing models are: the Brown-Proschan model (See Brown and Proschan [4]), the Kijima Type I and II models (see Kijima [5], [6]), the improvement factor method (see Malik [7]), the hazard rate model (see Nakagawa [8]), the hybrid model 0018-9529/$26.00 © 2011 IEEE (see Lin [9]), the geometric process (see Lam [10]), the quasi-renewal model (see Wang and Pham [11], [12]), and the superposed renewal process (see Kallen [13]). The statistical inference of the unknown parameters in the imperfect maintenance models has also been studied [14]- [21]. Most recently, Wu and Zuo [22] presented a comprehensive study to reveal the commonality and interrelationship among some models.…”