Estimation of failure intensity for the Weibull process

Tsokos, Chris P.; Rao, A. N. V.

doi:10.1016/0951-8320(94)90143-0

Cited by 11 publications

(6 citation statements)

References 14 publications

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“…Representatives of the functional form of the ROCOFs are the log-linear ROCOF and the power law process, which is also called as the Weibull process. They have been used for modeling various types of failure rate for repairable systems in the reliability engineering field (Lee 1980;Tsokos and Rao 1994;Shin et al 1996). The power law process may used to model the failure rate of repairable systems that show reliability growth or reliability deterioration.…”

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Modeling of Water Main Failure Rates Using the Log-linear ROCOF and the Power Law Process

Park

Jun

Kim

et al. 2007

Water Resour Manage

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This paper presents applications of the log-linear ROCOF and the power law process to model the failure rate and estimate the economically optimal replacement time of the individual pipes in a water distribution system. The performance of the two failure rate models is examined using the maximized log-likelihoods for different modeling approaches in which the method of observing failures differs. The optimal replacement time equations for the two models are developed by applying the methodology of Loganathan et al. (J Water Resour Plan Manage ASCE 128(4): [271][272][273][274][275][276][277][278][279] 2002) for the case in which modified time scales are used. It was found that the log-linear ROCOF showed better performance than the power law process when the 'failure-time-based' method is used. Furthermore, the 'failure-time-based' method is proved to be superior compared to the 'failure-numberbased' method for the water mains under study, implying that recording each failure time results in better modeling of the failure rate than observing failure numbers in some time intervals.

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confidence: 99%

Modeling of Water Main Failure Rates Using the Log-linear ROCOF and the Power Law Process

Park

Jun

Kim

et al. 2007

Water Resour Manage

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“…That is, the failure of one component does not change the failure intensity of the other components. The failure intensity is formulated using a Weibull power law, a common practice in modeling failures for repairable components (Tsokos and Rao, 1994). When failed components are rectified, they can either be minimally repaired or replaced.…”

Section: Problem Definition and Assumptionsmentioning

confidence: 99%

Periodic inspection frequency and inventory policies for ak-out-of-nsystem

Bjarnason

Taghipour

2015

IIE Transactions

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We investigate maintenance and inventory policy for a k-out-of-n system in which the components' failures are hidden and follow a non-homogeneous Poisson process. Two types of inspections are performed to find failed components: planned periodic inspections and unplanned opportunistic inspections. The latter are performed at system failure times when n-k+1 components are down simultaneously. In all cases, the failed components are either minimally repaired or replaced with spare parts from the inventory. The inventory is replenished either periodically or when the system fails. The periodic orders have a random lead-time, but there is no lead-time for emergency orders, as these are placed at system failure times. The key objective is to develop a method to solve the joint maintenance and inventory problem for systems with considerable number of components, long planning horizon, and large inventory. We construct a simulation model to jointly optimize the periodic inspection interval, the periodic reorder interval, and periodic and emergency order-up-to levels. Because of the large search space, it is infeasible to try all possible combinations of decision variables in a reasonable amount of time. Thus, the simulation model is integrated with a heuristic search algorithm to obtain the optimal solution.

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“…We believe that there are three possible reasons for this scarcity. First, most work has assumed the binary case, in which the failure time is either exactly known or it is right-or left-censored (Tsokos and Rao, 1994). Second, it is often assumed that the degradation process is continuously and perfectly monitored and therefore the life history is complete (Liao et al, 2006).…”

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confidence: 99%

Predictive analytics using a nonhomogeneous semi-Markov model and inspection data

et al. 2014

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Predicting the remaining useful life plays an important role in minimizing the overall maintenance cost of mechanical systems. Although most conventional reliability models deal with binary systems to perform such predictions, in most practical cases, mechanical systems experience multiple levels of degradation states before failure. When the degradation level associated with such a multistate deteriorating process is monitored only at fixed inspection points, extracted monitoring data are interval-censored. Interval censoring can influence both the parameter estimation (model training) and the calculation of principal reliability measures. This article studies the problem of parameter estimation and the development of principal prognostic-based reliability measures, including reliability function and mean residual life, for a multistate device under limited inspection capacity. The correctness of the introduced models is demonstrated through simulation-based numerical experiments. Finally, an example of the wear process of the shell of a bearing is used to demonstrate the application of the proposed models.

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Estimation of failure intensity for the Weibull process

Cited by 11 publications

References 14 publications

Modeling of Water Main Failure Rates Using the Log-linear ROCOF and the Power Law Process

Modeling of Water Main Failure Rates Using the Log-linear ROCOF and the Power Law Process

Periodic inspection frequency and inventory policies for ak-out-of-nsystem

Predictive analytics using a nonhomogeneous semi-Markov model and inspection data

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