Bayesian Confidence Bounds for the Weibull Failure Model

Papadopoulos, Alex G.; Tsokos, Chris P.

doi:10.1109/tr.1975.5215319

Cited by 21 publications

(4 citation statements)

References 2 publications

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“…Therefore, in Weibull reliability analysis, it is frequently the case that the value of the shape parameter is known, but that there is uncertainty in the scale parameter [32]. Other studies that assume a fixed shape and random scale parameter include Kwon [21], Papadopoulos and Tsokos [30], and Canavos and Tsokos [9]. In line with these studies, we also assume a known shape parameter and an uncertain scale parameter.…”

Section: Weibull Distributed Lifetimementioning

confidence: 96%

Optimum maintenance strategy under uncertainty in the lifetime distribution

Jonge

Klingenberg

Teunter

et al. 2015

Reliability Engineering & System Safety

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The problem of determining the optimal maintenance strategy for a machine given its lifetime distribution has been studied extensively. Solutions to this problem are outlined in the academic literature, prescribed in professional handbooks, implemented in reliability engineering software systems and widely used in practice. These solutions typically assume that the lifetime distribution and its parameter values are known with certainty, although this is usually not the case in practice. In this paper we study the effect of parameter uncertainty on the optimum age-based maintenance strategy. The effect of uncertainty is evaluated by considering both a theoretical uniform lifetime distribution and a more realistic Weibull lifetime distribution. The results show that admitting to the uncertainty does influence the optimal maintenance age and also provides a quantifiable cost benefit. The results can help maintenance managers in making maintenance decisions under uncertainty, and also in deciding when it is worthwhile to invest in advanced data improvement procedures.

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Section: Weibull Distributed Lifetimementioning

confidence: 96%

Optimum maintenance strategy under uncertainty in the lifetime distribution

Jonge

Klingenberg

Teunter

et al. 2015

Reliability Engineering & System Safety

View full text Add to dashboard Cite

show abstract

“…It is, on the other hand, very likely that there is substantial uncertainty in the value of the scale parameter [48]. Other studies that consider this setting include Canavos and Tsokos [7], De Jonge et al [14], Kwon [27], and Papadopoulos and Tsokos [37].…”

Section: Model Formulationmentioning

confidence: 99%

Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty

Jonge

Dijkstra

Romeijnders

2015

Reliability Engineering & System Safety

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We consider the problem of scheduling time-based preventive maintenance under uncertainty in the lifetime distribution of a unit, with the understanding that every time a maintenance action is carried out, additional information on the lifetime distribution becomes available. Under such circumstances, typically either point estimates for the unknown parameters are used, or expected costs are minimized taking the uncertainty in the parameters into account. Both approaches, however, ignore that the uncertainty is reduced much faster if preventive maintenance actions are postponed. Although this initially leads to higher costs due to a higher risk of breakdowns, the obtained additional information can be exploited thereafter as it enables better maintenance decisions going forward. We assess the longterm benefits of initially postponing preventive maintenance, and perform a numerical study to identify under what circumstances these benefits are largest. This study is the first to recognize that the choice of a maintenance strategy influences the information that becomes available, and aims to initiate follow-up research in the area of maintenance planning.

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“…An accelerated life testing approach in which the underlying sampling distribution is the two-parameter Weibull model was addressed before by De Souza [7], [8]. The two-parameter Weibull distribution was addressed before by Erto [9], Mann [10], Papadopoulos and Tsokos [11], Soland [12] and Tate [13]. In this work, we will develop an accelerated life testing approach in which the underlying sampling distribution is the three-parameter Weibull model.…”

Section: Introductionmentioning

confidence: 99%

Accelerated Life Testing With an Underlying Three-Parameter Weibull Model

Souza¹,

Somani²

2010

Engevista

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Abstract:The main objective of life testing is to obtain information concerning failure. This information should then be used in order to quantify reliability, improve product reliability, and to determine whether safety and reliability goals are being met. The amount of time available for testing directly at use conditions, that is, with practical test times and realistic (relatively) small test sample sizes, could be considerably less than the component's expected lifetime. To overcome such a problem, there is the life-testing alternative aimed at forcing components to fail by testing them at much higher than the intended application conditions. By doing this, we will get failure data that can be fitted to life distribution models. To go from the failure rate obtained at high stress to what a product or service is likely to experience at much lower stress, under use conditions, we will need additional modeling. These models are known as acceleration models. The accelerated life testing concept is such that a component, operating under predetermined (correct) levels of increased stress, will have exactly the same failure mechanism as observed when used at normal stress levels. For example, if the time of testing is measured in cycles, then the time squeezing may only require increasing the number of cycles per unit of time. In this study, we will develop an accelerated life-testing model in which the underlying sampling distribution is the three-parameter Weibull model. We will be assuming a linear acceleration condition. An example will illustrate the application of the proposed accelerated life-testing model.

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Bayesian Confidence Bounds for the Weibull Failure Model

Cited by 21 publications

References 2 publications

Optimum maintenance strategy under uncertainty in the lifetime distribution

Optimum maintenance strategy under uncertainty in the lifetime distribution

Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty

Accelerated Life Testing With an Underlying Three-Parameter Weibull Model

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