Abstract
This study presents a method for calculating the availability of a system depicted by availability block diagram, with identically distributed components, in the presence of estimating common cause hazard, we use the Marshall and Olkin formulation of the multivariate exponential distribution. That is, the components are subject to failure by Poisson failure processes that govern simultaneous failure of a specific subset of the components. A model is proposed for the analysis of systems subject to common-cause failures that are not considered to have a constant rate but that are assumed to obey a uniqueness of maximum likelihood estimators of the 2-parameter Weibull distribution. The method for calculating the system availability requires that a procedure exists for determining the system availability from component availabilities, under the statistically independent component assumption. The study includes an example to illustrate the method.
Highlights
Uniqueness of Maximum Likelihood Estimates (MLE) of the 2-parameter WeibullDistribution: We select an appropriate hazard rate for Common-Cause (CC) hazards are the failure of multiple components due to a single occurrence or condition
I = τ +1 α j could be described by different models, such as the Weibull distribution calculated from either complete failure data or from the behavior of the parameter Maximum Likelihood Estimates (MLE) of a 2parameter Weibull distribution[9]. It is the main objective of the present study to utilize the hazard rates, extracted from operational experience, to calculate the availability of a system depicted by an availability block diagram with Weibull distribution components, in the presence of commoncaused hazards
The resulting availability neglects, the system effects of common-cause failures and represents the prediction of a practitioner assessing all failures causes specific k-component subset out of an ncomponent system are operating at time t; hj(t) =Hazard rate; hj(t)dt= conditional probability of an event failing specific j components, and no others, during (t,t+dt), given no such event during (0,t); t hj(t) = ∫ h j(u)du : cumulative hazard function; (
Summary
Distribution: We select an appropriate hazard rate for Common-Cause (CC) hazards are the failure of multiple components due to a single occurrence or condition. The hazard function of a component following a 2parameter Weibull distribution can be described by: with statistically independent components. The component failure probability density function m exp[−( ti
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