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Bootstrapping computation of availability for a repairable system with standby subject to imperfect switching
Supplementary variable technique
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|摘要:||我們考慮一個具有不完美備元可修理系統，此系統包含四個主要和二個備用可修理機器。本文主要討論以五種拔靴法為基礎建構其可用度的信賴區間。我們假設主要和備用機器損壞的時間間隔服從指數分配，修護時間服從四種不同的分配：指數、伽瑪、均勻、混和分配，接著使用遞迴法和輔助變數技巧求得系統在穩態時的可用度，下一步則採用以拔靴法為基礎，利用標準拔靴法(standard bootstrap)、百分比拔靴法(percentile bootstrap)、誤差修正百分比拔靴法(bias-corrected percentile bootstrap)、加速並修正誤差百分比拔靴法(bias-corrected and accelerated percentile bootstrap) 以及樞
紐拔靴法(bootstrap pivotal) 等五種方法建構並計算出其信賴區間、覆蓋率和信賴長度以便探討它們的表現，最後，以一些實驗數據來說明結論。|
This paper deals with the availability behavior of a repairable system in which standby switched to primary is subject to breakdowns. The time-to-failure of the four primary and two standby units are assumed to be exponentially and generally distributed. In addtion, the repair time of service station follow four common distributions: exponential(EXP), Gamma(G), Uniform(U), Mixture(M). We use a recursive method, and the supplementary variable technique to develop the steadystate availability, Av. The estimator Aˆv is strongly consistent and asymptotically normal. The interval estimations of Av are constructed by five bootstrap approaches: standard bootstrap confidence interval(SB), the percentile bootstrap confidence interval(PB), the bias-corrected percentile bootstrap confidence interval(BCPB), the bias-corrected and accelerated confidence interval(BCa) and bootstrap pivot confidence interval(BP). Finally, some simulation computations are conducted in order to describe the performances of Aˆv on various interval estimation by calculating the coverage percentage and the average length of intervals.
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