Analysis for constant-stress model on multicomponent system from generalized inverted exponential distribution with stress dependent parameters
TL;DR: In this paper, a generalized inverted exponential distribution (GIED) model was proposed to estimate the lifetime of multicomponent system. But, the model parameters were assumed to be nonconstant and depend on the stress.
About: This article is published in Mathematics and Computers in Simulation.The article was published on 2022-03-01. It has received 1 citations till now. The article focuses on the topics: Mathematics & Extrapolation.
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TL;DR: In this article , the reliability analysis for a multicomponent stress-strength (MSS) model is discussed, and generalized estimates for MSS reliability based on constructed pivotal quantities, and associated Monte-Carlo sampling is provided for computation.
Abstract: Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) with common scale parameters, maximum likelihood estimate of MSS reliability is established along with associated existence and uniqueness, and approximate confidence interval is also obtained in consequence. Additionally, alternative generalized estimates are proposed for MSS reliability based on constructed pivotal quantities, and associated Monte-Carlo sampling is provided for computation. Further, classical and generalized estimates are also established under unequal strength and stress parameter case. For comparison, bootstrap confidence intervals are also provided under different cases. To compare the equivalence of the strength and stress parameters, likelihood ratio testing is presented as a complement. Finally, extensive simulation studies are carried out to assess the performance of the proposed methods, and a real data example is presented for application. The numerical results indicate that the proposed generalized methods perform better than conventional likelihood results.
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TL;DR: In this paper, a conditional method of inference is used to derive exact confidence intervals for several life characteristics such as location, scale, quantiles, and reliability when the data are Type II progressively censored.
Abstract: A conditional method of inference is used to derive exact confidence intervals for several life characteristics such as location, scale, quantiles, and reliability when the data are Type II progressively censored. The method is shown to be feasible and practical, although a computer program may be required for its implementation. The method is applied for the purpose of illustration to the extreme-value and the one- and two-parameter exponential models. Prediction limits for the lifelength of future units are also discussed. An example consisting of data from an accelerated test on insulating fluid reported by Nelson is used for illustration and comparison.
329 citations
TL;DR: In this article, a stress-strength model is formulated for s of k systems consisting of identical components and a minimum variance unbiased estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distributions are exponential with unknown scale parameters.
Abstract: A stress-strength model is formulated for s of k systems consisting of identical components. We consider minimum variance unbiased estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distributions are exponential with unknown scale parameters. The asymptotic distribution is obtained by expanding the unbiased estimate about the maximum likelihood value and establishing their equivalence. Performance of the two estimates for moderate samples is studied by Monte Carlo simulation. Uniformly most accurate unbiased confidence intervals are also obtained for system reliability.
193 citations
TL;DR: In this paper, a generalized version of inverted exponential distribution (IED) is introduced, which is capable of modeling various shapes of failure rates, and hence various shape of ageing criteria, and can be considered as another useful two-parameter generalization of the IED.
Abstract: A generalized version of inverted exponential distribution (IED) is introduced in this paper. This lifetime distribution is capable of modelling various shapes of failure rates, and hence various shapes of ageing criteria. The model can be considered as another useful two-parameter generalization of the IED. Statistical and reliability properties of the generalized inverted exponential distribution are derived. Maximum likelihood estimation and least square estimation are used to evaluate the parameters and the reliability of the distribution. Properties of the estimates are also studied.
137 citations
TL;DR: Optimum ALTSPs which satisfy the producer's and consumer's risk requirements and minimize the asymptotic variance of the test statistic for deciding the lot acceptability are obtained.
74 citations
TL;DR: In this article, a probabilistic modeling of fatigue damage accumulation for single stress level and multistress level loading is proposed, which uses linear damage accumulation model of Palmgren-Miner and an approach for a one-toone transformation of probability density functions to achieve the objective.
Abstract: A methodology for probabilistic modeling of fatigue damage accumulation for single stress level and multistress level loading is proposed in this paper. The methodology uses linear damage accumulation model of Palmgren-Miner, a probabilistic - curve, and an approach for a one-to-one transformation of probability density functions to achieve the objective. The damage accumulation is modeled as a nonstationary process as both the expected damage accumulation and its variability change with time. The proposed methodology is then used for reliability prediction under single stress level and multistress level loading, utilizing dynamic statistical model of cumulative fatigue damage. The reliability prediction under both types of loading is demonstrated with examples.
62 citations