Bayesian Analysis of a Simple Step-Stress Model Under Weibull Lifetimes

Ganguly, Ayon; Kundu, Debasis; Mitra, Sharmistha

doi:10.1109/tr.2014.2368871

Cited by 30 publications

(12 citation statements)

References 14 publications

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“…In this case, one can assume that the mean lifetime under the stress level

s_{2}

is smaller than the mean lifetime at the stress level

s_{1}

, which implies

β_{1} < β_{2}

. One way to investigate this case is to use restricted prior assumption, for more details one may refer to Mitra et al 19 and Ganguly et al 20 . In this paper, we assume the unrestricted prior assumption with joint prior density given by ().…”

Section: Bayesian Estimationmentioning

confidence: 99%

E‐Bayesian estimation and associated properties of simple step–stress model for exponential distribution based on type‐II censoring

Nassar

Okasha

Albassam

2020

Quality & Reliability Eng

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In this paper, expected Bayesian (E‐Bayesian) estimation for the simple step–stress model based on type‐II censoring scheme is considered. The case of exponential distribution for the underlying lifetimes is considered assuming a cumulative exposure model. The E‐Bayesian estimation is discussed by considering three different prior distributions for the hyperparameters. The E‐Bayesian estimators as well as the corresponding E‐posterior risks are obtained by using squared error and linear‐exponential (LINEX) loss functions. Some properties of the E‐Bayesian estimators are also derived. We conduct a simulation study to compare the various estimators and a simulated and real data sets are analyzed to show the applicability of the different estimators. The numerical results show that the E‐Bayesian estimators perform better than the classical and Bayesian estimators.

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“…In this case, one can assume that the mean lifetime under the stress level

s_{2}

is smaller than the mean lifetime at the stress level

s_{1}

, which implies

β_{1} < β_{2}

Section: Bayesian Estimationmentioning

confidence: 99%

E‐Bayesian estimation and associated properties of simple step–stress model for exponential distribution based on type‐II censoring

Nassar

Okasha

Albassam

2020

Quality & Reliability Eng

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“…The uncertainty of parameters can be reflected by their prior distributions. In Bayesian studies, a convenient approach is to directly assign prior distribution for each model parameter by assuming that the model parameters are mutually independent . However, this approach has some drawbacks.…”

Section: Bayesian Design Of the Adaptive Planmentioning

confidence: 99%

Designing adaptive accelerated life tests using Bayesian methods

Xiang

Yang

Shen

2017

Quality & Reliability Eng

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The traditional constant‐stress accelerated life test may encounter the problem of no or a few failures at the low stress level, if the test is stopped after a fixed period. Insufficient failures usually make it difficult to estimate reliability characteristics and to discover design deficiencies of the product. To mitigate the problem, the adaptive plan is designed based on Bayesian methods in this study. Under the constraints of test facilities, test units, time, and cost, the adaptive plan is optimized according to the criterion of minimizing the preposterior variance of the logarithm of a quantile of the lifetime distribution at the use condition. Large‐sample approximation is applied to reduce the computational burden. Genetic algorithm is adopted to determine the optimal design of the adaptive plan. Finally, a numerical example is given to demonstrate the advantages of the proposed adaptive plan.

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“…A Bayesian framework was developed to assess the reliability and performance of multi-state systems that consists of multiple multi-state components of which the degradation follows a Markov process [17]. For analyzing lifetime data obtained from accelerated life testing experiments model under Weibull lifetimes, a Bayesian analysis of a simple step-stress was used [18]. Monte Carlo simulations were performed to see the effectiveness of the proposed method, and a data set has been analyzed for illustrative purposes.…”

Section: Literature Reviewmentioning

confidence: 99%

Competing risk models in reliability systems, a gamma distribution model with bayesian analysis approach

Iskandar

2016

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. In this paper our effort is to introduce the basic notions that constitute a competing risks models in reliability analysis using Bayesian analysis approach with Gamma distribution as our model and presenting their analytic methods. The Gamma distribution is widely used in reliability analysis and it is known as an natural extension of the exponential distribution. The cases are limited to the models with independent causes of failure, only the scale parameter is a random variable, and uniform prior distribution is used in our analysis. This model describes the likelihood function and follows with the description of the posterior function and the estimations of the point, interval, hazard function, and reliability. The net probability of failure if only one specific risk is present, crude probability of failure due to a specific risk in the presence of other causes, and partial crude probabilities are also included.

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Bayesian Analysis of a Simple Step-Stress Model Under Weibull Lifetimes

Cited by 30 publications

References 14 publications

E‐Bayesian estimation and associated properties of simple step–stress model for exponential distribution based on type‐II censoring

E‐Bayesian estimation and associated properties of simple step–stress model for exponential distribution based on type‐II censoring

Designing adaptive accelerated life tests using Bayesian methods

Competing risk models in reliability systems, a gamma distribution model with bayesian analysis approach

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