Statistical Inference for a Simple Constant Stress Model Based on Censored Sampling Data From the Kumaraswamy Weibull Distribution

AL-Dayian, G. R.; EL-Helbawy, A. A.; Rezk, Hoda

doi:10.5539/ijsp.v3n3p80

Cited by 9 publications

(11 citation statements)

References 23 publications

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“…-135-3. Suppose that, for a particular pattern of stress, units run at stress j S starting at time The cumulative exposure model for j steps can be written as follows; (11), it is seen that () Gx , for a step-stress pattern which consists of segments of the CDF, 12 , ,..., k F F F , can be written in the form;…”

Section: Basic Assumptionsmentioning

confidence: 99%

Statistical Inference For A Simple Step–Stress Model With Type–II Hybrid Censored Data From The Kumaraswamy Weibull Distribution

Ibrahim¹,

Semary²

2021

Journal of Data Science

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In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress factors on the lifetimes of experimental units. In this paper, a step-stress model is considered in which the life-testing experiment gets terminated either at a pre-fixed time (say, 1 m T + ) or at a random time ensuring at least a specified number of failures (Say, y out of n ). Under this model in which the data obtained are Type-II hybrid censored, the Kumaraswamy Weibull distribution is used for the underlying lifetimes. The maximum Likelihood estimators (MLEs) of the parameters assuming a cumulative exposure model are derived. The confidence intervals of the parameters are also obtained. The hazard rate and reliability functions are estimated at usual conditions of stress. Monte Carlo simulation is carried out to investigate the precision of the maximum likelihood estimates. An application using real data is used to indicate the properties of the maximum likelihood estimators.

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Section: Basic Assumptionsmentioning

confidence: 99%

Statistical Inference For A Simple Step–Stress Model With Type–II Hybrid Censored Data From The Kumaraswamy Weibull Distribution

Ibrahim¹,

Semary²

2021

Journal of Data Science

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“…The lifetime at level of stress , , i=1, 2, ..., , j=1, 2, ..., k, is considered to have KumW distribution with the pdf in (2). It is assumed that the stress effects on the shape parameter of the KumW distribution only through the log linear model as in (5).…”

Section: Bayesian Estimation Based On Type II Censoringmentioning

confidence: 99%

Bayesian Approach for Constant-Stress Accelerated Life Testing for Kumaraswamy Weibull Distribution with Censoring

EL-Helbawy¹,

AL-Dayian

Rezk

2016

Pak.j.stat.oper.res.

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The accelerated life tests provide quick information on the life time distributions by testing materials or products at higher than basic conditional levels of stress such as pressure, high temperature, vibration, voltage or load to induce failures. In this paper, the acceleration model assumed is log linear model. Constant stress tests are discussed based on Type I and Type II censoring. The Kumaraswmay Weibull distribution is used. The estimators of the parameters, reliability, hazard rate functions and p-th percentile at normal condition, low stress, and high stress are obtained. In addition, credible intervals for parameters of the models are constructed. Optimum test plan are designed. Some numerical studies are used to solve the complicated integrals such as Laplace and Markov Chain Monte Carlo methods.

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“…In practical use, most products run at constant stress as a constant stress test mimics actual use, it is simple and has a lot of advantages over time-dependent stress loadings because most of real products are operated at a constant-stress condition, see Nelson [1]. For more details about ALT, see Bai and Chung [2], Balakrishnan and Han [3], AL-Dayian et al [4], also Basak and Balakrishnan [5] among others.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation and Prediction Based on Constant Stress-Partially Accelerated Life Testing for Topp Leone-Inverted Kumaraswamy Distribution

AL-Dayian

EL-Helbawy

Refaey

et al. 2021

JAMCS

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Accelerated life testing or partially accelerated life tests is very important in life testing experiments because it saves time and cost. Partially accelerated life tests are used when the data obtained from accelerated life tests cannot be extrapolated to usual conditions. This paper proposes, constant–stress partially accelerated life test using Type II censored samples, assuming that the lifetime of items under usual condition have the Topp Leone-inverted Kumaraswamy distribution. The Bayes estimators for the parameters, acceleration factor, reliability and hazard rate function are obtained. Bayes estimators based on informative priors is derived under the balanced square error loss function as a symmetric loss function and balanced linear exponential loss function as an asymmetric loss function. Also, Bayesian prediction (point and bounds) is considered for a future observation based on Type-II censored under two samples prediction. Numerical studies are given and some interesting comparisons are presented to illustrate the theoretical results. Moreover, the results are applied to real data sets.

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Statistical Inference for a Simple Constant Stress Model Based on Censored Sampling Data From the Kumaraswamy Weibull Distribution

Cited by 9 publications

References 23 publications

Statistical Inference For A Simple Step–Stress Model With Type–II Hybrid Censored Data From The Kumaraswamy Weibull Distribution

Statistical Inference For A Simple Step–Stress Model With Type–II Hybrid Censored Data From The Kumaraswamy Weibull Distribution

Bayesian Approach for Constant-Stress Accelerated Life Testing for Kumaraswamy Weibull Distribution with Censoring

Bayesian Estimation and Prediction Based on Constant Stress-Partially Accelerated Life Testing for Topp Leone-Inverted Kumaraswamy Distribution

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