On classical and Bayesian order restricted inference for multiple exponential step stress model

Samanta, Debasis; Ganguly, Ayon; Gupta, Arindam; Kundu, Debasis

doi:10.1080/02331888.2018.1526285

Cited by 18 publications

(3 citation statements)

References 16 publications

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“…It should be noted that further inferential problems can be studied for the discussed model. For instance, the subsequent topics may be investigated for k ‐step SLT by analogy with the following references discussing simple step stress testing: alternative lifetime distributions like two‐parameter exponential or Weibull distributions (see, e.g., Kateri & Balakrishnan, 2008; Mitra et al, 2013), other inferential methods like Bayesian approaches or order restricted inference (see, e.g., Samanta, Ganguly, Kundu, & Mitra, 2017; Samanta, Kundu, & Ganguly, 2018; Samanta, Ganguly, Gupta, & Kundu, 2019) or more advanced models like competing risks (see, e.g., Balakrishnan & Han, 2008; Ganguly & Kundu, 2016).…”

Section: Maximum Likelihood Estimation Under K‐step Sltmentioning

confidence: 99%

k‐step stage life testing

Laumen

Cramer

2020

Statistica Neerlandica

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The model of stage life testing proposed in Laumen and Cramer (2019b) is extended from two to k stages. It is illustrated that this model can be seen as an extension of progressive censoring with fixed censoring times as well as of simple step stress testing. Extending the first model, the new approach allows to incorporate information from progressively censored units subject to additional life testing. On the other hand, simple step stress modeling is generalized in the sense that only parts of the units under test are put on another stress level whereas the others remain on the initial level. The model is further studied for exponential lifetimes assuming a cumulative exposure model. We obtain the exact (conditional) distribution of the maximum likelihood estimators which is applied to construct (exact) confidence intervals for the distribution parameters. Finally, we investigate the situation of Weibull distributed lifetimes on the initial stage. The study is supplemented by illustrative simulations.

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Section: Maximum Likelihood Estimation Under K‐step Sltmentioning

confidence: 99%

k‐step stage life testing

Laumen

Cramer

2020

Statistica Neerlandica

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“…Balakrishnan et al 14 first incorporated this information and considered the order restricted estimation of model parameters for exponentially distributed lifetimes. Recently, Samanta et al, 15 Samanta and Kundu 16 and Pal et al 10 also considered this problem for some of the other related distributions. However, in all these cases, it has been assumed that the units in the underlying population will eventually experience the event of interest if followed up for long.…”

Section: Introductionmentioning

confidence: 99%

Order restricted inference for a multiple step‐stress model with long‐term survivors for a general family of distributions

Pal

Mitra

Kundu

2023

Appl Stoch Models Bus & Ind

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In this article, we propose a failure rate based step‐stress accelerated life testing (SSALT) model assuming that the time‐to‐event distribution belongs to a fairly general family of distributions and the underlying population consists of long term survivors. With increase in stress levels, it is expected that the mean time to the event of interest gets shortened leading to an order restriction among the mean times‐to‐event. We propose here a method of obtaining order restricted maximum likelihood estimators (MLEs) based on expectation maximization (EM) algorithm coupled with the method of generalized isotonic regression technique. Additionally, we address the testing of hypothesis problem for the presence of long term survivors in the underlying population based on both asymptotic and non‐asymptotic approaches. To illustrate the effectiveness of the proposed method, extensive simulation experiments are carried out and a real data set is analyzed.

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“…Kundu and Ganguly 5 introduced various step-stress models in detail, with emphasis on CEM assumption. Samanta et al 6 focused on multiple step-stress tests considering order restriction. They derived maximum likelihood estimates by algorithm proposed in this paper and Bayesian estimates using importance sampling.…”

Section: Introductionmentioning

confidence: 99%

Inference for cumulative risk model under step-stress experiments and its application in nanocrystalline data

Qiao

Gui

2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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With the popularity of step-stress accelerated life testing, researchers are exploring more possibilities for models that relate the life distributions under different stress levels. Cumulative risk model assumes that the effects of stress changes have a lag period before they are fully observed, which guarantees the continuity of the hazard rate function. This paper studies the cumulative risk model for Lomax distribution with step-stress experiments. For maximum likelihood estimation, Newton-Rapson method is adopted to get point estimates. Meanwhile, the asymptotic normality of the maximum likelihood estimator is used to obtain asymptotic confidence intervals. For Bayesian estimation, point estimates and highest posterior density credible intervals under squared error loss function with informative prior and non-informative prior are derived using Metropolis-Hastings method and Metropolis-Hastings within Gibbs algorithm. To evaluate the effects of stress change time and the length of lag period, as well as the performance of different methods, numerical simulations are conducted. Then a real nanocrystalline data set is analyzed.

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On classical and Bayesian order restricted inference for multiple exponential step stress model

Cited by 18 publications

References 16 publications

k‐step stage life testing

k‐step stage life testing

Order restricted inference for a multiple step‐stress model with long‐term survivors for a general family of distributions

Inference for cumulative risk model under step-stress experiments and its application in nanocrystalline data

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