On the simple step-stress model for two-parameter exponential distribution

Mitra, Sharmistha; Ganguly, Ayon; Samanta, Debasis; Kundu, Debasis

doi:10.1016/j.stamet.2013.04.003

Cited by 25 publications

(9 citation statements)

References 14 publications

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“…Notice that, although the joint CDF of (μ,σ ) can be expressed in closed form in the non-adaptive case, exact inference does not work as usual since the distribution ofσ is not stochastically monotone in σ in general. This was noticed in [15] in a different context involving E (μ, σ ), but it is true here, too.…”

Section: Example 4 For the Two-parameter Exponential Distribution E (supporting

confidence: 68%

Adaptive Progressive Censoring

Cramer

Iliopoulos

2015

Ordered Data Analysis, Modeling and Health Research Methods

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The notion of adaptive progressive Type-II censoring has been introduced in Cramer and Iliopoulos (2010) to analyse data from a progressively Type-II censored life test with observation dependent removals of units. Such a scheme gives more flexibility to the experimenter since it allows him/her to choose the number of units to be removed at each failure time during the life test. In this paper, the idea is generalised to a more general setting of progressive censoring. Our generalised model allows for arbitrary inspection times and possible removals of units during the experiment. The inspection times and removals depend on what has been observed so far. In particular, this approach includes adaptive progressive Type-I and Type-II censoring with random or fixed inspection timepoints.

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Section: Example 4 For the Two-parameter Exponential Distribution E (supporting

confidence: 68%

Adaptive Progressive Censoring

Cramer

Iliopoulos

2015

Ordered Data Analysis, Modeling and Health Research Methods

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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 order to incorporate the different testing levels in the model, we assume a cumulative exposure model as has been introduced in Sedyakin (1966) (see also Bagdonavičius, 1978; Nelson & Meeker, 1978). In fact, we follow the ideas developed in simple step‐stress testing as developed in, for example, Balakrishnan, Kundu, Ng, and Kannan (2007), Balakrishnan, Xie, and Kundu (2009), Kateri, Kamps, and Balakrishnan (2009), Mitra, Ganguly, Samanta, and Kundu (2013) (for reviews, see Balakrishnan 2009; Gouno & Balakrishnan, 2001; Kundu & Ganguly, 2017) where a similar idea has been successfully utilized. In our setting, we consider distribution functions F 0 , F 1 , … , F k − 1 corresponding to stages s 0 , s 1 , … , s k − 1 .…”

Section: Introductionmentioning

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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On the simple step-stress model for two-parameter exponential distribution

Cited by 25 publications

References 14 publications

Adaptive Progressive Censoring

Adaptive Progressive Censoring

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

k‐step stage life testing

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