Estimation of stress–strength reliability in the inverse Gaussian distribution under progressively type II censored data

Rostamian, Somayeh; Nematollahi, Nader

doi:10.1007/s40096-019-0289-1

Cited by 12 publications

(6 citation statements)

References 53 publications

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“…Various censoring schemes are defined in the literature and these schemes are handled in the context of stress strength reliability. For instance in recent studies, SS reliability under progressive censoring scheme studied by Maurya and Tripathi 5 for Burr‐XII model, by Mahto et al 6 for a general class of inverted exponentiated distributions, by Jha et al 7 for unit Gompertz distribution, by Wang et al 8 for a general family of truncated distributions, by Rostamian and Nematollahi 9 for inverse Gaussian distribution, by Saraçoğlu et al 10 for the exponential distribution, by Bai et al 11 for finite mixture distributions under progressively interval censoring.…”

Section: Introductionmentioning

confidence: 99%

Inference ofP(X>Y) for the Burr‐XII model under generalized progressive hybrid censored data with binomial removals

Çetinkaya

2023

Concurrency and Computation

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In this paper, we studied the estimation of R = P(X > Y) based on the Burr-XII distribution under the generalized progressive hybrid censoring scheme. This censoring scheme has become quite popular depending progressive hybrid censoring scheme cannot be applied when few failures occur before pre-determined time T. In this progressive censoring plan, amount of units withdrawn at each failure is assumed to be random and subject to the binomial distributions. Inferences of R are obtained under equal shape parameters and different shape parameters, respectively. Maximum likelihood (MLE) and the Bayesian estimation methods are used. We obtain the MLEs of the parameters using Newton-Raphson (NR) and expectation maximization (EM) methods, respectively. In the Bayesian section, Lindley's approximation and Markov Chain Monte Carlo (MCMC) method with Metropolis-Hasting algorithm are used. Simulation studies are used to evaluate the performance of the proposed estimators and two real-data examples are provided to exemplify the theoretical outcomes.

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Section: Introductionmentioning

confidence: 99%

Inference ofP(X>Y) for the Burr‐XII model under generalized progressive hybrid censored data with binomial removals

Çetinkaya

2023

Concurrency and Computation

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“…Commonly used stochastic processes include Wiener, gamma and inverse Gaussian processes. [22][23][24] These methods require sufficient degradation data for support. They are essentially a reliability model based on degradation increment, and they cannot accurately evaluate the fluctuation degree of the complete performance degradation trajectory.…”

Section: Introductionmentioning

confidence: 99%

“…They are widely used degradation modelling methods. Commonly used stochastic processes include Wiener, gamma and inverse Gaussian processes 22–24 . These methods require sufficient degradation data for support.…”

Section: Introductionmentioning

confidence: 99%

Reliability evaluation of a complex system that considers the influence of the fluctuation degree of the performance degradation trajectory

Feng,

Yang,

Chen

et al. 2023

Quality & Reliability Eng

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In this paper, a reliability evaluation method based on the hidden Markov model (HMM) considers the influence of degradation trajectory fluctuation. To address the problem in which the performance degradation trajectory modelling of complex systems is limited by sampling time points, this method constructs an approximate degradation trajectory model based on effective discrete data points through a radial basis function to realize the degradation data expansion of small samples. Then, the average degradation rate is defined, and the fluctuation degree of the degradation trajectory is quantitatively evaluated to obtain the evaluation function of the fluctuation degree of the degradation trajectory. In addition, to determine the relationship between the fluctuation degree of the degradation trajectory and the operating state of the system, the method combines HMM with the evaluation function of the fluctuation degree of the degradation trajectory and obtains the transition probability matrix of different operating states of the system affected by the fluctuation degree of the degradation trajectory. On the basis of the probability matrix of the failure state, the reliability change curve of the system is derived. Finally, the effectiveness of the proposed method is verified via an example of a computer numerical control machine tool.

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“…Birnbaum and Mccarty 21 further developed this model. Some literatures have studied inferential procedures of the reliability

R

under different stress and strength distributions, for example, normal distribution, 22, 23 Weibull distribution, 24–26 , Burr XII distribution, 27 Gamma distribution, 28 generalized exponential distribution, 29, 30 IG distribution, 31 among others. Kotz et al 32 provided many results and applications for stress–strength model.…”

Section: Introductionmentioning

confidence: 99%

Interval estimation for inverse Gaussian distribution

Wang

Pan

et al. 2021

Quality & Reliability Eng

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In this paper, we consider interval estimation for the inverse Gaussian (IG) distribution. Using generalized pivotal quantity method, we derive the generalized confidence intervals (GCIs) for the model parameters and some quantities such as the quantile, the reliability function of the lifetime, the failure rate function, and the mean residual lifetime. We verify that the GCI of the scale parameter is the same as its commonly used exact CI. We also obtain the generalized prediction intervals (GPIs) for future failure times based on the observed failure data set. In addition, we get the GCI for the reliability of the stress–strength model when the stress and strength variables follow the IG distributions with different parameters. We compare the proposed GCIs and GPIs with the Wald CIs and bootstrap‐p CIs by simulation. The simulation results show that the proposed GCIs and GPIs are superior to the Wald CIs and the bootstrap‐p CIs in terms of the coverage probability. Finally, two examples are used to illustrate the proposed procedures.

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Estimation of stress–strength reliability in the inverse Gaussian distribution under progressively type II censored data

Cited by 12 publications

References 53 publications

Inference ofP(X>Y) for the Burr‐XII model under generalized progressive hybrid censored data with binomial removals

Inference ofP(X>Y) for the Burr‐XII model under generalized progressive hybrid censored data with binomial removals

Reliability evaluation of a complex system that considers the influence of the fluctuation degree of the performance degradation trajectory

Interval estimation for inverse Gaussian distribution

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