Abstract
Using progressive first-failure censored samples, we mainly study the inferences of the unknown parameters and the reliability and failure functions of the Inverted Exponentiated Half-Logistic distribution. The progressive first-failure censoring is an extension and improvement of progressive censoring, which is of great significance in the field of lifetime research. Besides maximum likelihood estimation, we use Bayesian estimation under unbalanced and balanced losses: General Entropy loss function, Squared Error loss function and Linex loss function. Approximate explicit expression of Bayesian estimation is given using Lindley approximation method for point estimation and Metropolis-Hastings method for point and interval estimation. Bayesian credible intervals and asymptotic confidence intervals are derived in the form of average length and coverage probability. To show the research effects, a simulation study and practical data analysis are carried out. Finally, we discuss the optimal censoring mode under four different criteria.
Highlights
In lifetime experiment and reliability research, there are limitations like time, money, resources, or due to personnel transfer and accidents, data cannot be recorded completely
Under progressive first-failure censoring scheme, we mainly discuss the Bayesian estimations of the unknown parameters and reliability characteristics of Inverted Exponentiated Half-Logistic distribution (IEHLD)
Let φ(γ, β) represents the function related to γ and β, the Bayesian estimation under Squared Error loss function (SELF) is the posterior expectation of φ(γ, β), say, R +∞ R +∞
Summary
In lifetime experiment and reliability research, there are limitations like time, money, resources, or due to personnel transfer and accidents, data cannot be recorded completely. To better improve the experimental efficiency, Wu and Ku [4] proposed the progressive first-failure censoring This mode is of great significance in reliability research. Rastogi [10] estimated the parameters and reliability characteristics of EHLD using MLE and Bayes estimation under progressive Type-II censoring scheme. Studied the maximum likelihood estimations and Bayesian estimations of parameters of inverted exponentiated Rayleigh distribution under adaptive Type-II progressive hybrid censoring scheme. When the value of the shape parameter is set to be 1, the IEHLD can be transformed into the usual HLD, it has greater inclusiveness and flexibility in the practice of reliability research and lifetime test correspondingly. This paper mainly studies the parameters and the reliability and failure functions of IEHLD using progressive first-failure censored samples.
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