The statistical inference of the reliability and parameters of the stress-strength model has received great attention in the field of reliability analysis. When following the generalized progressive hybrid censoring (GPHC) scheme, it is important to discuss the point estimate and interval estimate of the reliability of the multicomponent stress-strength (MSS) model, in which the stress and the strength variables are derived from different distributions by assuming that stress follows the Chen distribution and that strength follows the Gompertz distribution. In the present study, the Newton-Raphson method was adopted to derive the maximum likelihood estimation (MLE) of the model parameters, and the corresponding asymptotic distribution was adopted to construct the asymptotic confidence interval (ACI). Subsequently, the exact confidence interval (ECI) of the parameters was calculated. A hybrid Markov chain Monte Carlo (MCMC) method was adopted to determine the approximate Bayesian estimation (BE) of the unknown parameters and the high posterior density credible interval (HPDCI). A simulation study with the actual dataset was conducted for the BEs with squared error loss function (SELF) and the MLEs of the model parameters and reliability, comparing the bias and mean squares errors (MSE). In addition, the three interval estimates were compared in terms of the average interval length (AIL) and coverage probability (CP).
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http://dx.doi.org/10.3390/e24050619 | DOI Listing |
MethodsX
June 2024
Prince Sattam Bin Abdulaziz University, College of Arts and Sciences, KSA, Saudi Arabia.
It typically takes a lot of time to monitor life-testing experiments on a product or material. Units can be tested under harsher conditions than usual, known as accelerated life tests to shorten the testing period. This study's goal is to investigate the issue of partially accelerated life testing that use generalized progressive hybrid censored samples to estimate the stress-strength reliability in the multicomponent case.
View Article and Find Full Text PDFMath Biosci Eng
March 2023
School of Mathematics and Physics, Anhui University of Technology, Maanshan, China.
This paper considers the reliability analysis of a multicomponent stress-strength system which has $k$ statistically independent and identically distributed strength components, and each component is constructed by a pair of statistically dependent elements. These elements are exposed to a common random stress, and the dependence among lifetimes of elements is generated by Clayton copula with unknown copula parameter. The system is regarded to be operating only if at least $s$($1 \leq s \leq k$) strength variables in the system exceed the random stress.
View Article and Find Full Text PDFBull Malays Math Sci Soc
January 2023
Departamento de Matemáticas, Estadística e Investigación Operativa, Universidad de La Laguna, 38071 La Laguna, Tenerife Spain.
The statistical inference of multi-component reliability stress-strength system with nonidentical-component strengths is considered for the modified Weibull extension distribution in the presence of progressive censoring samples. For this aim, we study the estimation of multi-component reliability parameter in classical and Bayesian inference. So we derive some point and interval estimates such as maximum likelihood estimation, asymptotic confidence intervals, uniformly minimum variance unbiased estimation, approximate and exact Bayes estimation and highest posterior density intervals.
View Article and Find Full Text PDFEntropy (Basel)
April 2022
College of Science, Inner Mongolia University of Technology, Hohhot 010051, China.
The statistical inference of the reliability and parameters of the stress-strength model has received great attention in the field of reliability analysis. When following the generalized progressive hybrid censoring (GPHC) scheme, it is important to discuss the point estimate and interval estimate of the reliability of the multicomponent stress-strength (MSS) model, in which the stress and the strength variables are derived from different distributions by assuming that stress follows the Chen distribution and that strength follows the Gompertz distribution. In the present study, the Newton-Raphson method was adopted to derive the maximum likelihood estimation (MLE) of the model parameters, and the corresponding asymptotic distribution was adopted to construct the asymptotic confidence interval (ACI).
View Article and Find Full Text PDFJ Appl Stat
February 2022
Department of Statistics, University of Delhi, Delhi, India.
In this paper, the inference of multicomponent stress-strength reliability has been derived using progressively censored samples from Topp-Leone distribution. Both stress and strength variables are assumed to follow Topp-Leone distributions with different shape parameters. The maximum likelihood estimate along with the asymptotic confidence interval are developed.
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