Inference on Nadarajah–Haghighi distribution with constant stress partially accelerated life tests under progressive type-II censoring

Utilizing Bayesian inference in accelerated testing models under constant stress via ordered ranked set sampling and hybrid censoring with practical validation

This research investigates the application of the ordered ranked set sampling (ORSSA) procedure in constant-stress partially accelerated life-testing (CSPALTE). The study adopts the assumption that the lifespan of a specific item under operational stress follows a half-logistic probability distribution. Through Bayesian estimation methods, it concentrates on estimating the parameters, utilizing both asymmetric loss function and symmetric loss function. Estimations are conducted using ORSSAs and simple random samples, incorporating hybrid censoring of type-I. Real-world data sets are utilized to offer practical context and validate the theoretical discoveries, providing concrete insights into the research findings. Furthermore, a rigorous simulation study, supported by precise numerical calculations, is meticulously conducted to gauge the Bayesian estimation performance across the two distinct sampling methodologies. This research ultimately sheds light on the efficacy of Bayesian estimation techniques under varying sampling strategies, contributing to the broader understanding of reliability analysis in CSPALTE scenarios.

Fuzzy multicomponent stress-strength reliability in presence of partially accelerated life testing under generalized progressive hybrid censoring scheme subject to inverse Weibull model

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. Also, the fuzziness of the model is considered that gives more sensitive and accurate analyses about the underlying system. Maximum likelihood estimation method under the inverse Weibull distribution and using the generalized progressively hybrid censoring scheme is introduced to obtain an estimator for the fuzzy multicomponent stress-strength reliability. Also, an asymptotic confidence interval is deduced to examine the reliability of the fuzzy multicomponent stress-strength. Simulation study is conducted using maximum likelihood estimates and confidence intervals for the fuzzy multicomponent stress-strength reliability for different values of the parameters and different schemes. A real data application representing the data for the failure times for a certain software model is introduced to obtain the fuzzy multicomponent stress-strength reliability for different schemes.•The fuzzy multicomponent stress-strength reliability is investigated under partially accelerated life testing and the generalized progressively hybrid censored scheme.•An algorithm is introduced to simulate data for the censoring scheme.•A real data application is presented to obtain the fuzzy multicomponent stress-strength reliability at different schemes.

Different estimation techniques for constant-partially accelerated life tests of chen distribution using complete data

The issue of various estimation techniques in constant partially accelerated life tests with complete data is the main subject of this research. The Chen distribution is regarded as an item's lifetime under use conditions. To estimate the distribution parameters and the acceleration factor, maximum likelihood estimation, least square estimation, weighted least square estimation, Cramér Von-Mises estimation, Anderson-Darling estimation, right-tail Anderson-Darling estimation, percentile estimation, and maximum product of spacing estimation are presented for classical estimation. For illustrative purposes, two real data sets are analyzed. The investigation of the two real data sets reveals that the suggested techniques are practical and can be used to solve some engineering-related issues. In order to compare the results of the several estimation techniques that have been offered based on mean square error and absolute average bias, a simulation study is presented at the end. When adopting the smallest values for mean square error and absolute average bias, this study demonstrates that maximum product of spacing estimation is the technique that is most effective among the alternatives in most cases.

Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models

Recently, an improved adaptive Type-II progressive censoring scheme is proposed to ensure that the experimental time will not pass a pre-fixed time and ends the test after recording a pre-fixed number of failures. This paper studies the inference of the competing risks model from Weibull distribution under the improved adaptive progressive Type-II censoring. For this goal, we used the latent failure time model with Weibull lifetime distributions with common shape parameters. The point and interval estimation problems of parameters, reliability and hazard rate functions using the maximum likelihood and Bayesian estimation methods are considered. Moreover, making use of the asymptotic normality of classical estimators and delta method, approximate intervals are constructed via the observed Fisher information matrix. Following the assumption of independent gamma priors, the Bayes estimates of the scale parameters have closed expressions, but when the common shape parameter is unknown, the Bayes estimates cannot be formed explicitly. To solve this difficulty, we recommend using Markov chain Monte Carlo routine to compute the Bayes estimates and to construct credible intervals. A comprehensive Monte Carlo simulation is conducted to judge the behavior of the offered methods. Ultimately, analysis of electrodes data from the life-test of high-stress voltage endurance is provided to illustrate all proposed inferential procedures.

Survival Analysis and Applications of Weighted NH Parameters Using Progressively Censored Data

A new weighted Nadarajah–Haghighi (WNH) distribution, as an alternative competitor model to gamma, standard half-logistic, generalized-exponential, Weibull, and other distributions, is considered. This paper explores both maximum likelihood and Bayesian estimation approaches for estimating the parameters, reliability, and hazard rate functions of the WNH distribution when the sample type is Type-II progressive censored order statistics. In the classical interval setup, both asymptotic and bootstrap intervals of each unknown parameter are constructed. Using independent gamma priors and symmetric squared-error loss, the Bayes estimators cannot be obtained theoretically. Thus, two approximation techniques, namely: Lindley and Markov-Chain Monte Carlo (MCMC) methods, are used. From MCMC variates, the Bayes credible and highest posterior density intervals of all unknown parameters are also created. Extensive Monte Carlo simulations are implemented to compare the performance of the proposed methodologies. Numerical evaluations showed that the estimates developed by the MCMC sampler performed better than the Lindley estimates, and both behaved significantly better than the frequentist estimates. To choose the optimal censoring scheme, several optimality criteria are considered. Three engineering applications, including vehicle fatalities, electronic devices, and electronic components data sets, are provided. These applications demonstrated how the proposed methodologies could be applied in real practice and showed that the proposed model provides a satisfactory fit compared to three new weighted models, namely: weighted exponential, weighted Gompertz, and new weighted Lindley distributions.

Parameter Estimation in Step Stress Partially Accelerated Life Testing under Different Types of Censored Data

A long testing period is usually required for the life testing of high-reliability products or materials. It is possible to shorten the testing process by using ALTs (accelerated life tests). Due to the fact that ALTs test products in harsher settings than are typical use conditions, the life expectancy of the objects they evaluate is reduced. Censored data in which the specific failure timings of all units assigned to test are not known, or all units assigned to test have not failed, may arise in ALTs for a variety of reasons, including operational failure, device malfunction, expense, and time restrictions. In this paper, we have considered the step stress partially accelerated life test (SSPALT) under two different censoring schemes, namely the type-I progressive hybrid censoring scheme (type-I PHCS) and the type-II progressive censorship scheme (type-II PCS). The failure times of the items are assumed to follow NH distribution, while the tampered random variable (TRV) model is used to explain the effect of stress change. In order to obtain the estimates of the unknown parameters, the maximum likelihood estimation (MLE) approach is adopted. Furthermore, based on the asymptotic theory of MLEs, the approximate confidence intervals (ACIs) are also constructed. The point estimates under two censoring schemes are compared in terms of root mean squared errors (RMSEs) and relative absolute biases (RABs), while ACIs are compared in terms of their lengths and coverage probabilities (CPs). The performance of the estimators has been evaluated and compared under two censoring schemes with various sample sizes through a simulation study. Simulation results show that estimates with type-I PHCS outperform estimates with type-II PCS in terms of RMSEs, RABs, lengths, and CPs. Finally, a real-world numerical example of insulating fluid failure times is presented to show how the approaches will work in reality.

Analysis of Modified Kies Exponential Distribution with Constant Stress Partially Accelerated Life Tests under Type-II Censoring

This study investigates, for the first time, the product of spacing estimation of the modified Kies exponential distribution parameters as well as the acceleration factor using constant-stress partially accelerated life tests under the Type-II censoring scheme. Besides this approach, the conventional maximum likelihood method is also considered. The point estimates and the approximate confidence intervals of the unknown parameters are obtained using the two methods. In addition, two parametric bootstrap confidence intervals are discussed based on both estimation methods. Extensive simulation studies are conducted by considering different censoring schemes to examine the efficiency of each estimation method. Finally, two real data sets for oil breakdown times of insulating fluid and minority electron mobility are analyzed to show the applicability of the different methods. Moreover, the reliability function and the mean time-to-failure under the normal use condition are estimated using both methods. Based on Monte Carlo simulation outcomes and real data analysis, we recommend using the maximum product of spacing to evaluate both the point and interval estimates for the modified Kies exponential distribution parameters in the presence of constant-stress partially accelerated Type-II censored data.