Çağatay Çetinkaya

An s-out-of-k type of multi-component system is handled in the case of strength components exposed to common random stress. In this reliability scheme, random stress has been considered in the competing risk setup. Each stress and strength component is assumed to follow the general scale family of distributions. Classical inferences are obtained using the maximum likelihood method with the corresponding approximate confidence intervals. Bootstrap confidence intervals are also provided using the logit transformation method as an alternative to the asymptotic confidence intervals. Further, Bayesian inferences and their corresponding highest posterior density credible intervals with the conjugate priors are obtained using Lindley's approximation method and Monte Carlo Markov chains. In Bayesian process, different loss functions are considered as symmetric and asymmetric. The theoretical outcomes' performance is evaluated with simulated data sets and real-data examples.

In the case of operating conditions in a much shorter time, the accelerated life test models are commonly used method since these models let the experimenters control the higher stress levels to be used for components or items in the life tests. Among different accelerated life test methods, constant stress accelerated life test models have a relationship between “failure time” and “stress” and these models are quite popular since they help the experimenters save time and cost. In this study, we evaluate the performances of the parameter estimations of the two-parameter bathtub-shaped lifetime distribution introduced by Chen (Stat Probab Lett 49(2):155–161, 2000) under the constant stress accelerated life test model using the well-known eight different inference methods. Then, we investigate the optimal stress levels using some popular criteria. Then, the performances of the estimations are compared with simulation schemes. Simulation results showed that the maximum likelihood method provides better estimation performances than others. The estimation performances of the other methods can be changed according to the stress level of the accelerated life test model. Further, it is observed that increasing stress levels provide optimal accelerated life test schemes under fixed first stress levels. Finally, we use a real data example to illustrate the theoretical outcomes.

The generalized progressive censoring scheme has been considered one of the most general cases of censoring schemes. In this study, we consider two Weibull populations under a jointly generalized progressive hybrid censoring scheme as a more flexible extension of the exponential distribution. The methods presented in this paper let experimenters evaluate life testing studies in the case of the most generalized censoring scheme based on a flexible istribution that has increasing, constant, and decreasing failure rates. The maximum likelihood method is used to obtain point estimates of the unknown parameters and the corresponding approximate confidence intervals by using asymptotic theory and bootstrap sampling. The Bayesian inferences are handled under informative and non-informative priors. The highest posterior density credible intervals are also obtained for the Bayesian estimations. We further obtained results with a challenging task an optimal censoring scheme using the A-optimality, D-optimality, and F-optimality criterion to let researchers determine the optimal censoring plan before conducting experiments or collecting data. Following the numerical results within this paper, A-optimality and D-optimality proposed the same scheme, while F-optimality proposed a scheme similar to them. In the last part of the study, we provide simulation studies under different censoring plans and use a numerical example to exemplify the theoretical outcomes. It is observed that the best estimation performances are obtained by informative Bayesian methods.

Summary: In this paper, we studied the estimation of 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 . 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 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.

This paper deals with the improved point estimations of the inverse power Lindley distribution. The maximum likelihood estimation method, and a simulated annealing algorithm, a heuristic alternative method, are considered. The bias-corrected estimation methods are also used to evaluate the bias reduction of the estimates. These bias-corrected estimates are obtained with theoretical and bootstrap methods. The performances of the estimators are evaluated with simulation studies and two real-data examples.