Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions

Accelerated life tests are used to explore the lifetime of extremely reliable items by subjecting them to elevated stress levels from stressors to cause early failures, such as temperature, voltage, pressure, and so on. The alpha power inverse Weibull (APIW) distribution is of great significance and practical applications due to its appealing characteristics, such as its flexibilities in the probability density function and the hazard rate function. We analyze the step stress partially accelerated life testing model with samples from the APIW distribution under adaptive type II progressively hybrid censoring. We first obtain the maximum likelihood estimates and two types of approximate confidence intervals of the distributional parameters and then derive Bayes estimates of the unknownparameters under different loss functions. Furthermore, we analyze three probable optimum test techniques for identifying the best censoring under different optimality criteria methods. We conduct simulation studies to assess the finite sample performance of the proposed methodology. Finally, we provide a real data example to further demonstrate the proposed technique

Statistical inference for dependent competing risks data under adaptive Type-II progressive hybrid censoring

In this article, we consider statistical inference based on dependent competing risks data from Marshall-Olkin bivariate Weibull distribution. The maximum likelihood estimates of the unknown model parameters have been computed by using the Newton-Raphson method under adaptive Type II progressive hybrid censoring with partially observed failure causes. The existence and uniqueness of maximum likelihood estimates are derived. Approximate confidence intervals have been constructed via the observed Fisher information matrix using the asymptotic normality property of the maximum likelihood estimates. Bayes estimates and highest posterior density credible intervals have been calculated under gamma-Dirichlet prior distribution by using the Markov chain Monte Carlo technique. Convergence of Markov chain Monte Carlo samples is tested. In addition, a Monte Carlo simulation is carried out to compare the effectiveness of the proposed methods. Further, three different optimality criteria have been taken into account to obtain the most effective censoring plans. Finally, a real-life data set has been analyzed to illustrate the operability and applicability of the proposed methods

Analysis of Generalized Inverted Exponential Distribution under Adaptive Type-I Progressive Hybrid Censored Competing Risks Data

The estimation of the unknown parameters of generalized inverted exponential distribution under adaptive type-I progressive hybrid censored scheme (AT-I PHCS) with competing risks data will be discussed. The reason why AT-I PHCS has exceeded other failure censored types; Time censored types enable analysts to accomplish their trials and experiments in a shorter time and with higher efficiency. In this regards, we obtain the maximum likelihood estimation of the parameters and the asymptotic confidence intervals for the unknown parameters. Further, Bayes estimates of the parameters which obtained based on squared error and LINEX loss functions under the assumptions of independent gamma priors of the scale parameters. For Bayesian estimation, we take advantage of Markov Chain Monte Carlo techniques to derive Bayesian estimators and the credible intervals. Finally, two data sets with Monte Carlo simulation study and a real data set are analyzed for illustrative purposes

Inference for Step-Stress Partially Accelerated Life Test Model with an Adaptive Type-I Progressively Hybrid Censored Data

Consider estimating data of failure times under step-stress partially accelerated life tests based on adaptive Type-I hybrid censoring. The mathematical model related to the lifetime of the test units is assumed to follow Rayleigh distribution. The point and interval maximum-likelihood estimations are obtained for distribution parameter and tampering coefficient. Also, the work is conducted under a traditional Type-I hybrid censoring plan (scheme). A Monte Carlo simulation algorithm is used to evaluate and compare the performances of the estimators of the tempering coefficient and model parameters under both progressively hybrid censoring plans. The comparison is carried out on the basis of mean squared errors and bias

Inference In The Log-Logistic Distribution Based On An Adaptive Progressive Type-Ii Censoring Scheme

The primary aim of this study is to explore the maximum likelihood estimation (MLE) and the Bayesian approach to estimate the parameters of log-logistic model and calculate the approximate confidence interval for the parameters and the survival function in both methods based on an adaptive progressive type-II censoring scheme. The parameters of the probability distribution are estimated via the Newton-Raphson Method and the Bayes estimators, based on squared error loss function (SELF). The approximate confidence interval for the reliability function has been calculated using the delta method; the approximate credible intervals for the unknown parameters and the survival function using the Bayesian approach have been constructed using Markov Chain Monte Carlo (MCMC) method. Moreover, a Monte Carlo study has performed to examine the proposed methods under different situations, based on mean squared error, bias, coverage probability, and expected length estimated criteria. Application to real life data is included, in order to view how the proposed methods, work in practice. It is observed that the Bayesian approach is better than MLE for estimating the log-logistic model parameters

Different Estimation Methods and Joint Condence Region for the Inverse Burr Distribution Based on Progressively First-Failure Censored Sample with Application to the Nanodroplet Data

In this article, the point and interval estimation of parameters for an in-verse Burr distribution based on progressively rst-failure censored sampleis studied. In point estimation, the maximum likelihood and Bayesian meth-ods are developed for estimating the unknown parameters. An expectation-maximization algorithm is applied for computing the maximum likelihoodestimators. The Bayes estimates relative to both the symmetric and asym-metric loss functions are provided using the Lindley's approximation andthe Metropolis-Hastings algorithm. In interval estimation, approximate andexact condence intervals with the exact condence region for the two parameters have been introduced. Moreover, the proposed methods are carriedout to a real data set contains the spreading of nanodroplet impingementonto a solid surface in order to demonstrate the applicabilities

Stress-strength reliability estimation for the inverted exponentiated Rayleigh distribution under unified progressive hybrid censoring with application

In this paper, we studied the estimation of a stress-strength reliability model (R = P(X>Y)) based on inverted exponentiated Rayleigh distribution under the unified progressive hybrid censoring scheme (unified PHCS). The maximum likelihood estimates of the unknown parameters were obtained using the stochastic expectation-maximization algorithm (stochastic EMA). The asymptotic confidence intervals were also created. Under squared error and Linex and generalized entropy loss functions, the Gibbs sampler together with Metropolis-Hastings algorithm was provided to compute the Bayes estimates and the credible intervals. Extensive simulations were performed to see the effectiveness of the proposed estimation methods. Also, parallel to the development of reliability studies, it is necessary to study its application in different sciences such as engineering. Therefore, droplet splashing data under two nozzle pressures were proposed to exemplify the theoretical outcomes

Estimations and optimal censoring schemes for the unified progressive hybrid gamma-mixed Rayleigh distribution

Censoring is a common occurrence in reliability engineering tests. This article considers estimation of the model parameters and the reliability characteristics of the gamma-mixed Rayleigh distribution based on a novel unified progressive hybrid censoring scheme (UPrgHyCS), where experimenters are allowed more flexibility in designing the test and higher efficiency. The maximum likelihood estimates of the model parameters and reliability are provided using the stochastic expectation–maximization algorithm based on the UPrgHyCS. Further, the Bayesian inference associated with any parametric function of the model parameters is considered using the Markov chain Monte Carlo method with the Metropolis-Hastings (M-H) algorithm. Asymptotic confidence and credible intervals of the proposed quantities are also created. The maximum a posteriori estimates of the model parameters are acquired. Due to the importance of determining the optimal censoring scheme for reliability problems, different optimality criteria are proposed and derived to find it. This method can help to design experiments and get more information about unknown parameters for a given sample size. Finally, comprehensive simulation experiments are provided to investigate the performances of the considered estimates, and a real dataset is analyzed to elucidate the practical application and the optimality criterion work in real life scenarios. The Bayes estimates using the M-H technique show the best performance in terms of error value

Inference About The Generalized Exponential Quantiles Based On Progressively Type-Ii Censored Data

In this study, we are interested in investigating the performance of likelihood inference procedures for the ℎ quantile of the Generalized Exponential distribution based on progressively censored data. The maximum likelihood estimator and three types of classical confidence intervals have been considered, namely asymptotic, percentile, and bootstrap-t confidence intervals. We considered Bayesian inference too. The Bayes estimator based on the squared error loss function and two types of Bayesian intervals were considered, namely the equal tailed interval and the highest posterior density interval. We conducted simulation studies to investigate and compare the point estimators in terms of their biases and mean squared errors. We compared the various types of intervals using their coverage probability and expected lengths. The simulations and comparisons were made under various types of censoring schemes and sample sizes. We presented two examples for data analysis, one of them is based on simulated data set and the other one based on a real lifetime data. Finally, we compared the classical inference and the Bayesian inference procedures. We concluded that Bias and MSE for classical statistics estimators show bitter results than the Bayesian estimators. Also, Bayesian intervals which attain the nominal error rate have the best average widths. We presented our conclusions and discussed ideas for possible future research