Statistical analysis of Gompertz distribution based on progressively type-II censored competing risk model with binomial removals

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimators is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods

Statistical analysis of Gompertz distribution based on progressively type-II censored competing risk model with binomial removals

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimators is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods

Stress-strength reliability of Weibull distribution based on progressively censored samples

Based on progressively Type-II censored samples, this pape r deals with inference for the stress- strength reliability R = P ( Y < X ) when X and Y are two independent Weibull distributions with different scale parameters, but having the same shape param eter. The maximum likelihood esti- mator, and the approximate maximum likelihood estimator of R are obtained. Different confidence intervals are presented. The Bayes estimator of R and the corresponding credible interval using the Gibbs sampling technique are also proposed. Further, we consider the estimation of R when the same shape parameter is known. The results for exponenti al and Rayleigh distributions can be obtained as special cases with different scale parameter s. Analysis of a real data set as well a Monte Carlo simulation have been presented for illustrativ e purposes.Peer Reviewe

Stress-strength reliability of Weibull distribution based on progressively censored samples

Based on progressively Type-II censored samples, this paper deals with inference for the stress-strength reliability R = P(Y < X) when X and Y are two independent Weibull distributions with different scale parameters, but having the same shape parameter. The maximum likelihood estimator, and the approximate maximum likelihood estimator of R are obtained. Different confidence intervals are presented. The Bayes estimator of R and the corresponding credible interval using the Gibbs sampling technique are also proposed. Further, we consider the estimation of R when the same shape parameter is known. The results for exponential and Rayleigh distributions can be obtained as special cases with different scale parameters. Analysis of a real data set as well a Monte Carlo simulation have been presented for illustrative purposes

Estimation and prediction for proportional hazard family based on a simple step-stress model with Type-II censored data

The accelerated life testing is the key methodology of assessing product reliability rapidly. This type of life testing is more efficient with low cost than the classical reliability testing. For this, estimating of the underlying model and predicting the future life failure times are issues deserve the attention and follow-up. In this paper, a simple step-stress testing experiment is considered when the lifetime data comes from a proportional hazard family under Type-II censoring. We discuss frequentist and Bayes estimates of the underlying model parameters. Prediction of unobserved or censored lifetimes is also tackled here, and frequentist and Bayesian predictors are developed. An algorithm is presented to generate ordered lifetime data from the proportional hazard family under the simple step-stress accelerated lifetime testing. Two numerical examples are also provided to illustrate the estimation and prediction methods presented in this paper. Finally, a Monte Carlo simulation experiment is performed to evaluate the performance of the various estimation and prediction methods developed in this paper

Evaluations of the mean residual lifetime of an m-out-of-n system

The mean residual lifetime is an important measure in the reliability theory and in studying the lifetime of a living organism. This paper presents sharp upper bounds on the deviations of the mean residual lifetime of an m-out-of-n system from the mean of a residual life random variable Xt=(X-tX>t), for any arbitrary t>0 in various scale units generated by central absolute moments. The results are derived by using the greatest convex minorant approximation combined with the Hölder inequality. We also determine the distributions for which the bounds are attained. The optimal bounds are numerically evaluated and compared with other classical rough bounds.