Analysis of Two Generalized Exponential Populations Under Joint Type-I Progressive Hybrid Censoring Scheme

This paper discussed inference for two generalized exponential using the joint type-I progressively hybrid censoring (JPHC-I) scheme. It assumed that the lifetime distribution of the items from the two populations follow generalized exponential distribution. Based on the JPHC-I scheme, we first consider the maximum likelihood estimators of the unknown parameters along with thier asymptotic confidence intervals. Next, we provide the Bayesian inferences of the unknown parameters under the assumptions of independent gamma priors on the scale parameters using squared error (SE) and linear-exponential (LINEX) loss functions. Markov Chain Monte Carlo (MCMC) techniques is applied to carry out the Bayesian estimation procedure and in turn calculate the credible intervals. To evaluate the performance of the estimators, numerical example is carried out

An Estimation of the Entropy for a Fréchet Distribution Based on Generalized Hybrid Censored Samples

In this paper, under generalized type-I hybrid censored samples; we derive the estimators for the entropy function of the Fréchet distribution. We also compare the introduced estimators in the sense of the relative mean squared error (RMSE) for various censored samples

New methods for modeling accelerated life test data

An accelerated life test (ALT) is often used to obtain timely information for highly reliable items. The increased use of ALTs has resulted in nontraditional reliability data which can not be analyzed with standard statistical methodologies. I propose new methods for analyzing ALT data for studies with (1) two independent populations, (2) paired samples and (3) limited failure populations (LFP). Here, the Weibull distribution, which can accommodate a variety of failure rates, is assumed for the models I develop. For case (1), a parametric hypothesis test, a Bayesian analysis and a test using partial likelihood are proposed and discussed. For paired samples, I show that there is no exact test for the equality of the survival distributions. Thus, several tests are investigated using a simulation study of their Type I errors. A Bayesian approach that allows for the comparison and estimation of the failure rates is also considered. For computation, Markov Chain Monte Carlo (MCMC) methods are implemented using BUGS. Certain types of devices (such as integrated circuits) that are operated at normal use conditions are at risk of failure because of inherent manufacturing faults (latent risk factors). A small proportion of defective units, p, may fail over time under normal operating conditions. For the non-defective units, the probability of failing under normal conditions during their technological lifetime is zero. Meeker ([29], [31]) called a population of such units a limited failure population (LFP). I propose a new model for LFP in which the number of latent risk factors and the times at which they become fatal depend on the stress level. This model allows for a fraction of the population to be latent risk free. For analyzing this model, I propose a classical as well as a Bayesian approach, which can be very useful when an engineer has expert knowledge of the manufacturing process. In all cases, a real data set is analyzed to demonstrate my procedures

Measurement Error Bias Reduction in Unemployment Durations

The impact of duration response measurement error is investigated by using small variance approximations. The inconsistency of GMM estimators that ignore measurement error is studied for both single spell models with right censoring, and for a two spell lagged duration dependence model. The results suggest a corrected GMM estimator for the error free and measurement error distributions. When the error free density is known, identification is achieved by using the moment condition that defines the measurement error sensitive specification score test. The results are applied to unemployment duration data from the BHPS.