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In manufacturing industries and several other fields, accelerated life testing is used widely to obtain sufficient failure time data of test units quickly as compared to normal use conditions. It is assumed that the lifetime of a product at constant stress level follows generalized inverse Lindley distribution. It is a common observation that while estimating the parameters of a model, one usually adopts the maximum likelihood estimation method as the starting point. In this paper, we consider eight frequentist methods of estimation, besides using the maximum likelihood method for estimating the parameters of the generalized inverse Lindley distribution under constant stress accelerated life test. In addition, the shape parameter and the reliability function of the model under usual conditions are obtained using nine considered estimation methods. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their mean relative estimates and mean square errors using small, medium and large sample sizes. One accelerated life test data set is analyzed for illustrative purposes. In addition, bootstrap confidence intervals of the parameters are obtained as part of data analysis based on the considered estimation methods.

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.

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