Abstract
For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.
Highlights
Bathtub-Shaped DistributionChen [1] used the term ‘bathtub-shaped distribution’ to refer to a lifetime distribution that possesses an increasing or bathtub-shaped hazard function with two parameters
Prior distributions as well as loss functions affect the accuracy of estimation under the Bayesian method
It is more efficient to estimate parameters under Type-I GHCS for product testing situations in practice, as this could save the time of testing and the cost resulting from failures of units
Summary
Chen [1] used the term ‘bathtub-shaped distribution’ to refer to a lifetime distribution that possesses an increasing or bathtub-shaped hazard function with two parameters. As it could depict the lifetimes for multiple mechanical and electrical products, this distribution is widely used in practice. [4] considered the Bayes estimations and estimates of two unknown parameters based on the maximum likelihood method under a bathtub-shaped distribution. A considerable amount of literature has been published on estimations under bathtub-shaped distribution based on a censoring scheme. The researchers in [6] investigated the Fisher information matrix, maximum likelihood estimates, and confidence intervals for unknown parameters under hybrid censored data.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
