Comparison of Different Confidence Intervals under Type-I Censoring Scheme

Abstract

In a life testing experiment, the successive failure times at putting $n$ units under test are recorded under consideration that the advance fixed experiment is terminated at time T. This type of censoring scheme, called conventional Type-I censoring scheme, is used widely. In this paper, we assume that the items’ failure times are independent and distributed with exponential lifetime distribution with parameter $\theta$ . The estimator with maximum likelihood method is obtained in an exact form and its distribution is also obtained with the unknown parameter. We proposed the exact confidence interval, for estimators $\widehat{\theta }$ and $\text{ln}\widehat{\theta }$ , asymptotic confidence intervals, confidence interval under likelihood ratio test, and finally, two bootstrap confidence intervals. Under the Bayesian approach, the unknown parameter is estimated and the corresponding credible interval is obtained considering the prior information formulated with the inverted gamma distribution. The Monte Carlo simulation study is used to compare different methods. Finally, for illustrative purposes, the real dataset is used and analyzed.