Abstract
This paper describes a method for computing estimates for the location parameter μ > 0 and scale parameter λ > 0 with fixed shape parameter α of the alpha power exponential distribution (APED) under type-II hybrid censored (T-IIHC) samples. We compute the maximum likelihood estimations (MLEs) of (μ, λ) by applying the Newton-Raphson method (NRM) and expectation maximization algorithm (EMA). In addition, the estimate hazard functions and reliability are evaluated by applying the invariance property of MLEs. We calculate the Fisher information matrix (FIM) by applying the missing information rule, which is important in finding the asymptotic confidence interval. Finally, the different proposed estimation methods are compared in simulation studies. A simulation example and real data example are analyzed to illustrate our estimation methods.
Highlights
In experiments involving life testing and reliability, complete failure time information may not be achieved for all items
The primary purpose of the present paper is to propose an estimation method for the parameters and the reliability characteristics for alpha power exponential distribution (APED) using incomplete sample observations obtained by a type-II hybrid censored (T-IIHC)
The asymptotic confidence intervals (ACIs) based on the asymptotic normal distribution of the maximum likelihood estimations (MLEs) are approximated as the inverse of the observed Fisher information matrix evaluated at the MLE
Summary
In experiments involving life testing and reliability, complete failure time information may not be achieved for all items. T-ICS and T-IICS can be combined to form a hybrid censoring scheme (HCS), as first presented by Epstein [1], who studied the properties of the one-parameter exponential distribution. If the test is stopped at time T = max{Xr:n, T}, the HCS is called T-IIHC [5] The advantage of this approach is that it allows the complete lifetimes of at least r units to be recorded before the experiment is stopped. They considered applying MLEs and Bayes’ estimation for parameter and reliability studies, see Dong et al [15]. The primary purpose of the present paper is to propose an estimation method for the parameters and the reliability characteristics for APED using incomplete sample observations obtained by a T-IIHC.
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