Affiliations: [a]
Department of Mathematics, Faculty of Science, The Hashemite University, Zarqa, Jordan
| [b]
Department of Mathematics, Faculty of Science, Ajloun National University, Ajloun, Jordan
Correspondence:
[*]
Corresponding author. Hatim Solayman Migdadi, Department of Mathematics, Faculty of Science, The Hashemite University, P. O. Box 330127, Zarqa 13133, Jordan. E-mail: [email protected].
Abstract: In this paper, a new extension of the standard Rayleigh distribution called the Power Rayleigh distribution (PRD) is investigated for the accelerated life test (ALT) using the geometric process (GP) under Type-I censored data. Point estimates of the formulated model parameters are obtained via the likelihood estimation approach. In addition, interval estimates are obtained based on the asymptotic normality of the derived estimators. To evaluate the performance of the obtained estimates, a simulation study of 4, 5 and 6 levels of stress is conducted for ALT in different combinations of sample sizes and censored times. Simulation results indicated that point estimates are very close to their initial true values, have small relative errors, are robust and are efficient for estimating the model parameters. Similarly, the interval estimates have small lengths and their coverage probabilities are almost converging to their 95% nominated significance level. The estimation procedure is also improved by the approach of finding optimum values of the acceleration factor to have optimum values for the reliability function at the specified design stress level. This work confirms that PRD has the superiority to model the lifetimes in ALT using GP under any censoring scheme and can be effectively used in reliability and survival analysis.
Keywords: Accelerated life test, geometric process, power ryleigh distribution, maximum likelihood estimation, optimum test plan
