Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

• Main Authors: E. H. Hafez, Fathy H. Riad, Sh. A. M. Mubarak, M. S. Mohamed
• Format: Article
• Language: English
• Published: MDPI AG 2020-12-01
• Series: Symmetry
• Subjects: type II of progressive censored sample; reliability function; simple step-stress accelerated life test; bayesian estimation; kolmogorov–smirnov; symmetric loss function
• Online Access: https://www.mdpi.com/2073-8994/12/12/2080

Saving money and time are very important in any research project, so we must find a way to decrease the time of the experiment. This method is called the accelerated life tests (ALT) under censored samples, which is a very efficient method to reduce time, which leads to a decrease in the cost of the experiment. This research project includes inference on Lindley distribution in a simple step-stress ALT for the Type II progressive censored sample. The paper contains two major sections, which are a simulation study and a real-data application on the experimental design of an industry experiment on lamps. These sections are used to conduct results on the study of the distribution. The simulation was done using Mathematica 11 program. To use real data in the censored sample, we fitted them to be compatible with the Lindley distribution using the modified Kolmogorov–Smirnov (KS) goodness of fit test for progressive Type II censored data. We used the tampered random variable (TRV) acceleration model to generate early failures of items under stress. We also found the values of the distribution parameter and the accelerating factor using the maximum likelihood estimation of (MLEs) and Bayes estimates (BEs) using symmetric loss function for both simulated data and real data. Next, we estimated the upper and lower bounds of the parameters using three methods, namely approximate confidence intervals (CIs), Bootstrap CIs, and credible CIs, for both parameters of the distribution, <inline-formula><math display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi>ζ</mi></semantics></math></inline-formula>. Finally, we found the value of the parameter for the real data set under normal use conditions and stress conditions and graphed the reliability functions under normal and accelerated use.