Inference on adaptive progressive hybrid censored accelerated life test for Gompertz distribution and its evaluation for virus-containing micro droplets data

Abstract

In this paper, we discuss the problem of estimating the unknown parameters of the Gompertz distribution and the acceleration factor under constant-stress partially accelerated life test model. Based on adaptive Type II progressive hybrid censored samples, the maximum likelihood estimates of the model parameters and acceleration factor are derived. From Bayesian aspect, the Bayes estimates of the unknown parameters are obtained using the Gibbs sampler together with Metropolis-Hastings (GMH) algorithm. Based on the interval estimation viewpoint, the asymptotic, Bayesian credible and bootstrap confidence intervals for model parameters and acceleration factor are also constructed. In order to investigate the impact of estimation procedures and methodologies adopted, a simulation study is performed. Finally, a real life example contains the persistence of the virus-containing micro droplets is analyzed to illustrate the application of the partially accelerated life test model. It is observed that the GMH algorithm is superior for estimating the parameters of partially accelerated life test model after comparison. The results of real example analysis show that the proposed model can be applied to the engineering problem and the considered methods are suitable for the modeling of the virus-containing micro droplets lifetime data under two co-current air flow velocities.

Keywords

• Adaptive Type II progressive hybrid
• Bayesian estimation
• Bootstrap method
• Constant-Stress partially accelerated life tests
• Virus-containing micro droplets