Optimum Step-Stress Accelerated Life Test Plan for Lomax Distribution with an Adaptive Type-II Progressive Hybrid Censoring
Amal S. Hassan
Institute of Statistical Studies & Research, Cairo University, Egypt.
Salwa M. Assar
Institute of Statistical Studies & Research, Cairo University, Egypt.
A. Shelbaia *
Institute of Statistical Studies & Research, Cairo University, Egypt.
*Author to whom correspondence should be addressed.
Abstract
The adaptive type-II progressive hybrid censoring has the advantage of saving both the total test time and the cost of the experiment; also it increases the efficiency of the statistical analysis. This article discusses k-level step stress accelerated life tests based on an adaptive type-II progressive hybrid censoring with product's life time following Lomax distribution. The scale parameter of the Lomax failure time distribution at constant levels is assumed to be a log linear function of the stress level. Maximum likelihood estimators of the model parameters are derived. Based on normal approximation to the asymptotic distribution of maximum likelihood estimators, the approximate confidence intervals for model parameters are obtained. The optimal times of changing stress levels are discussed under D-optimality and A-optimality criteria. Such methods maximize the determinant and the trace of Fisher's information matrix for the model parameters. Analysis of the numerical data has been presented for illustrative proposes.
Keywords: Adaptive type-II progressive censoring, -level step stress accelerated life testing, Cumulative exposure model, Optimum test plan, Lomax distribution.