A New Modified Lifetime Distribution via a series-parallel system Approach

Mathematical Formulation, Estimation with Simulation Study under Progressive Type II Censoring Scheme and Real Data Validation

Abstract

Motivated by the series-parallel arrangement of a system, a new modified lifetime distribution is introduced by compounding the Alpha Power Modified Weibull Distribution with the Geometric Distribution twice, named Alpha Power Modified Weibull-2 Geometric Distribution. The new family can allow various hazard rate curves that compete well with other alternatives in fitting real data. We derive formal expressions for its moments, generating function, mean residual lifetime, and other reliability functions. Keeping the perspective of the importance of censoring in reliability and lifetime studies, the maximum likelihood estimation method under progressive type II censoring is used to estimate the model parameters. To investigate the performance of these methods, a simulation study is administered. Finally, application of the distribution to 2 real data sets is presented to illustrate the flexibility of the proposed distribution for both the uncensored and censored samples, and also for a comparative study with other competing distributions.