Reliability Analysis of Hybrid System Using Geometric Process in Multiple Level of Constant Stress Accelerated Life Test through Simulation Study for Type-II Progressive Censored Masked Data

Abstract

Numerous studies have already been attempted to explore the reliability of systems considering mask data, though the mass of them has largely focused on basic series or parallel systems, where component failures are assumed to follow an exponential or Weibull distribution. However, most electrotonic products and systems are made up of numerous components integrated in parallel-series, series-parallel, and other bridge hybrid structures, and the number of studies in the area of accelerated life testing (ALT) employing masked data for hybrid systems is limited. In this paper, the constant-stress ALT (CSALT) is explored based on type-II progressive censoring scheme (TIIPCS) for a four-component hybrid system using geometric process (GmP). The failure times of the components of the system are assumed to follow the generalized Pareto (GP) distribution. The maximum likelihood estimate (MLE) technique is used to establish statistical inference for the model's unknown parameters under the premise that the failure reasons are unknown for the hybrid system. In addition, the asymptotic confidence intervals (ACIs) are also obtained by inverting the fisher information matrix. Finally, a simulation study is given to explain the proposed techniques and to evaluate the performance of the estimates. The performance of MLEs is assessed in terms of root mean square errors (RMSEs) and relative absolute biases (RABs), whereas the performance of ACIs is assessed in terms of their interval length (IL) and coverage probabilities (CPs). The findings show that the technique can deliver good estimation performance with small and intermediate sample sizes, and the estimates are more accurate when more failures are observed, showing the estimation method's efficiency.

Some Extended Geometric Processes and Their Estimation Methods

“…This phenomenon can be described by the geometric process (GP), which was first introduced by [1]. Since then, the GP has been widely applied in different fields such as software reliability analysis [2], [3], reliability analysis [4], maintenance policy optimisation [5], [6], warranty analysis [7] and electricity pricing, etc. [8]- [11].…”