Parameter estimation for load‐sharing system subject to Wiener degradation process using the expectation‐maximization algorithm

Abstract

In practice, many systems exhibit load‐sharing behavior, where the surviving components share the total load imposed on the system. Different from general systems, the components of load‐sharing systems are interdependent in nature, in such a way that when one component fails, the system load has to be shared by the remaining components, which increases the failure rate or degradation rate of the remaining components. Because of the load‐sharing mechanism among components, parameter estimation and reliability assessment are usually complicated for load‐sharing systems. Although load‐sharing systems with components subject to sudden failures have been intensely studied in literatures with detailed estimation and analysis approaches, those with components subject to degradation are rarely investigated. In this paper, we propose the parameter estimation method for load‐sharing systems subject to continuous degradation with a constant load. Likelihood function based on the degradation data of components is established as a first step. The maximum likelihood estimators for unknown parameters are deduced and obtained via expectation‐maximization (EM) algorithm considering the nonclosed form of the likelihood function. Numerical examples are used to illustrate the effectiveness of the proposed method.

Prediction intervals for load‐sharing systems in accelerated life testing

“…Hence, the load increases nonlinearly. Note that this load-sharing rule has previously been used 12,31 but without the function h. The Basquin link was also used by Kong and Ye 15 for load-sharing models based on exponentially distributed lifetimes of the components. We are aware that our model does not include damage accumulation and aging.…”

Load-Sharing Model under Lindley Distribution and Its Parameter Estimation Using the Expectation-Maximization Algorithm

“…[ 14 ] investigated the load-sharing system model, in which the failure times of each component can be either constant or time-dependent. It deserves mentioning that Bayesian analyses of the load-sharing systems with several well-known distributions of lifetime components have also been investigated in the literature [ 15 , 16 , 17 ]. For instance, Xu et al.…”

“…Xu et al. [ 17 ] proposed the expectation-maximization (EM) algorithm for estimating the parameters in the load-sharing system with continuous degradation.…”

“…Singh and Gupta [12,13] and Singh et al [14] investigated the load-sharing system model, in which the failure times of each component can be either constant or time-dependent. It deserves mentioning that Bayesian analyses of the load-sharing systems with several well-known distributions of lifetime components have also been investigated in the literature [15][16][17]. For instance, Xu et al [15] studied a test scheme for reliability demonstration test on load-sharing systems with Weibull-distributed (including exponential) lifetime components.…”

“…More recently, Singh and Goel [16] studied a multi-component parallel system model by assuming a load-sharing tendency on its components. Xu et al [17] proposed the expectation-maximization (EM) algorithm for estimating the parameters in the load-sharing system with continuous degradation.…”