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Reliability Analysis of Load-sharing Systems using a Flexible Model with Piecewise Linear Functions

Aiming for accurate estimation of system reliability of load-sharing systems, a flexible model for such systems is constructed by approximating the cumulative hazard functions of component lifetimes using piecewise linear functions. The advantages of the resulting model are that it is data-driven and it does not use prohibitive assumptions on the underlying component lifetimes. Due to its flexible nature, the model is capable of providing a good fit to data obtained from load-sharing systems in general, thus resulting in an accurate estimation of important reliability characteristics. Estimates of reliability at a mission time, quantile function, mean time to failure, and mean residual time for load-sharing systems are developed under the proposed model involving piecewise linear functions. Maximum likelihood estimation and construction of confidence intervals for the proposed model are discussed in detail. The performance of the proposed model is observed to be quite satisfactory through a detailed Monte Carlo simulation study. Analysis of a load-sharing data pertaining to the lives of a two-motor load-sharing system is provided as an illustrative example. In summary, this article presents a comprehensive discussion on a flexible model that can be used for load-sharing systems under minimal assumptions.