This study examines common-cause failure (CCF) in complex multi-state systems (MSSs), arising from factors such as external environmental influences and the aging of internal units. The random variables associated with system unit parameters are not restricted to exponential distributions and may instead follow various distribution types. The working time of each system unit is modeled using PH distributions, and a matrix-based analytical approach is applied. An improved universal generating function (UGF) is developed on the basis of the PH distribution, forming a reliability analysis method that integrates the enhanced UGF with PH modeling. The reliability of individual units under CCF is evaluated using the weight influence vector method and the factor model, and compared with those obtained under independent unit failures. Conducting CCF analysis is necessary, as it substantially reduces errors in practical applications. The variable speed hydraulic system of a pipe-lifting machine is used to demonstrate the accuracy and applicability of the method, and maintenance strategies are formulated to enhance system reliability. Protective measures are developed based on actual operating conditions to reduce CCF and improve system reliability. The study addresses the research gap in constructing a reliability model and performing corresponding computational analysis for cases in which unit parameter random variables in a multi-state system (MSS) may follow different distribution types under common-cause aging in engineering practice. Accounting for distributional differences in unit parameters provides new approaches for reliability analysis, strengthens the theoretical framework of MSSs, and offers practical guidance for engineering applications.
Z et al. (Tue,) studied this question.