Purpose The purpose of this paper is the reliability analysis for systems with dependent gamma degradation process and Weibull failure time. Design/methodology/approach Consider a life testing experiment in which a sample of n devices starts to operate at t=0 and the data are available on failure time and failure-evolving process on each individual, called in some contents wear or degradation. Ignoring the between performance characteristics dependency structure may lead us to different reliability estimations, while the dependency justly exists. In previous research, dependency between the degradation process and hard failure time has been studied in limited detail (special closed form expression). Thereafter, the dependency between two degradation processes with the same structure (gamma process) in a system is considered using the copula function. Findings The results indicate that ignoring the dependency structure may lead us to different reliability estimations while the dependency justly exists. Originality/value This study gives some contributions that evaluate reliability metrics with more than one failure mechanism that may not be independent and possibly follow a different distribution function. The authors have used the copula function as a basis to develop a proposal model and analysis methods. In addition, the authors discussed the identifiability of the copula. Finally, simulation data were used to review the suggested approach.

The step-stress accelerated degradation test (SSADT) is one of the most commonly used time-dependent types of stress loading tests that enables a shorter test duration. This test is more economical and flexible compared to accelerated degradation test or accelerated failure time (ADT/AFT) test plans. This test is suitable when constraints by test facilities, conditions, or samples exist. SSADT is more useful for developing products when there is inadequate knowledge for test conditions. Important aspects here are to evaluate each failure mode in the presence of the other modes by assuming some dependency structure between the failure modes due to the non-applicability of studying test units with isolated competing failure modes. This paper aims to propose a modeling approach to simultaneously analyze linear degradation data and failure time data with dependent competing risks in an SSADT experiment. We use the copula function to consider the dependency structures between two failure modes. The proposed model is applied to acceleration data, to simulation data sets and two real data sets-bus tire data set and plastic substrate active matrix light-emitting diodes (AMOLED) data set, accompanied by sensitivity analysis.

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