A study of reliability of phased mission systems using time varying copula and stress dependent parameters

The present paper focuses on reliability analysis of a phased mission system (PMS) with time-varying dependence structure used to account for environmental disturbances over a specified number of mission cycles. Gumbel-Hougaard copula parameterized to depend on time is used for the purpose. It is assumed that the copula parameter is generated by Autoregressive Moving Average ( ARMA)(1,1) process . Each component in a phase is assumed to follow Weibull life distribution. The effect of external environmental factors such as temperature and pressure on each component resulting in its degradation is modelled using generalized Eyring relationship . The performances of a PMS after each cycle are measured using reliability and mean residual life time. The method developed has been explained using a numerical example of an aircraft flight PMS wherein the PMS model with time-varying copula has been compared with that based on constant copula parameter, and also compared with that without environmental stress factors for a given number of cycles.