Modelling failure rates according to time and influencing factors

Reliability of systems often depends on their age (aging or burn‐in period), on intrinsic factors (dimensioning, quality of components, material, etc.) and on conditions of use (environment, load rate, stress, etc.). Modelling of failure rates as a function of time and influencing factors is therefore proposed. The latter combines a Weibull distribution and a Cox proportional hazards model. A rather flexible representation of the system life phases is then possible, as well as consideration of a large variety of qualitative or quantitative, precise or approximate, influencing factors. The approach which is presented uses feedback data to define the model parameters by maximum likelihood estimations. An application on safety valves provides an illustration of this approach and an evaluation of the model performances.