System reliability models with stress covariates for changing load profiles

This paper presents various models to estimate reliability for a future profile with increased stress using the current observations to develop a model for future reliability. For the foreseeable future the equipment itself will not change, and thus the increase of the load or stress, that the system is exposed to, may decrease reliability and increase maintenance. The model is required to determine the impact of these future pro files. This paper is motivated by an actual application modeling the current and anticipated future reliability of naval aircraft launch and recovery equipment (ALRE). The cycles-to-failure data (CTF) was generated by simulation and serves as the basis in explaining four methods that will be evaluated during 2011-2012. System reliability models are presented and demonstrated to anticipate system reliability and availability for changing and increasing applied loading distributions. These models are int ended for systems whose components are exposed to predictable and quantifiable, but changing loading patterns. In the intended application, the models will be used to estimate the future reliability of naval aircraft catapult and arresting gear when subjected to different air wing compositions. Each air wing usage profile is potentially different, forming a distribution of usage stresses, and this distribution is shifting with time, as aircraft weight and missions change. The current ALRE systems will continue to be used for the foreseeable fut ure and the model is required to predict future performance and to identify the most unreliable components or problems within the existing design. Weibull distribution models are used in the typical fashion to model component failure times, but the initial Weibull distribution parameters are mathematical functions of the current, known applied stress distributions. These component models are then used within a discrete event simulation model to predict system reliability and availability. After this initial evaluation, models and software normally applied for accelerated life testing applications are used to develop models which have Weibull distribution parameters that are both mathematical functions with usage stress covariates and also mathematical functions of the distribution or variations in the changing applied loading conditions. Four specific modeling approaches are presented, and compared and contrasted based on data requirements, practicality and other criteria. The four modeling approaches involved models and data analysis at the component-level based on (i) linear stress adjusted usage measures in place of time, (ii) nonlinear stress adjusted usage measures in place of time, (iii) Weibull shape parameters modeled using a general log-linear model based on the mean and standard deviation of critical stress measures in a changing environment, and (iv) Weibull shape parameters modeled using a general log-linear model based on the distributional form of critical stress measures in a changing environment. The component models are then assembled into a system model. This methodology is demonstrated and compared on an example system using simulated data. The models collectively provide a practical methodology to use existing failure and usage stress data to predict future reliability based on a changing and increasing loading pattern.