Incorporation of expert estimates in the Weibull representation of age-dependent reliability

This paper presents a calculation procedure that can be used to incorporate expert estimates of the impact of various engineering changes (e.g., design and manufacturing process changes) into the Weibull representation of an age-dependent reliability analysis. To account for uncertainty in reliability prediction, this framework of analysis characterizes reliability using a family of Weibull curves. Each member of this family of curves is assigned with a probability representing the probability of it being the true distribution. To reflect the uncertainty in the expert assessment of the impact of engineering changes on the future reliability performance, expert estimates are expressed in terms of best estimate and uncertainty bounds. This simple representation of the uncertainty in expert estimates is adopted to avoid unnecessary complexity in estimates with little solid data or information. The effects of the various engineering changes can be aggregated to obtain an overall estimate of improvement/deterioration on reliability performance. This overall estimate can then be combined with the estimate from previous prediction to derive a new projection at specific age level(s). Based on these new reliability values, new sets of parameter values for the Weibull curves can be derived and used to represent the future reliability performance. As such, this calculation process entails the use of a consistent framework with consideration of uncertainty, which can be used for the update of reliability prediction based on new information on design and manufacturing changes, changes in product usage environment, test results, and field performance. It provides a more mechanistic process for establishing prior probability distributions for Bayesian analysis, which are generally considered as the most difficult or controversial aspect of the Bayesian approach.