Bayesian dynamic forecasting for attribute reliability

In this paper, we consider a Bayesian dynamic forecasting model that utilizes both the engineering knowledge about the product reliability and attributes (success or failure) data gathered from the inspection of the early stage of development or storage. We assume that a prior distribution of reliability follows a beta distribution. The expected reliability is represented as a cumulative logistic function of the length of time that a new product has been under development or a finished item has been stockpiled in storage. As periodic testing produces attribute data, a prior distribution is updated. The expected reliability and forecasting errors are obtained from a posterior distribution that reflects the uncertainty involved in forecasting. The proposed method is applied to predict the expected reliability decay of a gyroscope in a missile stockpile.