Using age and usage for prediction of reliability of an arbitrary system from a finite population

For single-use non-repairable systems, reliability is commonly estimated as a function of age and usage. For the effective management of individual systems or populations of systems, it is frequently important and necessary to predict the reliability in the future for age and usage values not yet observed. When predicting future system reliability, the age of the future system is easily predicted whereas future usage values will typically be unknown. In this paper we present the methodology for how to estimate both individual and population reliability summaries based on the currently known age and usage values. Projected usage values for future points in time can be obtained based on observed usage patterns or user-specified patterns of usage rates. Individual system summaries can be used to answer the questions ‘For a given system of age A and usage U, what is its reliability with associated uncertainty?’ or ‘For a given system with known current age A and usage U, but unknown usage in the future, what is its reliability with associated uncertainty?’ The population summary of interest predicts the probability that a system randomly selected from the population of systems works. This summary takes into consideration the estimation of future usage, the estimated probability of individual systems working at their given ages and usage values, and the life cycle demographics of the population of interest. In this paper we discuss these questions for a given application.