Stochastic modeling of aggregates and products of variable failure rates

This paper develops an unconventional but powerful approach to analyzing the observed and/or estimated failure rates of complex systems that operate in series and/or in parallel under varying operational and environmental conditions. Consequently such failure rates can be construed as time series which are complex in the sense that they are aggregates and/or products of two or more time series. Hence special time-series techniques are required for their analysis. Some of the results recently developed apply to the analysis of such time series. These results can also be used for the analysis of the reliability decay (growth) processes, actual failure times, times between failures, and interactions between failure times and maintenance times of complex systems