Non-stationary functional series modeling and analysis of hardware reliability series: a comparative study using rail vehicle interfailure times

A novel reliability modeling and analysis framework based upon the distinct class of non-stationary Functional Series (FS) models is introduced. This framework allows for non-stationary reliability modeling, evolution assessment, analysis (including non-stationarity assessment, dependency assessment, as well as cycle detection), and prediction. The Functional Series framework is used for the modeling and analysis of two rail vehicle reliability series (Times Between Failures, TBFs), while comparisons with alternative (ARIMA, adaptive RARMA–RML, and Bayesian) modeling approaches are also made. The results indicate the advantages and usefulness of the Functional Series framework, as the TBF modeling accuracy is improved, its non-stationarity and serial dependency are established, the presence of cyclic patterns is revealed, and reliability evolution is assessed. It is conjectured that the cycles revealed in the TBF series may be related to maintenance policies. Finally, reliability prediction is shown to be feasible, although the “larger” excursions in the TBF series are difficult to accurately predict.