Degradation modeling using threshold exceedance data

In certain applications important decisions are based on degradation processes exceeding a threshold, while in other situations only upcrossing data are available for analysis. An upcrossing is defined as a process crossing a threshold from below. Two major topics are covered in this thesis: hypothesis test for trend and estimation for trend. We compare the performance of various tests and estimators when the raw data degrade to upcrossing data.;We investigate using nonparametric methods to test for trend in the underlying process using high/low exceedance data and upcrossing data. We propose modifications for nonparametric tests to remedy the non-monotonic trend problem in upcrossing intervals. We invent a new test based on Markov chains and the combined Markov and modified Spearman test is shown to perform well.;We use two different approaches to estimate the deterioration trend using upcrossing data. The all-sample-path (ASP) method uses a likelihood function which is obtained by listing all possible high/low paths between two upcrossings. The approximate odd and even (AOE) method models the upcrossing process as a Markov chain which reaches its steady state after two transitions. The AOE method is shown to have similar performance as ASP but is much simpler and faster. The robustness of AOE method is studied against non-normality, autocorrelation, fat tails and non-constant variance. We also compare AOE with ordinary least squares (OLS) using a Gaussian white noise with linear trend model.;We propose rules for selecting optimal threshold values for the hypothesis test and parametric estimation. A 0 threshold is preferred for the hypothesis test but a high threshold is preferred for the parametric estimation.;An application to jet engine exhaust gas temperature (EGT) is given. We build a regression model to relate EGT with other operating factors such as ambient temperature, airport altitude, etc. We apply AOE to the Loess smooth residuals from EGT and the AOE RMSE is about 10-20 times larger than that of OLS. When we apply it to the raw EGT data to track the local trend through a moving window, the AOE RMSE is only 2 times larger than OLS, but it uses much less information than OLS.