Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

Abstract

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

Estimated Maximal Safe Dosages of Tumescent Lidocaine

“…[39][40][41] Figure 1. No subject experienced a peak serum lidocaine concentration larger than 4.4 μg/mL.…”

Estimated Maximal Safe Dosages of Tumescent Lidocaine

“…We used tolerance interval analysis to estimate the probability that a future milligram per kilogram dosage of tumescent lidocaine given to an individual would result in a Cmax ≥6 μg/mL. 39 – 41 Tolerance intervals were calculated at a 99% level of confidence.…”

Application of Tolerance Limits to the Characterization of Image Registration Performance

“…Using this concept, we can derive tolerance limits on the initial conditions that reliably lead to successful registration, while accounting for the variability in the performance of the algorithm observed from the data used in the evaluation. Tolerance limits have been applied in numerous application domains [12], such as clinical chemistry [13], assessment of bioequivalence [14] and characterization of degradation processes in electronic components for aerospace applications [15]. In general, a tolerance limit allows one to ensure a fixed proportion of a population exceeds a bound with specified confidence [5].…”