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