An approach to response-based reliability analysis of quasi-linear Errors-in-Variables models

Abstract

The paper presents an approach to internal reliability analysis of observation systems known as Errors-in-Variables (EIV) models with parameters estimated by the method of least squares. Such problems are routinely treated by total least squares adjustment, or orthogonal regression. To create a suitable environment for derivations in the analysis, a general nonlinear form of such EIV models is assumed, based on a traditional adjustment method of condition equations with unknowns, also known as the Gauss-Helmert model. However, in order to apply the method of reliability analysis based on the approach to response assessment in systems with correlated observations, presented in the earlier work of this author, it was necessary to confine the considerations to a quasi-linear form of the Gauss-Helmert model, representing quasi-linear EIV models. This made it possible to obtain a linear disturbance/response relationship needed in that approach. Several specific cases of quasi-linear EIV models are discussed. The derived formulas are consistent with those already functioning for standard least squares adjustment problems. The analysis shows that, as could be expected, the average level of response-based reliability for such EIV models under investigation is lower than that for the corresponding standard linear models. For EIV models with homoscedastic and uncorrelated observations, the relationship between the average reliability indices for the independent and the dependent variables is formulated for multiple regression and coordinate transformations. Numerical examples for these two applications are provided to illustrate this analysis. © 2012 The Author(s).