MULTIVARIATE REGRESSION OF COMPONENTS AND OPERATIONS

Multivariate linear regression analysis for components and operations is not widely used in practice, instead most researchers use multiple linear regression procedures with one dependent variable at a time. However, simulation studies by prominent researchers suggest that this type of practice is ill advised. If the primary goal of a study is prediction accuracy, they recommend the use of multivariate linear regression analysis. Multivariate procedures take into account the correlations among the component surface quality variables, which is ignored by univariate analysis. This is also the case for multivariate procedures used to select the best subset of variables when building multivariate models.

Multivariate linear regression procedures are used in practice to explain variation in a vector of dependent variables (component surface quality conditions) by employing a set of independent variables (operating conditions ) using observational data (e.g manufacturing data). In our settings, an integrated reliability of components and process operations with Technological Inheritance Model is applied to select a subset or all of the operating conditions that accounts for the variation of the component surface qualities and its control parameters. The control parameter for operating conditions, - "b" is known as technological inheritance coefficient for operating condition control, while "a" is Technological Inheritance Coefficient for surface quality control. These parameters are used to determine the initial set of predictor variables. In such cases, the goal is to discover the relationship between component surface quality conditions and the best subset of operating conditions (variables).

Multivariate linear regression procedure are also used with experimental data. In these situations, the regression coefficients are employed to evaluate the marginal or partial effect of surface finish conditions (component surface quality conditions and operating conditions) in the model. In both cases, one is concerned with estimation of the model parameters, model specifications and variable selection or in general mode calibration and sample model fit.

Regression models are also developed to predict some outcome variable such as job performances. In our situation, operating conditions are selected to maximize the predictive power of the linear model. Technological Inheritance Model uses the maximum outcome data of the multivariate regression to predict time of failure, find the root cause of failure and detect the failures at any point in time as well as determine component quality factor, component/system reliability and its lifetime.