A Weibull Split-Plot Design Model and Analysis

Abstract

In this research, a class of nonlinear split plot design model where the mean function of the split-plot model is not linearizable is presented. This was done by fitting intrinsically nonlinear split-plot design (SPD) models using Weibull function. The fitted model parameters were estimated using ordinary least square (OLS) and estimated generalized least square (EGLS) techniques based on Gauss-Newton with Taylor series expansion by minimizing their respective objective functions. The variance components for the whole plot and subplot random effects are estimated using maximum likelihood estimation (MLE) and restricted maximum likelihood estimation (REML) techniques. The adequacy of the fitted intrinsically nonlinear SPD model was tested using four median adequacy measures namely resistant coefficient of determination, resistant prediction coefficient of determination, resistant modeling efficiency statistic and median square error prediction statistic based on the residuals of the fitted models which are influenced by the two parameter estimation techniques being applied, that is, the OLS and EGLS. Akaike’s information criteria (AIC), Corrected Akaike’s information criteria (AICC) and Bayesian information criteria (BIC) statistics were used to select the best parameter estimation technique. The results obtained showed that the Weibull SPD model is adequate and a good fit based on OLS but of less reliability and stability when the standard errors of the parameter estimates were compared to EGLS-MLE and EGLS-REML parameter estimates standard errors.