The effects of model misspecification on shelf-life prediction of nano-sols under pH acceleration

Abstract

ABSTRACT Shelf-life prediction of liquid-type (such as nano-sol) products is an interesting research topic. Recently, a pH acceleration method has been proposed in the literature to address the shelf-life prediction of nano-sol. The time evolution of particle-size distribution was obtained and modelled. There are two approaches for modelling the particle-size distribution, either by using a parametric approach (mixture-normal distribution) or a distribution-free approach. The main goal of this study is to quantify the seriousness of model misspecification on the shelf-life prediction when the true particle-size distribution follows a mixture-normal distribution, but wrongly treated it by a distribution-free model. The results demonstrated that the relative bias of shelf-life prediction may be under-estimated up to 13.66%, while its relative variability may be seriously inflated up to 13.35 times by using a distribution-free approach. The study shows that these effects of model misspecification are moderately large and cannot be neglected even when the sample size and the measurement times are small.