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.

液体类型（例如纳米溶胶）产品的保质期预测是一个有趣的研究主题。近来，在文献中已经提出了一种pH促进方法来解决纳米溶胶的保质期预测。获得了粒度分布的时间演化并进行了建模。有两种方法可以通过使用参数方法（混合正态分布）或无分布方法来对粒度分布进行建模。这项研究的主要目的是量化当真实粒径分布遵循混合正态分布但被无分布模型错误地对待时，货架期预测模型错误指定的严重性。结果表明，货架期预测的相对偏差可能被低估了13.66％，而使用无分布方法可能会严重夸大其相对可变性达13.35倍。研究表明，模型错误指定的这些影响适度大，即使样本量和测量时间很小，也不能忽略。