Abstract
This article addresses the shelf-life prediction of a nano-sol product. From a preliminary analysis of the dataset in a real example, we found pH is an appropriate accelerating variable for the purpose of predicting the shelf-life of a nano-sol product. In addition, we found that the histogram-valued frequency plots of the particle-size distribution of a nano-sol can be reasonably decomposed into a mixture of two normal distributions. Therefore, a pH accelerated degradation model is proposed to characterize the time evolution of the particle size distributions. By using an expectation/conditional maximization algorithm, we analytically obtain the shelf-life prediction of nano-sol (under the use condition) and its corresponding 95% confidence interval. The main contribution of this study is that the shelf-life prediction of the nano-sol products can be statistically achieved via the pH acceleration.