Abstract
Motivated by nano-sol data set, this thesis addresses the shelf-life prediction of a nano-sol product. Instead of using temperature, humidity or voltage to do accelerated life/degradation experiments in the past, this study used pH as accelerating factor to predict the shelf-life of nano-sol product. The observed distribution data of nano-particles in the nano-sol are histogram-valued frequencies. A mixture of two normal distributions was used to describe the particle size distribution. The time evolution of the particle size distribution under different pH values was described by a pH accelerated degradation model. The maximum likelihood estimator (MLE) for unknown parameters in the pH accelerated degradation model can be solved by applying Expectation/Conditional Maximization (ECM) algorithm. The estimated shelf-life under normal-use-condition and corresponding 95% confidence intervals can then be obtained. An optimal test plan for pH accelerated degradation model can be obtained by minimizing the approximate variance of the estimated shelf-life of the nano-sol product under the constraint that the total experimental cost not exceeding a pre-specified budget. The sensitivity analysis reveals that the optimal test plan is quite robust to moderate departures from the model parameters. Finally, the effects of model mis-specification were discussed. Specifically the asymptotic large sample distribution of the shelf-life estimates was derived when the particle size distribution described in the first topic is wrongly fitted with inappropriate model. The result show that the effects on the accuracy and precision of the product’s shelf-life are critical.