Quantiles are values of a function associated with specific probabilities. Two very specific quantiles, that is, ±3, are usually used for estimating probabilistic distribution of the function. Aiming at the engineering complex implicit function, the article provides an algorithm for calculating these values efficiently and rapidly. First, build kriging model with initial high-efficiency samples and the model is taken as the approximate initial analytical expression of the original function. Then, seek for the approximate most probable point with kriging model and performance measure approach. The most probable points found every time and their corresponding function responses are taken as new samples to reconstruct the built kriging model. After several times of reconstructing kriging model, the convergence value for the corresponding quantile can be obtained. Finally, the illustrative cases in this article demonstrate that the quantile-based method can provide accurate results with high efficiency and in this way, the quantile convergence value can be obtained by a few samples.

The municipal domestic waste (MDW) generated in China is increasing year by year, but the waste that has been regenerated is very little. In order to efficiently sort low-value recyclable waste (LVRW), which is the largest recyclable part of MDW, we designed and manufactured a machine vision pneumatic sorting equipment with waste recognition accuracy higher than 92%. Furthermore, an automated sorting method combining Mechanical sorting, near-infrared (NIR) sorting and machine vision sorting was developed specifically for MDW sorting. In field applications, the entire automated production line we built divides MDW (100%) into six types (37.7%) of single material waste and three types (33%) of composite waste, which is very beneficial to the recycling of resources in the future.