Study on Life Distributions of the Elements Based on Rough Function Theory

Abstract

In view of the facts that complexity of life distributions of the parts, classical exponential distributions can't truthfully and profoundly portray it due to inconsideration depreciation behavior impacts in process of the elements life, therefore, under many situations, the acquired results do not accord with objectivity. However, once deviating from the assumption of the exponential distributions, quantitative analysis of the stochastic life will face difficulties. Therefore, in accordance with the characteristics of phase-type(PH) distributions of its approaching all distributions in nature, the paper applies the rough function concept to construct the PH distribution function sets called the upper approaching and the lower approaching sets, the upper approaching function set is those smallest distribution functions whose lives are bigger than practical life, the lower approaching distribution function set is those largest distribution functions whose lives are smaller than practical life, the boundary between them is a measurable domain of practical life distributions. The section is created in [0,+infin) by PH distribution function classes, after a larger number of the elements lives are tested and processed, the life distributions of the tested elements only rely on its location in the boundary. Obviously, the lower approaching function sets are those PH distributions that all tested elements lives are bigger than their lives, and the upper approaching function sets are those PH distributions that all tested elements lives are lower than their lives, the remained PH distribution classes can more accurately approach practical life of the elements. The paper forecasts the life distributions of the elements by using of mixed Erlang distribution, a sort of PH distribution function classes, research results show that the method is simple and flexible, and is an instruction idea for evaluation of life or life distributions of the elements, and relatively more accurate than conventional ways based on exponential distributions, and more robust