Uncertain Production Risk Process

To reasonably handle the likelihood that something will occur,there are two axiomatic mathematical tools,one is probability theory and the other is uncertainty theory.It is suitable to use probability theory for modelling the frequencies,and use uncertainty theory for modelling the belief degrees.That means,for certain quantity,if its estimated distribution function is close enough to frequency,then the quantity should be regarded as a random variable.Otherwise,it has to be regarded as an uncertain variable.For the practical problems in production,the estimated distribution functions of the quantities such as production amounts and cycle times are not close enough to the real frequency.In fact,it is almost impossible to work without any emergency just like machine breakdowns,and the historical data become unavailable in this situation.Furthermore,for a new product,the data are always inadequate for the producers.Therefore,it is unrealistic to assume that the distribution function obtained by the producers(no matter how to get it)is close enough to the real frequency.This dissertation first introduces uncertainty theory to deal with the uncertain quantity in production.Then the concept of uncertain production risk process is presented,and the models of the uncertain production risk processes in different cases are proposed.To estimate the belief degree that the shortage may occur,this dissertation applies uncertain measure to calculating the shortage indexes.Moreover,the concept of first hitting time is extended to the first time that shortage will happen,and the definitions of the shortage times are provided.Based on the uncertainty distribution of shortage time,the decision support for the practical production process can be given to the producers.In summary,this dissertation has the following innovations and contributions:· This dissertation first applies uncertainty theory to quantifying the problems in pro-duction.Moreover,the uncertain production risk processes in different cases are modelled,and their uncertainty distributions can be obtained;· The concepts of shortage indexes are proposed,and the analytic formulas are given;· The concepts of shortage times are suggested,and the analytic formulas for their uncertainty distributions which can characterize when the shortage will first occur are provided.