Uncertain delayed production risk process and its application in the shortage for a production process system

Classical production scheduling based on stochastic process cannot deal with the cases that the estimated distribution function is not close enough to the real frequency. Unfortunately, since uncertainty is common for a production process system with machine breakdowns or innovative products, uncertainty theory proposed by Professor Baoding Liu in 2007 should be applied. To analyze the effect of delayed time existing in a production process, this paper first introduces uncertain delayed production risk process and proposes the concepts of delayed shortage index as well as delayed shortage time for measuring the function and its failure of the production process system. Moreover, some numerical examples are documented to illustrate the calculation for the delayed shortage index and the uncertainty distribution of the delayed shortage time.