Stochastic modeling of the grading pattern in presence of the environmental parameter

Abstract

This paper deals with the stochastic modeling of grading pattern, where grades are supposed to be influenced by environmental parameter c (say), (0 ≤ c ≤ 1). The model discussed here is an extension of Wang’s model (1981). The correlation coefficient between the two consecutive states is showed to be a function of the environmental parameter ‘c’. The operating characteristics namely first passage time distributions, mean waiting time in a particular grade are obtained. Also Numerical examples are worked out to study the limiting behavior of the change.