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.


DOI Code: 10.1285/i20705948v5n1p108

Keywords: grade, transition probability matrix (t.p.m.), mean recurrence time, Markov chain, Eigen vector.

References


[1]. Anderson T. W. and Goodman L. A. (1957), ‘Statistical Inference about Markov Chains’, The Annals of Mathematical Statistics, 28, 89-110.


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