Analogues of reliability analysis for matrix-variate cases

An attempt is made in this paper to extend various aspects of reliability analysis in the real scalar variable case to the corresponding real matrix-variate cases. Probability of a matrix random variable being bigger than a given matrix is defined in terms of norms and positive definite matrices. Then by using these definitions, various aspects of reliability analysis are extended to the corresponding matrix-variate cases. A multivariate, in the sense of many real scalar variables, pathway model is also defined and some probabilities connected with reliability are also evaluated here.