Stochastic "Three-Dependence" In Application to System Reliability Modeling  
Author Jerzy K. Filus


Co-Author(s) Lidia Z. Filus


Abstract A relatively new concept of stochastic 3-dependence as, between others, taking place in reliability modeling of three or more component systems, is described and analyzed. In that context we described the 3-dependence phenomena for k-variate probability distributions (k ≥ 3) of random vectors, say (X1, … ,Xk). First we introduce the concept for the k = 3 cases and then we extend it to an arbitrary higher dimension k = 4, 5, … . Some of the models with 3-dependence and r-dependence (for r ≥ 4), present, are known in literature but with no explicit reference to this stochastic phenomenon, while this was exhibited in this paper. Additionally, in this paper, one new model is proposed. This is a three-variate "modified normal density" with 3-dependence described. Notice, that 3-dependence is not present in classical 3-variate nor any k-variate ( k ≥ 4) normal distribution. Several versions of the obtained modified normal model were proposed too.


Keywords stochastic models in reliability, multivariate probability distributions, stochastic, 3-dependence, (new) modified three-variate normal density with 3-dependence
    Article #:  RQD28-348

Proceedings of 28th ISSAT International Conference on Reliability & Quality in Design
August 3-5, 2023