ABSTRACT
As the mean values E bl[ ]θ of the conditional sojourn times θbl are given by
M E tdH b l b lbl bl bl= = ≠v ∞∫[ ] ( )t , , , , , , ,θ 0
1 2
(1)
then from the formula for total probability, it follows that the unconditional distribution functions of the sojourn times θb , b v, , ..., , of the system operation process Z( )t at the operation states zb, b v, , ..., , are given by (Grabski 2002, Kołowrocki & Soszyńska-Budny 2011)
H p H b vb bl bl l
v ( )t ( )t , ,t , , ..., .≥=
0 1
1 INTRODUCTION
Most real technical systems are very complex and it is difficult to analyze their reliability. Large numbers of multistate components and subsystems and their operating complexity cause that the identification, evaluation and prediction of their reliability are complicated. The complexity of the systems’ operation processes and their influence on changing in time the systems’ structures and their components’ reliability parameters are very often met in real practice. Thus, the practical importance of an approach linking the multistate system reliability models (Hue 1985, Hue & Yang 1995a,b) and the system operation processes models (Kołowrocki & SoszyńskaBudny 2011, Kołowrocki 2006, 2008, 2014, Kołowrocki & Soszyńska 2006, 2010, Soszyńska 2007) into an integrated general model in reliability assessment of real technical systems is evident.
