ABSTRACT
From the linear equation (15) in (Kołowrocki & Soszyńska-Budny 2014), we can see that the mean value of the system unconditional lifetime μ(u), u z1 2, , ..., , is determined by the limit values of transient probabilities pb, b = 1 2, , ..., ν , of the system operation process at the operation states given by (3) and the mean values μb( )u , b = 1 2, , ..., ν , u z1 2, , ..., , of the system conditional lifetimes in the reliability state subsets { , , ..., }u z+1 , u z1 2, , ..., , given by (16) in (Kołowrocki & Soszyńska-Budny 2014). Therefore, the system lifetime optimization approach based on the linear programming ((Kołowrocki & Soszyńska-Budny 2011, Klajban & Adelman 2006, Kołowrocki & Soszyńska 2010, Tang, Yin & Xi 2007) can be proposed. Namely, we may look for the corresponding optimal values pb, b = 1 2, , ..., ν , of the transient probabilities pb, b = 1 2, , ..., ,ν of the system operation process at the operation states to maximize the mean value μ(u) of the unconditional system lifetimes in the reliability state subsets { , , ..., },u z+1 u z1 2, , ..., , under the assumption that the mean values μb( )u , b = 1 2, , ..., ,ν u z1 2, , ..., , of the system conditional lifetimes in the reliability state subsets are fixed. As a special and practically important case of the above formulated system lifetime optimization problem, if r, r z1 2, , ..., is a system critical reliability state, we may look for the optimal values pb, b = 1 2, , ..., ,ν of the transient probabilities pb, b = 1 2, , ..., ,ν of the system operation process at the system operation states to maximize the mean value μ( ) of the unconditional system
1 INTRODUCTION
The complex technical systems reliability improvement and decreasing the risk of exceeding a critical reliability state are of great value in the industrial practice (Kołowrocki & Soszyńska-Budny 2011, Kuo & Prasad 2000, Kuo & Zuo 2003, Vercellis 2009). In everyday practice, there are needed the tools that could be applied to improving the reliability characteristics of the multistate systems operating at variable conditions. There are needed the tools allowing for finding the distributions and the expected values of the optimal times until the exceeding by the system the reliability critical state, the optimal system risk function and the moment when the optimal system risk function exceeds a permitted reliability level and allowing for changing the system operation process after comparing the values of these characteristics with their values before the system operation process optimization in order to improve the system reliability (Kołowrocki & Soszyńska-Budny 2011, Klajban & Adelman 2006, Kołowrocki & Soszyńska 2010, Kołowrocki & Soszyńska-Budny 2014, Koowrocki 2014, Lisniansi & Levitin 2003, Tang, Yin & Xi 2007).
