Examples of distribution compositions of technical object and system up states L.M. Chybowski, Z.R. Matuszak Maritime Academy, Marine Power Plants Technical Operation Institute, Szczecin, Poland ABSTRACT: This article deals with compositions of distributions of technical object and system up states by combining exponential, Weibull, normal and gamma distributions. The compositions considered are those of two identical distributions with different parameters as well as compositions of different distributions. The analysis is illustrated with basic functional characteristics of the compositions. The data for these studies were collected from operational observations of failures in marine power plant systems. 1 INTRODUCTION In classical problems of the theory of dependability the determination of probabilistic characteristics of object dependability is combined with searching for a model of the examined object’s up time distribution. In this context the most common models are exponential, Weibull, normal, log- normal and gamma distributions. Sometimes the power distribution is used in cases when object up time has the upper bound, the constant b>0. For large complex technical objects none of the mentioned distributions may prove good enough as a model of the object up time. The reson for this is that a number of various streams of failures of the examined object sum up and each of the streams may have completely different probabilistic characteristics. Various authors [Bob 1980, Bob 1977, Soł 1983] propose the extenstion of the various mathematical models of up time with distribution compositions. To justify the proposal, we can compare the curve of empirical probability density obtained from field studies of the fuel oil installation and the sea water installation (Fig. 1 and 2) with the characteristics obtained from a simulation experiment for the composition of two distributions (Fig. 3). The installations observed were those of the marine power plant of ships owned by the Polish Steamship Company based in Szczecin [Prz 1997]. It can be observed that the probability density obtained for the distribution composition can assume a rather irregular form. This offers a chance to find a model appropriate for the distribution received from field studies. 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0 2 4 6 8 10 12 14 16 18 20 22 24 26 t [24 h] f(t) [1/h] Figure 1. The characteristic of up time probability density for the fuel oil installation obtained from field studies of the ship 1 power plant. 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 0,009 0 2 4 6 8 10 12 14 16 18 20 t [24 h] f(t) [1/h] Figure 2. The characteristic of up time probability density for the sea water installation obtained from field studies of the ship 2 power plant.