Safety, Reliability and Risk Analysis:Theory, Methods and Applications – Martorelletal.(eds) © 2009Taylor & Francis Group, London, ISBN 978-0-415-48513-5 Analysis of possibilities of timing dependencies modeling—Example of logistic support system J. Magott, T. Nowakowski, P. Skrobanek & S. Werbinska Wroclaw University of Technology, Wroclaw, Poland ABSTRACT: In the paper we consider the time dependent system of systems where the system total task must be executed during the constrained time resource. To model the delay times of operational system maintenance process performance, there is used Fault Trees with Time Dependency (FTTD) analysis. In the FTTD, events and gates are characterized by time parameters, which are derived from the time characteristics of system of systems’ processes performance. The FTTD analysis for calculations of proper value of time parameters for system of systems will be shown in this approach. 1 INTRODUCTION The main objective of any operational system is to perform continuously its intended functions. Failure of any working element affects the operational process and adds costs for spare parts, labour and maintenance materials. In addition to the losses on these accounts, there is also a loss of profit margin caused by system downtime. Sufficient inventory level of spare parts has to be maintained to keep the system in operating condition. When the spare elements are under stocked, it may lead to extended system downtime and, as a consequence, have a negative impact on the system availability level. On the other hand, maintenance of excessive spares can lead to large inventory holding costs. Moreover, the requirements for planning the logistics of spare elements necessary in maintenance actions of opera- tional systems differ from those of other materials in several ways: the service requirements are higher, the effects of stock-outs may be financially remarkable, the demand for parts may be sporadic and difficult to forecast, and the prices of individual parts may be very high. Consequently, one of the most important decisions faced by maintenance managers is the determination of optimal stocking levels which involves finding the answer to the following questions, such that the total expected inventory costs are minimized: • When to (re)order? • How many items to (re)order? There is a plethora of models in the literature on reliability theory regarding to the spares supply process optimization. A significant portion of them base on a classic inventory theory, where the pro- curement process parameters are usually optimized taking into account the cost constraints (see e.g. Sarjusz-Wolski, 1998). The surveys by Cho & Parlar (1991), Guide Jr & Srivastava (1997), Kennedy et al. (2002), Nahmias (1981), and Pierskalla & Voelker (1976) review the growing body of literature on spare parts inventories problem. The stock level of spare parts is dependent on the chosen maintenance policy. Therefore, maintenance programs should be designed to reduce both, the main- tenance and inventory related costs. As a result, the problems of system performance optimization can be solved by joint, rather than separate or sequential approach to define the maintenance and inventory policies. Consequently, there is used a ‘‘system of sys- tems’’ conception to model the interactions between operational system and its logistic support system. This conception is widely used in the defense sector, where logistic processes are aimed at supporting the warfighter/mission requirements. According to the definition (Crossley, 2006), the system of systems context arises when a need or a set of needs are met with a mix of multiple systems, each of which are capable of indepen- dent operation but must interact with each other in order to provide a given capability. More information can be found in (Werbi´ nska, 2007a, Werbi´ nska in prep.). Moreover, when designing such real-time sys- tems like logistic support of operational system per- formance, the following time parameters: parts’ 1055