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This report documents the results of an LDRD program entitled "System of Systems Modeling and Analysis" that was conducted during FY 2003 and FY 2004. Systems that themselves consist of multiple systems (referred to here as System of Systems or SoS) introduce a level of complexity to systems performance analysis and optimization that is not readily addressable by existing capabilities. The objective of the "System of Systems Modeling and Analysis" project was to develop an integrated modeling and simulation environment that addresses the complex SoS modeling and analysis needs. The approach to meeting this objective involved two key efforts. First, a static analysis approach, called state modeling, has been developed that is useful for analyzing the average performance of systems over defined use conditions. The state modeling capability supports analysis and optimization of multiple systems and multiple performance measures or measures of effectiveness. The second effort involves time simulation which represents every system in the simulation using an encapsulated state model (State Model Object or SMO). The time simulation can analyze any number of systems including cross-platform dependencies and a detailed treatment of the logistics required to support the systems in a defined mission. 4 AcknowledgmentsThe System of Systems Modeling and Analysis LDRD program team would like to acknowledge the significant support, time, and effort provided to the program by Robert Cranwell, LDRD Program Manager. The team also acknowledges the support of and guidance from the members of the Modeling and Simulation Thrust of the Emerging Threats Investment Area: Russell Skocypek, Alan Nanco, John Wagner, Robert Cranwell, and Ron Trellue. Finally, the team acknowledges and thanks Craig Lawton, Leon Chapman, and Chris Atcitty for their contributions to the program. Tables TABLE 3.1 FAILURE EVENTS AND THEIR PROPERTIES FOR THE EXAMPLE PROBLEM 26 TABLE 3.2 CAPTIONS AND LABELS FOR METRICS FOR NONREPAIRABLE PROBLEM 28 TABLE 3 5 Executive SummaryEvaluating design concepts for a complex system of systems (SoS) is an immediate need for military systems like Future Combat Systems (FCS). SoS analysis requires predicting performance at the SoS level in contrast to the traditional platform-by-platform approach. SoS analysis must examine a multitude of design and technology options in order to optimize mission effectiveness across wide parameter spaces. The U.S. Army is facing the need to establish SoS performance requirements and translate these SoS requirements down to optimal or near-optimal individual platform requirements for system design and development. This challenge is further extended by the complexity presented with new technology. Currently, about the only method to gain some performance knowledge at the SoS level is through traditional warfight simulation codes, which are costly and time-consuming.The goal of the System of Systems Modeling and Analysis LDRD program was to develop an integrated modeling and simu...

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This report presentsequationsand computationalalgorithmsfor analyzingreliabilityof severalforms of redundancyin repairable and non-repairablesystems. For repairable systems, active, standby, and R 0f N redundancy with and without repair are treated.For non-repairablesystems,active,standby,and R of N redundancyare addressed. These equationscan be used to calculate mean time between failures, mean time to repair, and reliabilityfor complexsystemsinvolvingredundancy.

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