The field of systems engineering has recently experienced a new push for unveiling its scientific foundations and using them to inform better practice. The majority of the research effort towards a theory of systems engineering has concentrated on the early phases of the system's lifecycle, especially in the areas of problem formulation and system architecture and design. However, and despite their importance for system success, the design of verification strategies has received little attention. Current work is of procedural nature, providing guidance instead of enabling computation, or is specific to a particular verification case. As a result, the definition of verification strategies in practice continues to be driven by heuristics and best practices. This has shown to be suboptimal. In order to fill in this gap, this paper contributes to the theory of systems engineering with a mathematical model of verification strategies. The mathematical model is generic, capturing verification comprehensively, and enables computation. First, a descriptive case is presented to facilitate understanding how the mathematical model relates to practice. Second, a quantitative case is presented to justify the need of the model. K E Y W O R D Ssystem modeling, verification and validation

This paper proposes a set of seven elemental patterns of verification strategies. These patterns can be useful in modeling verification strategies in a wide range of engineered systems. They form the building blocks under which any verification strategy can be modeled. The patterns lead to a fundamental understanding of the interplay between system parameters and verification activities, as well as an understanding of the mechanisms by which verification evidence builds up. For each pattern, we provide a description and a few examples of its application. A few important theoretical properties of the corresponding set of patterns are discussed, such as belief update, inferential properties, and graph disconnection, as well as some practical guidance to be taken into account when applying them to authentic verification problems. These patterns are intended to be a useful tool for researchers, practitioners, and educators, by formalizing the application of Bayesian networks to verification problems, hence facilitating instruction and communication among verification engineers and with researchers from other domains, particularly statisticians and Bayesian analysts.

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The design of large scale complex engineered systems (LSCES) involves hundreds or thousands of designers making decisions at different levels of an organizational hierarchy. Traditionally, these LSCES are designed using systems engineering methods and processes, where the preferences of the stakeholder are flowed down the hierarchy using requirements.The requirements represent what the stakeholder does not want rather than what is wanted. Value-Driven Design (VDD) offers a new perspective on complex system design, where the value preferences of the stakeholder are communicated through a decomposable value function. Previous work has indicated that value functions can be distributed to the lower levels in the hierarchy using scorecards that capture the value impact of attributes at a particular level, which then provides guidance for decision making. Past research in VDD has focused on including the interactions in the hierarchy and has failed to address the interactions/couplings across the entire system. The primary focus of this paper is to explore a mathematical formulation for capturing and incorporating couplings in system decomposition in the context of VDD. Multiple examples are used to examine the importance of capturing couplings, including an LSCES example of a communication satellite. Nomenclature SSL = Subsystem level SS = Subsystem A = Attribute V = Value function/Value TC = Total Cost Rev = Revenue P = Number of system level attributes p = System attribute number p 1-3 = SSL1 -SSL3 attribute number m 1-3= SSL1 -SSL3 subsystem number y = year r d = discount factor OL = Operational lifetime P payload = Power required by payload subsystem C payload = Cost of payload subsystem C ground = Cost of ground subsystem C power = Cost of power subsystem C SA = Cost of solar array C Batt = Cost of battery P 0 = Power required by all subsystems

The design of large-scale complex engineered systems involves hundreds to thousands of designers making decisions across different organizations and at different levels of organizational hierarchy. These systems are designed within a systems engineering framework, where requirements are used as proxies for stakeholder preference. Requirements drive the development process and are flowed across organizations and down through the organizational hierarchies. Value-driven design offers a new perspective where the preferences of the stakeholder are communicated directly through a decomposable value function, rather than decomposable requirements, thereby enabling improved consistency in system preference. This paper investigates two key aspects of achieving improved system consistency through a valuebased systems engineering approach, using a commercial satellite system as a testbed. The paper first contrasts the diverse systems that result from traditional requirements-based versus preference-based formulations, demonstrating how a value-based approach aids in capturing the true preferences of the stakeholder in problem formulation. The paper demonstrates the importance of using system couplings to enable an improved accuracy for value function decomposition. The paper demonstrates that ensuring system analysis consistency through use of system sensitivities can overcome issues pertaining to: dependencies of attributes; inadequately capturing system interactions; and direct modification of attributes to determine value impact. C⃝ 2017 Wiley Periodicals, Inc. Syst Eng 20: 21-44, 2017