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RESEARCH PAPERS

Risk-Based Decision-Making for Managing Resources During the Design of Complex Space Exploration Systems

[+] Author and Article Information
Ali Farhang Mehr

QSS Group,  NASA Ames Research Center, M/S 269, Moffett Field, CA 94035amehr@email.arc.nasa.gov

Irem Y. Tumer

NASA Ames Research Center, M/S 269, Moffett Field, CA 94035itumer@email.arc.nasa.gov

Note that the RUBIC design methodology is more general in principle and can be readily extended and generalized to other forms of modeling the design process (other than functional modeling).

In this paper, $E(.)$ and Var (.) refer to the expected value and variance of a random process, respectively.

In this paper, $σii$ denotes $Var(bi)$; $σij$ refers to $Cov(bi,bj)$, and $σi$ (with one index) refers to the standard deviation of $bi$, i.e., $σii=σi2$.

In our future research, we will consider using nonlinear S-shaped benefit functions that will taper off after a certain amount of investment (i.e., decreasing marginal risk reduction as the amount of investment increases.) For example, one might consider using a logistics s-curve function for the amount of risk reduction versus investment. This will eliminate the need for imposing non-negative constraints and will also better represent the reality where the actual added value of investing another dollar will taper off at a certain point. However, a nonlinear assumption will significantly complicate the portfolio optimization problem of the next section and is, therefore, left as part of the future research.

Note that we chose $σ$(TB) instead of Var(TB) because $σ$(TB) and E(TB) have the same units and can be used in a linear combination.

FMEA for instance, assigns a value to the failure rate based on reasonable estimations of the probability of occurrence obtained from experienced designers.

J. Mech. Des 128(4), 1014-1022 (Jan 29, 2006) (9 pages) doi:10.1115/1.2205868 History: Received November 18, 2005; Revised January 29, 2006

Abstract

Complex space exploration systems are often designed in collaborative engineering environments where requirements and design decisions by various subsystem engineers have a great impact on the overall risk of the mission. As a result, the system-level management should allocate risk mitigation resources (e.g., capital to place additional sensors or to improve the current technology) among various risk elements such that the main objectives of the system are achieved as closely as possible. Minimizing risk has been long accepted as one of the major drivers for system-level decisions and particularly resource management. In this context, Risk-Based Decision Making refers to a process that allocates resources in such a way that the expected risk of the overall system is minimized. This paper presents a new risk-based design decision-making method, referred to as Risk and Uncertainty Based Concurrent Integrated Design Methodology or RUBIC Design Methodology for short. The new approach is based on concepts from portfolio optimization theory and continuous resource management, extended to provide a mathematical rigor for risk-based decision-making during the design of complex space exploration systems. The RUBIC design method is based on the idea that a unit of resource, allocated to mitigate a certain risk in the system, contributes to the overall system risk reduction in the following two ways: (1) by mitigating that particular risk; and (2) by impacting other risk elements in the system (i.e., the correlation among various risk elements). RUBIC then provides a probabilistic framework for reducing the expected risk of the final system via optimal allocation of available risk-mitigation resources. The application of the proposed approach is demonstrated using a satellite reaction wheel example.

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Figures

Figure 1

A high-level functional model of a satellite reaction wheel at some point in its conceptual design phase. A satellite reaction wheel is used to position spacecrafts in the desired direction. Four major subsystems can be identified in this design (distinguished using different shades in the figure).

Figure 2

Triangular distribution for the random variable, bi. The benefit of investing a unit of resources is usually measured in dollars (x-axis). The y-axis shows the probability distribution function.

Figure 3

The thick curve represents the efficient frontier

Figure 4

A snapshot of the development window in the web-based RUBIC design tool (developed at NASA Ames Research Center)

Figure 5

The risk efficient frontier (total resources spent to mitigate risk (investment) = 100 units (or $1M); worst case scenario consequence (cost of loss of mission) =$20M; maximum expected risk reduction (vertical asymptote) = \$2.6M)

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