Sensitivity analysis for robust parameter design experiments

Abstract

We analyze the computation of sensitivities in network reliability analysis. The associated models are graphs whose components are weighted by probabilities (their reliabilities) and they are widely used, for instance, in the design of communication networks. The paper deals with the sensitivities of usual reliability network metrics, with respect to the reliabilities of the components. The importance of sensitivities in this context is discussed and it is shown how to efficiently estmate the vector of sensitivities using Monte Carlo procedures. A first result allows to evaluate sensitivities using the standard Monte Carlo approach. A second method is then presented to deal efficiently with the rare event case. The ideas presented here can be applied to other classes of reliability problems and/or methods. INTRODUCTION The ModelStochastic graphs are widely used models for representing complex multi-component systems subject to component failures. They consist of graphs whose elements (nodes and arcs or edges) are weighted by probabilities. The output usually obtained from this type of structure is the probability of events representing a desired behavior of the system modeled. In this paper we consider the problem of the computation of reliability measures and we focus on a fundamental family of metrics, called K-terminal reliability, in the following version: the input is a stochastic undirected graph G = (V, E) where V is the set of vertices and E is the set of edges. We denote by E the number of edges: E = |E|. The graph may represent, for instance, a communication network. In this case, the vertices correspond to nodes sending and receiving information and the edges model communication lines. This application is used as a reference in the paper. For instance, the terms vertex and node are used as synonymous, and the same with edge or line or link. At a fixed time τ , each line is in one of two states: either working (operational) or completely down (unoperational, behaving as if it did not exist in the network). To simplify the presentation, we assume that nodes are perfect and that only lines can fail, but this is not critical since we are using Monte Carlo techniques. The graph is also assumed to be undirected, that is, the lines of the modeled communication network are bi-directional (messages can pass in both directions.) Finally, we assume that the graph is connected and without loops.The state of line or edge e at time τ is a binary random variable X e with value 1 if the line is working or 0 if it does not work. A basic assumption now is that (X e , e ∈ E) is a family of independent random variables. The K-terminal problem is the following: Given the probability r e of the event {X e = 1} for each line e of the network and a subset K of the set of vertices V, compute the probability R that, at time τ , the nodes can communicate with each other. In other words, if the first graph G = (V, E) is fixed, the set E of operational lines at time τ defines a subgraph G = (V, E ) of the previous one.The number R...

Uncertainty analysis in building performance simulation for design support

“…(2) It allows the analysis of the robustness of a model [Litko, 2005]. (3) It makes aware of unexpected sensitivities that may lead to errors and/ or wrong specifications (quality assurance) [Lewandowska et al, 2004; Hopfe et al, 2006;Hopfe et al, 2007] (4) By changing the input of the parameters and showing the effect on the outcome of a model, it provides a "what-if analysis".…”

“…The purpose of uncertainty and sensitivity analysis can be described as identifying uncertainties in input and output of a system or simulation tool [Lomas, 1992; Fuerbringer, 1994;MacDonald, 2002]. In practice uncertainty and sensitivity analysis have many additional benefits including:(1) With the help of parameter screening it enables the simplification of a model [de Wit, 1997].(2) It allows the analysis of the robustness of a model [Litko, 2005]. (3) It makes aware of unexpected sensitivities that may lead to errors and/ or wrong specifications (quality assurance) [Lewandowska et al, 2004; Hopfe et al, 2006;Hopfe et al, 2007] (4) By changing the input of the parameters and showing the effect on the outcome of a model, it provides a "what-if analysis".…”

A Sensitivity Analysis for Thermal Performance of Building Envelope Design Parameters

“…Sensitivity analysis identifies the most important design parameters in terms of building performance. In practice, uncertainty and sensitivity analysis provide a number of additional advantages, including: (1) the use of parameter screening to simplify models [15,16]; (2) the evaluation of models' robustness [17]; (3) alerting designers to unexpected sensitivities that may result in errors, and/or incorrect specifications (quality assurance) [18][19][20][21][22]; and (4) providing a "what-if analysis" by changing the input parameters and displaying the effect on the outcome of a model (decision-support) [23].…”