System Architecture: Strategy and Product Development for Complex Systems, First Edition

Appendices

Appendix A: Effect of the Choice of Architecture Set on the Decision Sensitivity Metric

Chapter 15 introduced the sensitivity of a metric to a decision, a numerical value that tells us how sensitive a metric is to a given decision, or, equivalently, the average change in a metric when we change the value of a decision. We provided two formulations for the sensitivity metric. The first is based on main effects and is valid only for binary decisions:

$$\text{Main effect (Decision }i\text{, Metric }M\text{)}\equiv \frac{1}{N_1}{\displaystyle \sum _{\left\{x\right|x_i=1\}}M(x)-\frac{1}{N_0}}{\displaystyle \sum _{\left\{x\right|x_i=0\}}M(x)}$$

where N0 and N1 are the number of architectures for which xi = 0 and 1 respectively.

The second formulation extends this concept to k > 2 decisions:

$$\text{Sensitivity (Decision }i\text{, Metric }M\text{)}\equiv \frac{1}{K_1}{\displaystyle \sum _{k\in K}|\frac{1}{N_{1,k}}}{\displaystyle \sum _{\left\{x\right|x_i=k\}}M(x)-\frac{1}{N_{0,k}}}{\displaystyle \sum _{}}$$