Integrated stochastic metric of flexibility for systems with discrete state and continuous parameter uncertainties

Abstract

This paper addresses the problem of developing a quantitative measure for the flexibility of a design to withstand uncertainties in the continuous parameters and discrete states. The metric is denoted as the expected stochastic flexibility E(SF). For a given a linear model, a joint distribution for the parameters and probabilities of failure for the discrete states, the proposed metric predicts the probability of feasible operation for a design. A novel inequality reduction scheme is proposed to aid in performing the integration over the feasible region characterized by inequalities. A bounding scheme is also proposed to avoid the evaluation of the integrals over a large number of discrete states when determining the E(SF). An example problem is presented to demonstrate the fact that the proposed measure provides a framework for integrating flexibility and reliability in process design.