Robust parameter design with imperfect experimental control of noise

by Govind, Nirmal.

Robust Parameter Design (RPD) is a statistical methodology that focuses on minimizing the variation in performance of a system or product while ensuring that the average performance achieved is acceptable. RPD sets the levels of the control factors in order to minimize variation caused by changes in uncontrollable noise factors. Though noise is uncontrollable during the real operation of the system or use of the product, it has been assumed to be controllable and deterministic for experimentation purposes. In this dissertation, a response surface approach is used to develop a robust design framework that accounts for random variation in noise variables about a controllable mean during the experimentation phase. The Noise Perturbation Model (NPM) is proposed and an iterative method is developed that provides coefficient estimates for this model since ordinary and weighted least squares are not efficient. The NPM approach with the iterative estimation method is shown to provide estimates that have lower mean squared error when compared to ordinary least squares estimates. The practical advantage of using these estimates for robust design is also shown. In an application of the framework developed, the robust design of queueing systems is considered. Queueing systems are usually subject to several random and uncontrollable variables that need to be taken into account while designing the system. Though the average or mean performance has traditionally been used as a metric, variance is of considerable importance as a measure for evaluating queueing systems. iii The NPM approach is used to factor noise into the response surface models for the mean and variance of a queueing performance measure. Doing so accounts for noise variable fluctuation during the experimentation stage; for example, the inter-arrival time is a random variable, not only in reality, but also during the experimentation stage. A two-stage estimation technique, that is generally applicable to models of the form considered, is proposed to estimate the mean and variance response surfaces. Such response surfaces can be used to adjust system parameters without further experimentation when the properties of random variables affecting the system change. The impact of the approach proposed on the robustness of the system designed is explored. It is shown that the two-stage estimation technique can perform better than the currently available methods for estimating queueing system models and the practical advantage of using these estimates is highlighted. iv