Applications and Metrology at Nanometer Scale 1

2 Statistical Tools to Reduce the Effect of Design Uncertainties

The inclusion of the ability to resist potential design or process variations is an innovative product design approach. This includes managing critical parameters of the system, using security coefficients and applying more advanced techniques for reliability optimization. This approach consists of applying statistics to design a system that has the best performance although its parameters have potential variations. The designed product respects the required performance in spite of uncertainties and remains above a threshold of minimal performance for a given probability. These innovative engineering design methods are related to multi-objective optimization problems. This chapter presents several methods and practical applications for improving the system design by including potential uncertainties.

2.1. Introduction

When a product is mass manufactured, it is obvious that design parameters must respect both manufacturing tolerances and expected variable final use conditions. The corresponding unknown parameters must be taken into account during product design. The statistical tools that include system uncertainties rely on:

• – developing an approximate mathematical model of the physical system under study;
• – identifying and characterizing the sources of uncertainty among the parameters of the model;
• – studying the propagation of uncertainties and their impact on the output signal (response) of the system.