Joint Analysis of Mean and Variance Function Based on Second Order Polynomials

Abstract

Consider a response variable Y with mean µ(x) and variance σ ²(x), both depending on a vector x ∈ [–1, 1]^k. x represents standardized factor settings of k factors x ₁ ,…,x _k . The main purpose of many factorial experiments is to find factor settings such that the variance σ ²(x) will be minimized under the condition µ(x) = µ ₀, where µ ₀ is a given target value. TAGUCHI [8] distinguishes between factors that affect µ(x)/σ(x) and factors that affect µ(x) but not µ(x)/σ(x) (the so-called adjustment-factors). He proposes a two-step procedure: In the first step the signal to noise ratio µ(x)/σ(x) is maximized, in the second step by using the adjustment factors the mean value µ(x) is tuned so that µ(x)=µ ₀ .