Quality Engineering with Orthogonal Arrays: Algebraic Methods with and without Group Theory
My talk will primarily be about a single problem: the construction of a special class of fractional factorial experimental design (named mixed orthogonal arrays), motivated by Statistical Quality Control (SQC) applications. The problem’s solutions specifically focus on algebraic approaches, with two folds of using and not using group-theoretic computation. These algebraic methods and algorithms are based on elegant ideas from active fields of mathematics (as algebraic geometry) and statistics (as optimal balanced designs and more practically industrial statistics).
Quality is a broad concept, often it refers to a grade of excellence, literally means consistently meeting standards appropriate for a specific product or service. Quality Engineering and SQC particularly concern about mathematically designing goods for daily uses or accurate devices for engineering from which we could measure responses, collect numerical data, then analyze and control quality characteristics of those products before actually manufacture them on assembly lines in factories. Large firms have applied major principles of SQC in mass manufacturing of products for years, in various sectors of any economy, from dairy industry, telecommunication to automobile sector.
The first phase uses designed experiments – (DOE or Experimental Designs, and specifically Factorial Experimental Design– FED) – a sequence of experiments performed under controlled conditions which produces measurable outcomes; and in the second phase we could employ various popular Shewhart control charts, Six-Sigma and DMAIC methodology. Mathematically, the main aim of using FED (and other structures of DOE) is to identify an unknown function , determined on a full design , a mathematical model of a quantity of interest (favor, usefulness, best-buy, quality …) which has to be computed or optimized. When a firm’s budget is limited, practically the firm’s manager must accept using a subset of when investigating properties of a new product or service.