Reading Assignment:

Download and read Chapter 7 in Essentials of Quality With Cases and Experiential Exercises.  Review the Discussion Questions at the end of the chapter to be sure that you understand what you have read.

Even relatively simple systems are affected by a number of variables. For example, some of the factors which may affect the quality of a hole drilled in a block of wood include the type of drill bit, the sharpness of the bit, the rotational speed of the bit, the feed rate of the bit into the work, the type of wood, and the moisture content of the wood.   To really optimize the performance of this process, the quality engineer would need to determine the best settings for these six variables.  Many industrial processes involve hundreds of variables any or all of which can affect the quality of the output. Determining which of these variables are most important, how they may interact with each other, and how to adjust them for optimal performance is the domain of experimental design.  In our example, designed experiments can assist the quality professional in determining which type of drill bit, how long to use it before resharpening, how many revolutions per minute (rpm) to run the bit, how fast to feed the bit into the work, the type of wood being drilled, and how dry the wood should be before processing in order for the drilling process to produce consistent, top-quality holes.

An experiment where one variable is studied while the other variables are held constant can be inefficient and suffers from the inability to assess interactions among the variables. Factorial designs allow for the efficient testing of the main effects of the variables as well as the interaction effects among the variables. Interpretation of the data obtained from factorial designs is often accomplished using analysis of variance (ANOVA).  Factorial designs coupled with analysis using ANOVA enable the experimenter to determine all main effects (i.e. the effect on the process of changing one variable) and all interaction effects (the effect on the process of the interaction of several variables).

Genichi Taguchi made a significant contribution by adapting fractional factorial orthogonal arrays (balanced both ways) to experimental design so that the time and cost of experimentation is reduced while validity and reproducibility are maintained.  Taguchi's approach is disciplined and structured to make it easy for quality engineers to apply.  A full factorial design with 7 factors at 2 levels would require 2⁷ = 128 experiments.  Taguchi's L₈ orthogonal array requires only 8 experiments.  His approach to experimentation consists of 4 steps:
    1.    Brainstorm the quality characteristics and design parameters important to the product/process.
    2.    Design and conduct the experiments.
    3.    Analyze the results to determine the optimum conditions.
    4.    Run a confirmatory test(s) using the optimum conditions.
            Source:  Roy, R.  A Primer on the Taguchi Method.  New York:  Van Nostrand Reinhold.  1990.

In-class DOE Experiential Exercise with Catapult

Answer Discussion Questions 1-11 at the end of Chapter 7 of the text.

Do Problems 1-8 at the end of Chapter 7 of the text.

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