## Extending Beyond SPC Taguchi Methods

The classic approach described above is the foundation of much of statistical process control. It is simple, robust, and requires relatively little advanced statistical analysis. The fact that these methods were largely developed a half-century ago, before computers could assist with the calculations, reveals the importance of the contributions of Shewhart and others.

A major advance beyond the classic methods was developed by the Japanese engineer Genichi Taguchi in the 1980's.368a The methods that resulted are known as "Taguchi

368a Genichi Taguchi, Online Quality Control During Production (Tokyo, Japan: Japanese Standards Association, 1981). Other Taguchi methods resources area available from the American Supplier Institute, whose web site is: http://www.amsup.com.

methods," and are based on both statistics and critical insights into the role quality plays in the profitability of an enterprise. Because Taguchi methods look at the entire enterprise, rather than at the statistics of a production process, it can be considered from a management perspective that is accessible to a business economist. From this perspective, we summarize the key insights as follows:

• Customers become increasingly dissatisfied with products as they vary more frequently from the standard they expect.

• Variations arise not just from the production processes themselves, but also from other areas of the environment in which a product is produced, including human and managerial factors. Taguchi called these "noise factors."

• The variation in a process creates costs for the organization. These costs include not only the costs of returned or defective products, but also the additional managerial, production, and technical resources that must be devoted to the problem. These costs increase with variation.

• The cost of these variations can be expressed as a loss function. Such a loss function is a much richer formulation of the actual costs of imperfect processes than the classic approach, which relies largely on a discrete step function in which a process is either in control or out of control, and a product is either within specifications or outside specifications.

• In many situations, the cost of the variation (the loss function) can be modeled as a constant multiplied by the square of the deviations from the desired objective.3685

• This "quadratic loss" function allows an organization to estimate the value of reducing variation in a proces and to make appropriate management decisions.

The economic reasoning behind Taguchi methods is, in our opinion, more important than the statistical innovations.368c We view Taguchi's crowning insight as the treatment of "quality management" decisions not as solely engineering decisions, but as business management decisions. Such decisions are tractable from a classic microeconomic perspective and have implications for the profitability of the firm, the value of brands and intangible assets associated with a product, and the value of an enterprise.

Appendix Code Fragment 14-1. An SPC Demonstration Routine

% SQCdemo

% statistical quality control example routine % from MATLAB function descriptions and instructions % Edited PLA Nov 14 2001; calls MATLAB Statistical % Toolbox

% Part I: Shewhart Control Charts

% These are the Shewhart charts developed at Bell % labs in the 1920's.

%--load sample "parts" data, with samples of four % measurements taken 36 times load parts;

368b See, e.g., Charles Quesenberry, SPC Methods for Quality Control (New York: John Wiley & Sons, 1997), Section 9.9.

386c That is not to minimize the importance of the statistical innovations Taguchi introduced, such as the use of "orthogonal arrays" to reduce the number of examinations that must be conducted to evaluate a process. These are outside the scope of this book, but the use of Taguchi methods by business managers and business analysts is not.

whos; runout;

% then create Shewhart control chart (x-bar, or % sample means);

% then Shewhart standard deviation chart (similar to

figure(1), xbarplot (runout);

figure(2), schart(runout);

% Part II: Capability Charts

% A "capability plot" shows probability of a sample % measurement occurring within a specified range, % assuming a normal distribution. % Create data: normal with mean 1 and sd 1, 30X1

% vector data = normrnd(1, 1, 30, 1); % Calculate and create figure figure(3), p = capaplot (data,[-3 3]) % output of p = 0.9784 means that

% The probability of a new observation being within % specs is 97.84%

% MATLAB Resources % ------------------------------------------------

% type "help stats" and look at SPC for info. % see also "SPC" in stat toolbox user manual.

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