TABLE OF CONTENTS "The native of one of our flat English counties ... retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once."
SIR FRANCIS GALTON (PIONEER OF STATISTICAL CORRELATION AND REGRESSION)
Now we are ready to apply a tool called "propagation of error" (POE) that applies the tools of calculus to finds the flats on response surfaces. These regions are desirable, especially so if you become subject to six sigma standards, because they do not get affected much by variations in factor settings. The idea is to seek out the high plateaus of product quality and process efficiency. Without the addition of POE as a criterion, computer-aided optimization might set your process on a sharp peak of response. But such a location will not be robust to variation transmitted from input variables.
In Chapter 1 we introduced this topic with a fun, but hopefully very relevant, study on how to reduce variability of commuting time to work. For many workers, even those on salary, the boss exhibits little tolerance for deviation from the specified arrival time. The goal of six sigma is to reduce variation of processes, such as the commute to work, to such a degree that the failure rate drops to 3.4 parts per million or less. Let's see if we can translate this statistic to something more meaningful. According to the Michigan Department of...
