# Specifications, Target Values and Loss Function

One of the overall learning objectives for each of our Six Sigma programs is to teach students how to think differently and to do things differently when solving problems and improving processes.  A good example is the use of target values rather than specifications to define the output requirements of a process.
When a specification is used to define a range of possibilities for the output of a process, it is implied that any output value that falls within the specified range is equally acceptable to the customer.  A better approach is to determine the target value that provides the highest level of satisfaction for the customer, recognizing that variation from the target value will result in lower satisfaction.  Genichi Taguchi taught us that a loss to society occurs when the output of a process is not at the target value.  Society in this context means the sum total of producers and consumers.
Target values may be expressed in three ways:  nominal is best, more is better or less is better.  An example of nominal is best that was provided recently by one of our Master Black Belt students is the temperature of a hot tub at a health club.  For the purposes of this discussion, the specified temperature range for the hot tub was 98 degrees F to 105 degrees F.   It is implied that users of the hot tub will be well satisfied as long as the temperature falls somewhere in the range of temperatures between these two values.
An experiment was conducted using a thermometer that was tested and calibrated for accuracy.  Five subjects entered the hot tub at temperatures ranging from 105 degrees F down to 98 degrees F, and then again from 98 degrees F up to 105 degrees F.   Subjects were given 10 minutes between each temperature change to cool off and drink water.  After each trial, each person rated their satisfaction on a scale of one to five.  A value of one equated to the highest level of satisfaction, while a level of five equated to the lowest level of satisfaction.  The results of the experiment were that the highest level of satisfaction occurred when the temperature of the tub was 101 degrees F.  A lower or higher temperature resulted in less overall satisfaction.  There is an economic cost to heating the tub hotter than what is desired, as well as a potential loss of customers if the tub is too warm or too cool.
Everyday examples of “more is better” for target values include fuel economy and luggage capacity of a vehicle.   Examples of “less is better” include wind noise and tire noise in a vehicle.
Your comments or questions about this article are welcome, as are suggestions for future articles.  Feel free to contact me by email at roger@keyperformance.com.
About the author:  Mr. Roger C. Ellis is an industrial engineer by training and profession.  He is a Six Sigma Master Black Belt with over 45 years of business experience in a wide range of fields.  Mr. Ellis develops and instructs Six Sigma professional certification courses for Key Performance LLC.   For a more detailed biography, please refer to www.keyperformance.com.