Quality Loss Function - Common Methodology for Nominal-The-Best, Smaller-The-Better, and Larger-The-Better Cases

The quality loss function developed by Dr. Genichi Taguchi considers three cases including nominal-the-best, smaller-the-better, and larger-the-better. The methodology used to deal with the larger-the-better case is slightly different from that for the smaller-the-better and nominal-the-better cases. This paper attempts to bring about similarity among the three cases by introducing a term called the “target-mean ratio” and proposing a common formula for all three cases. The “target-mean ratio” can take different values to represent all three cases to bring about consistency and simplify the model. Also, it eliminates the assumption of target performance at infinite level and brings the model closer to reality. Characteristics such as efficiency, coefficient of performance (COP), and percent nondefective are presently not larger-the-better characteristics due to the assumption of target performance at infinity and the subsequent necessary derivation of the formulae. These characteristics can also be brought under the category of the larger-the-better characteristics. A hypothetical example of the efficiency of a machine is discussed to illustrate that the efficiency of any piece of equipment can also be considered as a larger-the-better characteristic. A graph illustrating the relationship between the “target-mean ratio” and quality loss is also presented.

Another example has been presented to suggest subtle differences between both methodologies.