Composite Desirability Index in Cases of Negative and Zero Desirability

Quantitative assessment of critical performance characteristics based on customer perception is of paramount importance for making business decisions. The concept of composite desirability can be used in such cases to arrive at a single quantitative index for assessment. However, in situations where perceptions are used as metrics/measurements, the scales usually take values between -k to +k for specified k. The present desirability functions either do not reflect or avoid using the negative and zero values. We use a negative exponential transformation to modify Gatza's desirability function in order to accommodate such values. The effects of the parameter of this function are studied for different levels of positive, negative and zero desirability values and a few chosen upper bounds of low positive composite desirability index.