Using PCR-TOPSIS to optimise Taguchi's multi-response problem

The Taguchi method is an efficient method used in off-line quality control where experimental design is combined with quality loss. This method includes three stages—system design, parameter design, and tolerance design. In the real world it is obvious that more than one quality characteristic should be considered for most industrial products; i.e., in most applications the customer's concern is with multi-response problems. Nevertheless, the Taguchi method is not appropriate for optimising a multi-response problem since engineering judgment is the main optimisation procedure in Taguchi method. In order to overcome this problem, this paper proposes an effective procedure called PCR-TOPSIS that is based on process capability ratio (PCR) theory and on the theory of order preference by similarity to the ideal solution (TOPSIS) to optimise multi-response problems. Using PCR-TOPSIS, multiple responses in each experiment will be transformed into a performance index. Therefore, the optimal factors/levels combinations for the multi-responses can be determined. Two case studies in Tarng et al. and Reddy et al. are resolved using the proposed procedure. The result indicates that PCR-TOPSIS can yield a satisfactory solution for multi-response problems.