Constructing multivariate process capability indices for short-run production

Job-shop factories (or short-run production facilities) are now becoming increasingly widespread as consumer requirements increase and production techniques are improved. The number of products in a short-run lot is small, so engineers cannot collect sufficient samples to determine the distribution of quality characteristics and estimate process parameters. Additionally, multiple quality characteristics must be simultaneously evaluated to determine product quality, when the complexity of the product design is high. In such a case, conventional process capability indices such as C-p and C-pk cannot satisfy practical requirements. Recently, multivariate process capability indices (MPCI) have been studied. However, these studies focus primarily on mass production and assume that quality characteristics are normally distributed in developing the MPCI. Studies to develop process capability indices, especially MPCI, for short-run production are few. On the basis of Clement's method, this study develops a procedure for constructing MPCI for short-run production using the technique of principal component analysis. A case study confirms the effectiveness of the proposed procedure.