Capability measure for processes yield with single characteristic has been investigated extensively, but is still comparatively neglected for processes with multiple characteristics. Wu and Pearn Wu, C.W., Pearn, W.L., 2005. Measuring manufacturing capability for couplers and wavelength division multiplexers (WDM). International Journal of Advanced Manufacturing Technology 25(5/6), 533–541 proposed a capability index for multiple characteristics called C PU T , which provides an exact measure on process yield for multiple characteristics with each characteristic normally distributed. However, the exact sampling distribution of C PU T (multiple characteristics) is analytically intractable. In this paper, we apply the bootstrap method for calculating the lower confidence bounds of the index C PU T , and determine the sample size for a specified estimation accuracy. In order to obtain a desired estimation quality assurance, the sample size determination is essential as it provides the accuracy of the lower bound obtained from the bootstrap method. For convenience of applications, we tabulate the sample size required for various designated accuracy for the engineers/practitioners to use. A real-world example from manufacturing process with multiple characteristics is investigated to illustrate the applicability of the proposed approach.