Multivariate Process Capability Index Based on the Additivity of Normal Distribution

This paper proposes a new multivariate process capability index (MPCI) based on the additivity of normal distribution. At the beginning, it carries out a series of hypotheses: (i) The quality characteristics are reciprocal independence; (ii) The quality characteristics obey normal distribution; (iii) The quality characteristics have the same sample size; (iv) All the quality characteristics are key or general ones, that is to say all of them have the same type. Then they are divided into five situations according to the specification limits and the population distribution feature to discuss the multivariate process capability index: (i) bilateral specification limits without deviation, (ii) bilateral specification limits with deviation, (iii) unilateral specification limit with only upper or lower limit, (iv) unilateral specification limit with upper and lower limit, (v) unilateral and bilateral specification limits mix. The paper proposes practical and theoretical MPCI and analyzes the reason of their difference, and finds two problems of this method and proposes modified method, and discusses the research method of general situation. At last, the paper studies its validity by Matlab creating random data.