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Process capability indices dedicated to bivariate non normal distributions

Philippe Castagliola (Département Qualité Logistique Industrielle et Organisation, Université de Nantes and IRCCyN UMR CNRS 6597, Institut Universitaire de Technologie de Nantes, Carquefou, France)
José‐Victor Garcia Castellanos (Instituto Tecnologico De Ciudad Juárez, Ciudad Juárez, Chihuahua, Mexico)

Journal of Quality in Maintenance Engineering

ISSN: 1355-2511

Publication date: 28 March 2008



Process capability indices (PCI) are frequently used in order to measure the performance of production processes. In their 2005 article, Castagliola and Castellanos proposed a new approach for the estimation of bivariate PCIs in the case of a bivariate normal distribution and a rectangular tolerance region. This paper proposes extending Castagliola and Garcia‐Castellanos's paper to the estimation of bivariate PCIs in the case of non‐normal bivariate distributions.


The proposed method is based on the use of Johnson's System of distributions/transformations in order to transform the bivariate non normal distribution into an approximate bivariate normal distribution. Numerical examples are presented and some criteria are given in order to choose the appropriate Johnson's distribution.

Research limitations/implications

The proposed method is only dedicated to the case of two quality characteristics and a rectangular tolerance region (the most common case).


The proposed method allows the evaluation of bivariate capability indices irrespective of the distribution of the data and thus allows obtaining more reliable estimates for these values.


The main originality of the method presented in this paper is its ability to compute bivariate capability indices when the distribution of the data is not a bivariate normal distribution, i.e. the general case.



Castagliola, P. and Garcia Castellanos, J. (2008), "Process capability indices dedicated to bivariate non normal distributions", Journal of Quality in Maintenance Engineering, Vol. 14 No. 1, pp. 87-101.



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