This paper oers a review of univariate and multivariate Process Capability Indices (PCIs). PCIs are used in the industry to quantify how well a process can meet customer requirements. Univariate PCIs describe the capability of one single product characteristic. Multivariate PCIs deal with the multivariate case in which the measures of all multiple product characteristics must be within specication limits to be conforming. When analyzing the capability of processes, decision makers of the industry may choose one PCI among all the PCIs existing in the literature, depending on dierent capability criteria. The aim of the review is to describe, cluster and discuss univariate and multivariate PCIs. This review may help researchers and decision makers to identify univariate and multivariate PCIs that can be used when monitoring univariate and multivariate production processes. On the one hand, the authors of this article suggest using PCIs obtained through the alternative denition for the C pk index when analyzing the capability of production processes, in which the estimation of the proportion of nonconforming parts is rated as crucial. On the other hand, all other multivariate PCIs presented in the literature can be applicable in capability analysis of production processes in which a direct relation to the proportion of nonconforming parts is not needed.

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The increasing demand and the globalization of the market are leading to increasing levels of quality in production processes, and thus, nowadays multiple product characteristics must be tested because they are considered critical. In this context, decision makers are forced to interpret a huge amount of quality indicators, when monitoring production processes. This fact leads to a misunderstanding as a result of information overload. The aim of this paper is to help practitioners when monitoring the capability of processes with a huge amount of product characteristics. We propose a methodology that reduces the amount of data in capability analysis by structuring hierarchically the multiple quality indicators obtained in the quality tests. The proposed methodology may help practitioners and decision makers of the industry in three aspects of statistical process monitoring: To identify the part of a complex production process that presents capability problems; to detect worsening over the time in multivariate production processes; and to compare similar production processes. Some illustrative examples based on dierent kinds of production processes are discussed in order to illustrate the methodology. A case of study based on a real production process of the automotive industry is analyzed using the proposed methodology. We conclude that the proposed methodology reduces the necessary amount of data in capability analysis; and thus, that it provides an added value of great interest for managers and decision makers.

Abstract-Multistage production processes are becoming more important in the industry to ensure levels of flexibility, efficiency and modularity. Thus, the way in which companies define optimal production parameters related to production costs and quality must be adapted to this reality. In this paper we introduce a multi-response optimization (MRO) model for a two stage production process. The model gives first stage quality specification limits which minimize the rework costs caused by the nonconforming parts of the whole process. The proposed model is applied to an example based on a production process of the automotive industry. The benefits of the model are evaluated by comparing the capability and the rework costs of the multistage production process before and after the optimization.