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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 stochastic models of systems with reverse logistics usually assume that the quantity of products returned is\ud independent of sales. This hypothesis is obviously not true and can lead to suboptimal production policies. In\ud this paper a new sales-dependent returns model is described. In this model, the returns depend on the useful\ud life of the products sold and on the probability of an end-of-life product being returned. A Markov decision\ud problem is formulated in order to obtain the optimal manufacturing policy. A numerical example is provided\ud to illustrate the use of the defined model. An approximated Markov decision model is defined where the\ud optimal policy is easily obtained. The optimal policies of the original and the approximated models are\ud compared.Peer ReviewedPostprint (published version