Int J Adv Manuf Technol (2009) 44:1036–1050 DOI 10.1007/s00170-008-1907-5 ORIGINAL ARTICLE Capability indices and nonconforming proportion in univariate and multivariate processes Isabel González · Ismael Sánchez Received: 11 September 2008 / Accepted: 15 December 2008 / Published online: 17 January 2009 © Springer-Verlag London Limited 2009 Abstract The main usefulness of a capability index is to relate the actual variability of the process with the admissible one. This admissible variability is, in turn, related with the nonconforming proportion. Hence, the capability index should be closely related to the nonconforming proportion. In univariate and centered processes, the classical C p index explicitly admits this interpretation. For instance, if C p = 0.5, the standard deviation should be reduced to 50% to attain C p = 1. However, for noncentered processes and multivariate processes, there is a lack of capability indices that ad- mit such an interpretation. This article fills this gap in the literature and proposes univariate and multivariate capability indices that have a direct interpretation of how much the variability of the process should increase or decrease to attain a unitary index. Some numerical examples are used to compare the proposed indices with the existing ones, showing the advantages of the proposals. Keywords Capability · Capability index · Multivariate processes · Nonforming proportion I. González (B ) Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avd. de la Universidad 30, 28911, Leganés, Madrid, Spain e-mail: imgfaria@ing.uc3m.es URL: http://turan.uc3m.es/uc3m/dpto/IN/dpin11/ fabdis/imgfaria.html I. Sánchez Department of Statistics, Universidad Carlos III de Madrid, Avd. de la Universidad 30, 28911, Leganés, Madrid, Spain e-mail: ismael@est-econ.uc3m.es URL: http://halweb.uc3m.es/ismael 1 Introduction One way of comparing the characteristics of the out- put of a manufacturing process with the engineering requirements is by using the concept of capability. In general, a process is capable if the probability of obtain- ing nonconforming items (outside some specifications) is small, typically 0.0027. Even though the interest is in the nonconforming proportion, it is customary to quantify the capability using a unitless index such that it can easily be computed and interpreted by the users. Typically, a process capability index (PCI) compares the natural variability of a stable process and the al- lowed variability. A general form of a PCI is measure of allowable process spread measure of actual process spread . (1) Therefore, a PCI is an index of the quality of the process that measures the risk of producing defective articles due to the natural variability of the process. It is used, for example, by quality engineers in their reports to their managers. It is also used when part of the production process is made by third parties, as it is customary, for instance, in the automotive industry. The report of a multivariate PCI is then included in the quality audit report. A large number of publications related to PCI for univariate processes are available. An overview of dif- ferent developments is provided in Kotz and Johnson [1]. In a univariate process, the quality is measured by one characteristic and the engineering requirements are usually represented by two specification limits: the upper and the lower specification limits. In the case of multivariate processes, some capability indices have also been proposed. In these processes, the quality is