Fuzzy estimation for process capability indices A. Parchami, M. Mashinchi * Fuzzy Set and Its Application Center of Excellence, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O. Box 76135, Kerman 133, Iran International Centre for Sciences and High Technology and Environmental Sciences, Kerman, Iran Received 19 June 2005; received in revised form 8 August 2006; accepted 9 August 2006 Abstract Process capability indices are summary statistics which measure the actual or the potential performance of process char- acteristics relative to the target and specification limits. In most traditional methods, precise estimation is used to assess the capability of manufacturing processes. In this paper we introduce an algorithm based on Buckley’s estimation approach, and use a family of confidence intervals to estimate process capability indices C p , C pk and C pm . The estimators of these indices thus obtained are triangular shaped fuzzy numbers. We also present and illustrate method for the comparison of estimated process capability indices. Numerical examples are given to show the performance of the method. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Fuzzy set; Process capability index; Fuzzy estimation; Confidence interval 1. Introduction A process capability index (PCI) is a real number which summarizes the behavior of a product or process characteristic relative to engineering specifications. Usually this comparison is made by forming the ratio of the width between the process specification limits to the width of the natural tolerance limits as measured by six process standard deviation units. These indices help us to decide how well the process meets the specifica- tions [14]. A process is said to be capable if, with high probability, the real valued quality characteristic of the produced items lies between the lower and upper specification limits. Several statistics such as C p , C pk and C pm are used to estimate the capability of a manufacturing process, which in most cases it is assumed we have a large sample from a normal population [10,11]. However, it may happen that, the specification limits are not precise numbers [21] and have uncertainty [26], but are expressed in fuzzy terms [20,21,25,26], and hence classical capability indices cannot be applied. For analyzing such situations Yongting [23] introduced a version of the capability index C p . This new C p , still 0020-0255/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2006.08.016 * Corresponding author. Address: Fuzzy Set and Its Application Center of Excellence, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O. Box 76135, Kerman 133, Iran. Tel./fax: +98 341 3221080. E-mail addresses: parchami@graduate.uk.ac.ir (A. Parchami), mashinchi@mail.uk.ac.ir (M. Mashinchi). Information Sciences 177 (2007) 1452–1462 www.elsevier.com/locate/ins