Yield‐Related Process Capability Indices for Processes of Multiple Quality Characteristics. (17th April 2012)

• Record Type: Journal Article
• Authors: Shiau, Jyh‐Jen Horng; Yen, Chia‐Ling; Pearn, W. L.; Lee, Wan‐Tsz
• Is Part Of: Quality and reliability engineering international. Volume 29:Number 4(2013:Jun.)
• Page Start: 487
• Page End: 507
• Publication Date: 2012-04-17
• Subjects: multivariate process capability indices -- yield assurance index -- normal approximation -- lower confidence bound -- bootstrap; Reliability (Engineering) -- Periodicals; Quality control -- Periodicals; High technology -- Periodicals; 620.00452
• DOI: 10.1002/qre.1397
• Languages: English
• ISSNs: 0748-8017

Abstract

Abstract : Process capability indices (PCIs) have been widely used in industries for assessing the capability of manufacturing processes. Castagliola and Castellanos ( Quality Technology and Quantitative Management 2005, 2(2):201–220), viewing that there were no clear links between the definition of the existing multivariate PCIs and theoretical proportion of nonconforming product items, defined a bivariate C pk and C p (denoted by BC pk and BC p, respectively) based on the proportions of nonconforming product items over four convex polygons for bivariate normal processes with a rectangular specification region. In this paper, we extend their definitions to MC pk and MC p for multivariate normal processes with flexible specification regions. To link the index to the yield, we establish a 'reachable' lower bound for the process yield as a function of MC pk . An algorithm suitable for such processes is developed to compute the natural estimate of MC pk from process data. Furthermore, we construct via the bootstrap approach the lower confidence bound of MC pk, a measure often used by producers for quality assurance to consumers. As for BC p, we first modify the original definition with a simple preprocessing step to make BC p scale‐invariant. A very efficient algorithm is developed for computing a natural estimator B C ^ p of BC p . This new approach of BC p can be easily extended to MC p for multivariate processes. For BC p, we further derive an approximate normal distribution for B C ^ p, which enables us to construct procedures for making statistical inferences about process capability based on data, including the hypothesis testing, confidence interval, and lower confidence bound. Finally, the proposed procedures are demonstrated with three real data sets. Copyright © 2012 John Wiley & Sons, Ltd.