ISSN: 1945-7553
CODEN: JTEVAB
Published Online: 13 May 2011
Page Count: 10

Process Capability Evaluation for Square Bumps with Mean Shift

Pearn, W. L.
Department of Industrial Engineering and Management, National Chiao Tung University,

Hung, H. N.
Institute of Statistics, National Chiao Tung University,

Tai, Y. T.
Department of Information Management, Kainan University, Taoyuan,

Hou, H. H.
Institute of Statistics, National Chiao Tung University,

(Received 30 November 2010; accepted 14 March 2011)

Abstract

Process capability indices have been widely used in manufacturing industries to provide numerical measures of process potential and performance. In in-plant applications, some inevitable process mean shift may be undetected when the statistical process control charts are applied, particularly, in the bumping process for square bumps. Bothe in 2002 provided a statistical reason for considering such a shift in the process mean to accommodate the undetected mean shifts for normally distributed processes when evaluating process capability. In this paper, we consider a bumping process for square bumps in which the data can be formulated as a non-central chi-square distribution, a class of non-normal distributions. To evaluate the popular yield-based process capability C_pk more accurately, we accommodate the magnitudes of undetected mean shifts using the modified capability evaluation formula and tabulate the detection powers under various subgroup sizes and non-central chi-square parameters. Based on the modified process capability evaluation, we can provide a more reliable process capability evaluation of capability index C_pk for square bumps and make more correct decisions. For illustration purpose, a real application in a bumping factory which is located on the Science-based Industrial Park in Hsinchu, Taiwan, is presented.

Keywords:
square bump, process capability evaluation, non-central chi-square, mean shift, stability control

Paper ID: JTE103641
DOI: 10.1520/JTE103641
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