Development of Non-Normal Multivariate Process Capability Indices for Nominal-the-Best and Smaller-the-Better Cases

• Main Authors: Wei-ChengShih, 石維謙
• Other Authors: Jeh-Nan Pan
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/11089517204503790396

碩士 === 國立成功大學 === 統計學系碩博士班 === 100 === Generally, an industrial product has more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, several multivariate process capability indices have been developed based on the assumption of normality in the past few years. However, the environmental performance, such as air pollution and energy utilization data may not follow normal distribution. Thus, in this research, we develop two non-normal multivariate process capability indices; RNMCp (Revised NMCp) and RNMCpm (Revised NMCpm) by relieving the normality assumption for both nominal-the-best and smaller-the-better cases. Based on the two normal multivariate process capability indices proposed by Pan and Lee (2010), we use weighted standard deviation method (WSD) to revise their NMCp and NMCpm indices. In addition, we also use WSD method to revise a multivariate process capability index (ND index) established by Niverthi and Dey (1995). Finally, we conduct simulation studies to compare the performance of correctly reflecting the true nonconforming rate among these multivariate indices. Simulation results show that our proposed indices outperform MCp, MCpm, NMCp, NMCpm and ND indices under different combinations of two right skewed/left skewed distributions regardless of the process mean hitting the target or not.