Estimation of Modified Flexible Capability Index Cjkp* for Non-Normal Processes

• Main Authors: Liu, Yen-Lun, 劉彥倫
• Other Authors: Pearn, Wen-Lea
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/71954334064445137333

碩士 === 國立交通大學 === 工業工程與管理系所 === 102 === The process capability indices (PCIs) which are the important references in quality control have been one of a numerical measure index in product process. In practice, practitioners widely use the NCPPM table of Cpk index to transform the Cpk value to the corresponding nonconformities (NCPPM). Cpk is only appropriate for normal processes. Johnson, Kotz and Pearn (1994) proposed the index Cjkp for non-normal processes. However, the exact sampling distribution of Cjkp is mathematically intractable, Cjkp could not assure that the process capability meet the requirement and since Cjkp hasn’t been widely used, the corresponding NCPPM table has not been developed. Therefore, in connection with Gamma, Weibull, Lognormal, Beta, and Chi-square distributions, we use curve fitting to modify the index Cjkp that can be applied to obtain the NCPPM using the existing NCPPM table for index Cpk. Then we use curve fitting to modify the estimator of Cjkp* index being approximately unbiased estimator. Consequently, when practitioners calculate the value of modified Cjkp, they can inquire the corresponding nonconformities (NCPPM) with the NCPPM table of Cpk. Finally, the thesis applies four Bootstrap methods to construct four lower confidence bounds of Cjkp and compares the coverage rates under different parameters for five distributions.