A Study of the Relationships between Process Capability Indices and Loss Functions

• Main Authors: Jui-I Lin, 林瑞益
• Other Authors: Jeh-Nan Pan
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/35af8m

碩士 === 國立成功大學 === 統計學系碩博士班 === 90 === Traditionally, engineers analyze the long-term and short-term process capabilities by using control charts and the histograms to understand the performances of key characteristics. When the process doesn’t perform well, quality improvement actions will be taken. The process capability indices, such as Cp and Cpk, can reflect the results of improvement. In addition, engineers should also estimate costs / losses in order to highlight the seriousness of the quality problem, so that the senior management will pay attention to the urgency of quality improvement and render their support. By associating process capability indices with quality losses, the results of process improvement can be reflected in a better way. This research systematically summarizes the process capability indices：Cp, Cpk and Cpm, and the associated formulae of loss functions：Taguchi Loss Function, INLF and RINLF, for both unilateral and the bilateral specifications under the following four distributions：（1）Normal（2）Uniform（3）Exponential（4）Lognormal. It will provide quality practitioners an easier way to calculate the process capability indices and expected losses. Moreover, the relationships between process capability indices and expected losses for normal distribution has been successfully derived. Based on the above formulae of relationships, a summary table that lists various process capability indices and their corresponding nonconforming rates and expected losses has also been established. It can serve as a convenient reference for quality practitioners.