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Unformatted text preview: 製程能力指標覆式信賴區間之敏感度分析 (NSC95-2221-E-025-013) 主持人：周昭宇 (國立臺中技術學院財務金融系教授) 1. Introduction Manufacturing industries have experienced increasing demand on quality since the latter part of 1970s. Process capability analysis is an engineering study to estimate process capability and to help to achieve the desired quality level for a production process. Process capability refers to the uniformity of the process. The process capability index is a simple and quantitative way to assess the capability of a process. There have been several process capability indices proposed over the years for the purpose of assessing the capability of a process to meet certain specifications. Kane (1986) comprehensively investigated the capability indices C p and C pk and their statistical properties, including estimation and hypothesis testing. The index C p only reflects the magnitude of the process variation relative to the specification limits, while the index C pk takes into account the process variation as well as the location of the process mean. Both C p and C pk do not consider the effect of process target, which should be an important parameter in process capability evaluation. Chan et al. (1988) presented the index C pm to involve the departure of the process mean from the target value. By combining C pk and C pm , Pearn et al. (1992) introduced the index C pmk as - +-- +- = 2 2 2 2 ) ( 3 LSL , ) ( 3 USL min T T C pmk μ σ μ μ σ μ , (1) where μ , σ and T are respectively the mean, standard deviation and the target value of the process characteristic, and USL and LSL are respectively the upper and lower specification limits of the process characteristic. The index C pmk is to measure the capability of the process by generalizing C pk and C pm in such a way that both target value and the mid point of specification limits are considered simultaneously. Both C pm and C pmk are called Taguchi indices because they are derived from Taguchi’s loss function. According to Kotz and Johnson (2002), the index C pmk is particularly suitable for an asymmetric-tolerance manufacturing process, i.e., for the case with that 2 / ) LSL USL ( + ≠ T . For example, suppose that USL = 61, LSL = 40 and T = 49. Consider the following two processes: Process A with mean 45 and standard deviation 2 and Process B with mean 54 and standard deviation 2. According to definitions, both processes have the same C pm value (which is 0.783) but different C pmk values. The C pmk of Process A is 0.373, while the C pmk of Process B is 0.522, which indicates that the capability of Process B is superior to that of Process A. This result is quite consistent with the concept of non-conformity. That is, if both processes are assumed to be normally distributed, then the non-conformity rates of Processes A and B are respectively 6209.67 ppm and 232.63 ppm, which also illustrates that Process B has better performance than Process A. also illustrates that Process B has better performance than Process A....
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This note was uploaded on 11/27/2009 for the course IM MA420 taught by Professor Mar,lee during the Spring '09 term at National Taiwan University.
- Spring '09