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ABSTRACT
Process capability index is a highly effective means of assessing product quality and process performance. Among many developed process capability indices, C p , C pk , C pm , and C pmk are the four most popular indices under normally distributed processes. Engineers always emphasize applicability and accuracy when a capability index is used to measure how a process performs. However, using these traditional indices to evaluate a non-normally distributed process often leads to inaccurate results. Thus, C Np , C Npk , C Npm , and C Npmk were proposed to overcome this shortcoming under non-normally distributed processes. Pearn and Kotz (Citation1994) compared the index C Npmk to C Np , C Npk , and C Npm as well as found C Npmk is more restrictive and sensitive with regard to process median deviation from the target value than the other indices. Thus, this study employed an appropriate index C Npmk to evaluate non-normally and normally distributed processes. However, the exact probability distribution of C Npmk is too complicated to be derived. Consequently, the related hypotheses testing and confidence interval cannot be developed. For this reason, the applicability of C Npmk is limited. The main purpose of this study is to utilize bootstrap simulation method to construct a 100(1 − 2α)% BCa confidence interval for the difference between two indices, C Npmk1 − C Npmk2. The proposed bootstrap interval can be effectively employed to determine which one of the two processes or suppliers has a better process capability. Moreover, engineers without much statistics background can also easily adopt the proposed index and related procedures to compare processes or select suppliers. If this research procedure performs effectively, the industries can use it to analyze the capabilities of any process distributions in the future.
Notes
Upper specification: 340, lower specification: 280, target value: 310.
Upper specification: 250, lower specification: 5, target value: 35.
Upper specification: 353, lower specification: 273, target value: 313.
Upper specification: 355, lower specification: 275, target value: 315.
∗Indicates that the simulation performance of the parameter combination does not meet the 95% performance level.
∗Indicate the simulation performance of the parameter combination does not meet the 95% performance level.
∗Indicates that the simulation performance of the parameter combination does not meet the 95% performance level.
∗Indicates that the simulation performance of the parameter combination does not meet the 95% performance level.