Lower confidence limits of process capability indices for non‐normal process distributions

When the process probability distribution is non‐normal or is unknown, the process mean and standard deviation may not properly describe the distribution’s shape. Consequently, the traditional process capability indices (PCI) C p , C pk , C pm and C pmk cannot express the actual process capability. This paper presents a procedure to construct lower confidence limits for PCIs when the process distribution is unknown. First, the order statistics are utilized to find the estimators of C p , C pk , C pm and C pmk . Bootstrap simulation method is then utilized to construct the lower confidence limits of PCIs, thereby allowing the process’s capability to be evaluated. A numerical example demonstrates the effectiveness of the proposed procedure.