The Performance of Bootstrap Confidence Intervals of Cрк Index Based on Mm-Estimator - Mohamad @ Sulaiman, Hanissah (2002)
A Cрк index is used to measure whether a production process is capable of producing items that satisfy a customer requirements(i.e specification limits). The c' index is based on the sample mean, x and sample standard deviation, s which are known to be very sensitive to the presence of outliers. As an alternative, we may turn to the robust location and scale estimate based on a robust MM estimates which are Jess affected by outliers. A major step toward the correct understanding and interpretation of Cрк index is by constructing it's confidence interval. The construction of such intervals assume that the measurement process having a normal distribution. However, many process are not nomlal and have a rat-tailed distribution which are prone to produce outliers. An allemative approach is to use bootstrap method such as the Percentile (P) and Bias Corrected and Acceleration (Bca) for calculating approximates confidence intervals of Cрк index. It is computer intensive based method that can be utilized without relying any assumption on the underlying distribution. The results of the studies reveal that the Bca method seems to perfonn better than the Percentile method for both nonnal and skewed process. The performance of the Cрк-MM estimates were investigated for further by comparing the bootstrap confidence interval for Cрк index MM estimates and the wellknown classical Cрк estimates. Based on simulation studies, show that the MM estimates produced more reliable confidence interval compared to the classical Cрк estimates.