ASSESING THE GENERALIZED PROCESS CAPABILITY INDEX Cpyk FOR LOMAX DISTRIBUTION USING DIFFERENT ESTIMATION METHODS AND BOOTSTRAP CONFIDENCE INTERVAL

Process capability index is an important tool to assess the process performance used mostly in industrial areas. Many process capability indices have been proposed in the literature. In this article, we consider different estimation methods to estimate generalized process capability index, Cpyk, introduced by Maiti et al. [32] for the Lomax distribution. Maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cram´er-von Mises (CVM), Anderson Darling (AD), right-tail Anderson Darling (RAD) and maximum product of spacings (MPS) methods are used during the estimation process. Next, bootstrap confidence intervals, namely, standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile (BCPB) are considered to obtain 95% confidence intervals for the proposed estimators of Cpyk. The performances of proposed estimators are compared via Monte-Carlo simulation study for different parameter settings. Furthermore, we perform a simulation study to compare the coverage probabilities (CP) and average lengths (AL) of bootstrap confidence intervals. Finally, two real data sets are analyzed for an illustrative purposes.