Versatility in control theory and real-world applications

Abstract

The inspiration of this manuscript is reflected power function (RPF) and size biased distributions. We present a size-biased reflected power function (SBRPF) distribution using highly flexible reflected power function distribution. The resulting distribution is also flexible enough to fit all types of data either J shaped, reverse J shaped, positive skewed and negative skewed. We also drive various important properties of the suggested model. We show the comprehensive analysis of the proposed model detailing the asymptotic behavior of the function. We use diverse methods of estimation such as modified maximum likelihood method (MMLM) , maximum likelihood method (MLE) , percentile estimator (PE). The numerical analysis shows that the SBRF distribution remains consistent while mean square error (MSE) does not decrease as sample size increases. The real-life data sets demonstrate that SBRPF distribution is a better choice to be compared with other models exist in the literature. We also reported the use of two control charts Exponential weighted moving averages (EWMA) and Extended Exponentially weighted moving averages (EEWMA) for the shape parameter of the proposed model. From both Simulation studies and real-life application, we observe that EEWMA is a more effective control chart for detecting early change during a process for SBRPF distribution.