Classical estimator based modified control charts for phase‐II monitoring in real life

Abstract

We discuss some classical estimator based modified control charts for phase‐II monitoring in real life. The modification of some existing control charts such as exponentially weighted moving average (EWMA) and extended exponentially weighted moving average (EEWMA) is proposed and compared for the situation when the assumption of normality is not fulfilled due to some unavoidable factors. We first estimate the shape parameter of power function distribution using percentile estimator and maximum likelihood estimator and then propose EWMA and EEWMA based on these estimators. Monte Carlo simulation studies are used to compare the introduced control charts. The findings will be helpful for the practitioners and statisticians to devise the real‐life solution to the problems.

Modified calibrated control charts for monitoring the population mean under stratified sampling

“…We have modified Jabeen et al 10 . and propose the following estimators, $$$$\begin{equation}\hat y1\, = \,\mathop \sum \limits_{h = 1}^k {w_h}.\bar y_h^*\end{equation}$$$$…”

“…have done their work on hybrid exponentially weighted moving average (HEWMA) control chart by using the auxiliary information. The studies to control process parameters for different situations are given by Jabeen et al 10 , 11 . The shape parameter of the skewed distributions is studied by Zaka et al 23 …”

“…19 proposed the estimate for population total assuming that the auxiliary variable and study variable have negative correlation to each other. Jabeen et al 10 proposed new idea to use calibration approach by reducing the distance between the design weights and calibrated weights under Randomized response technique.…”

“…Noor-ul-Amin et al 17 have done their work on hybrid exponentially weighted moving average (HEWMA) control chart by using the auxiliary information. The studies to control process parameters for different situations are given by Jabeen et al 10 , 11 The shape parameter of the skewed distributions is studied by Zaka et al 23 . Jabeen and Zaka 24 provided some modifications to existing control chart to study the process shape parameter for weighted power function distribution.…”

“…In this paper we have provided three different estimators which are better to be used to estimate the number of errors produced by software and help the manufacturer to control the average number of errors by providing some efficient control chart as compare to the standard control charts exist in literature. We get motivation from Jabeen et al 10 and proposed calibration ratio estimator, calibration exponential ratio estimator and calibration log ratio estimator. Also we have modified Shewhart, EWMA and HEWMA to monitor the process mean and made a detailed comparison on the use of above mentioned control charts.…”