Monitoring of three-phase variations in the mortality of COVID-19 pandemic using control charts: where does Pakistan stand?

Background: At the end of December 2019, the world in general and Wuhan, the industrial hub of China, in particular, experienced the COVID-19 pandemic. Massive increment of cases and deaths occurred in China and 209 countries in Europe, America, Australia, Asia and Pakistan. Pakistan was first hit by COVID-19 when a case was reported in Karachi on 26 February 2020.

A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean.

The usual practice of using a control chart to monitor a process is to take samples from the process with fixed sampling interval (FSI). In this paper, a synthetic X control chart with the variable sampling interval (VSI) feature is proposed for monitoring changes in the process mean. The VSI synthetic X chart integrates the VSI X chart and the VSI conforming run length (CRL) chart.

Optimal designs of the median run length based double sampling X chart for minimizing the average sample size.

Designs of the double sampling (DS) X chart are traditionally based on the average run length (ARL) criterion. However, the shape of the run length distribution changes with the process mean shifts, ranging from highly skewed when the process is in-control to almost symmetric when the mean shift is large. Therefore, we show that the ARL is a complicated performance measure and that the median run length (MRL) is a more meaningful measure to depend on.