Design of Improved EWMA Control Chart for Monitoring the Process Mean Using New Median Quartile Double Ranked Set Sampling

It is essential to monitor the mean of a process regarding quality characteristics for the ongoing production. For enhancement of mean monitoring power of the exponentially weighted moving average (EWMA) chart, a new median quartile double ranked set sampling (MQDRSS) based EWMA control chart is proposed and named as EWMA-MQDRSS chart. In order to study the performance of the developed EWMA-MQDRSS chart, performance measures; average run length, and the standard deviation of run length are used. The shift detection ability of the proposed chart has been compared with counterparts, under the simple random sampling and ranking based sampling techniques. The extensive simulation-based results indicate that the EWMA-MQDRSS chart performs better to trace all kinds of shifts than the existing charts. An illustrative application concerning monitoring the diameter of the piston ring of a machine is also provided to demonstrate the practical utilization of the suggested chart.

Assessing the use of the moving window approaches when monitoring social networks using a degree corrected stochastic block model

PurposeThis study aims to assess the effect of updating the Phase I data – to enhance the parameters' estimates – on the control charts' detection power designed to monitor social networks.Design/methodology/approachA dynamic version of the degree corrected stochastic block model (DCSBM) is used to model the network. Both the Shewhart and exponentially weighted moving average (EWMA) control charts are used to monitor the model parameters. A performance comparison is conducted for each chart when designed using both fixed and moving windows of networks.FindingsOur results show that continuously updating the parameters' estimates during the monitoring phase delays the Shewhart chart's detection of networks' anomalies; as compared to the fixed window approach. While the EWMA chart performance is either indifferent or worse, based on the updating technique, as compared to the fixed window approach. Generally, the EWMA chart performs uniformly better than the Shewhart chart for all shift sizes. We recommend the use of the EWMA chart when monitoring networks modeled with the DCSBM, with sufficiently small to moderate fixed window size to estimate the unknown model parameters.Originality/valueThis study shows that the excessive recommendations in literature regarding the continuous updating of Phase I data during the monitoring phase to enhance the control chart performance cannot generally be extended to social network monitoring; especially when using the DCSBM. That is to say, the effect of continuously updating the parameters' estimates highly depends on the nature of the process being monitored.

Design and Application of a Modified EWMA Control Chart for Monitoring Process Mean

The modified exponentially weighted moving average (modified EWMA) control chart is an improvement on the performance of the standard EWMA control chart for detecting small and abrupt shifts in the process mean. In this study, the effect of varying the constant and exponential smoothing parameters for detecting shifts in the mean of an autoregressive process with exogenous variables (ARX(p,r)) with a trend and exponentially distributed white noise on the standard and modified EWMA control chart was investigated. The performances of the two control charts were compared via their average run lengths (ARLs) computed by using explicit formulas and the numerical integrated equation (NIE) technique. A comparative study of the two ARL methods on the modified and traditional EWMA control charts shows that the modified schemes had better detection ability at all levels of shift size. Finally, two examples using real datasets on gold and silver prices are given to illustrate the applicability of the proposed procedure. Our findings advocate that the modified EWMA chart is excellent for monitoring ARX(p,r) processes with exponentially distributed white noise

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. Several methods were presented to model the death rate due to the COVID-19 pandemic and to forecast the pinnacle of reported deaths. Still, these methods were not used in identifying the first day when Pakistan enters or exits the early exponential growth phase. Objective The present study intends to monitor variations in deaths and identify the growth phases such as pre-growth, growth, and post-growth phases in Pakistan due to the COVID-19 pandemic. Methods New approaches are needed that display the death patterns and signal an alarming situation so that corrective actions can be taken before the condition worsens. To meet this purpose, secondary data on daily reported deaths in Pakistan due to the COVID-19 pandemic have been considered. The $ c$ and exponentially weighted moving average (EWMA) control charts have been used for monitoring variations. Results The $ c$-chart shows that Pakistan switches from the pre-growth to the growth phase on 31 March 2020. The EWMA chart demonstrates that Pakistan remains in the growth phase from 31 March 2020 to 17 August 2020, with some indications signaling a decrease in deaths. It is found that Pakistan moved to a post-growth phase for a brief period from 27 July 2020 to 28 July 2020. Pakistan switches to re-growth phase with an alarm on 31/7/2020, right after the short-term post-growth phase. The number of deaths starts decreasing in August in that Pakistan may approach the post-growth phase shortly. Conclusion This amalgamation of control charts illustrates a systematic implementation of the charts for government leaders and forefront medical teams to facilitate the rapid detection of daily reported deaths due to COVID-19. Besides government and public health officials, it is also the public’s responsibility to follow the enforced standard operating procedures as a temporary remedy of this pandemic in ensuring public safety while awaiting a suitable vaccine to be discovered.

Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso

Purpose: When applying exponentially weighted moving average (EWMA) multivariate control charts to multivariate statistical process control, in many cases, only some elements of the controlled parameters change. In such situations, control charts applying Lasso are useful. This study proposes a novel multivariate control chart that assumes that only a few elements of the controlled parameters change. Methodology/Approach: We applied Lasso to the conventional likelihood ratio-based EWMA chart; specifically, we considered a multivariate control chart based on a log-likelihood ratio with sparse estimators of the mean vector and variance-covariance matrix. Findings: The results show that 1) it is possible to identify which elements have changed by confirming each sparse estimated parameter, and 2) the proposed procedure outperforms the conventional likelihood ratio-based EWMA chart regardless of the number of parameter elements that change. Research Limitation/Implication: We perform sparse estimation under the assumption that the regularization parameters are known. However, the regularization parameters are often unknown in real life; therefore, it is necessary to discuss how to determine them. Originality/Value of paper: The study provides a natural extension of the conventional likelihood ratio-based EWMA chart to improve interpretability and detection accuracy. Our procedure is expected to solve challenges created by changes in a few elements of the population mean vector and population variance-covariance matrix.