Performance evaluation of conventional exponentially weighted moving average (EWMA) and p-value cumulative sum (CUSUM) control chart

This paper is aimed at comparing the performances of the conventional Exponentially Weighted Moving Average (EWMA) and p-value Cumulative Sum (CUSUM) control chart. These charts were applied in monitoring the outbreak of pulmonary tuberculosis in Delta State University Teaching Hospital (DELSUTH), Oghara for a period of eighty four (84) calendar months. Line chart and histogram were plotted to test for stationary and normality of the data. Autocorrelation plot was also used to study the randomness of the data. The results of the control charts show that conventional EWMA chart detects shifts faster in monitoring process mean than the p-value CUSUM control chart. Keywords and Phrases: Exponentially Weighted Moving Average (EWMA), p-value, Cumulative Sum (CUSUM), Autocorrelation, Randomness

A new CUSUM control chart under uncertainty with applications in petroleum and meteorology

In these last few decades, control charts have received a growing interest because of the important role they play by improving the quality of the products and services in industrial and non-industrial environments. Most of the existing control charts are based on the assumption of certainty and accuracy. However, in real-life applications, such as weather forecasting and stock prices, operators are not always certain about the accuracy of an observed data. To efficiently monitor such processes, this paper proposes a new cumulative sum (CUSUM) X¯ chart under the assumption of uncertainty using the neutrosophic statistic (NS). The performance of the new chart is investigated in terms of the neutrosophic run length properties using the Monte Carlo simulations approach. The efficiency of the proposed neutrosophic CUSUM (NCUSUM) X¯ chart is also compared to the one of the classical CUSUM X¯ chart. It is observed that the NCUSUM X¯ chart has very interesting properties compared to the classical CUSUM X¯ chart. The application and implementation of the NCUSUM X¯ chart are provided using simulated, petroleum and meteorological data.

The Performance of CUSUM Control Chart for Monitoring Process Mean for Autoregressive Moving Average with Exogenous Variable Model

The objective of this study was to derive explicit formulas for the average run length (ARL) of an autoregressive moving average with an exogenous variable (ARMAX(p,q,r)) process with exponential white noise on a cumulative sum (CUSUM) control chart. To check the accuracy of the ARL derivations, the efficiency of the proposed explicit formulas was compared with a numerical integral equation (NIE) method in terms of the absolute percentage error. There was excellent agreement between the two methods, but when comparing their computational times, the explicit formulas only required 1 second whereas the NIE method required 599.499–835.891 s. In addition, real-world application of the derived explicit formulas was illustrated using Hong Kong dollar exchange rates data with an exogenous variable (the US dollar) to evaluate the ARL of an ARMAX (p,q,r) process on a CUSUM control chart.