Abstract The Cumulative Sum (CUSUM) chart is widely used and has many applications in
different fields such as finance, medical, engineering, and other fields. In real applications …

In this paper, the average run length (ARL) for the cumulative sum (CUSUM) control chart
based on SAR (P) L with trend process is developed using Fredholm integral equation …

The exponentially weighted moving average (EWMA) control chart is a popular tool used to
monitor and identify slight unnatural variations in the manufacturing, industrial, and service …

In this paper we use a Fredholm integral equation approach to derive an explicit formula for
the average run length (ARL) of a cumulative sum (CUSUM) chart for random observations …

Control charts are one of the tools in statistical process control widely used for monitoring,
measuring, controlling, improving the quality, and detecting problems in processes in …

This paper presents an approximate average run length (ARL) of CUSUM chart for long-
memory process by using numerical integral equation (NIE) method based on Gauss …

Statistical process control methods are widely used in several fields for monitoring and
detecting process problems. One of them is the control chart which is powerful and effective …

Numerical Integral Equation (NIE) methods for evaluating the Average Run Length (ARL) on
Extended Exponentially Weighted Moving Average (Extended EWMA) control chart for …

This study aims to develop a precise formula for calculating the average run length in the
context of an exponentially weighted moving average (EWMA) control chart, specifically in …

In this study, we apply the Fredholm-type integral equation method to derive the explicit
formulas of the average run length (ARL) for an autoregressive moving average process …