Average Run Length by Numerical Integral Equation of Modified EWMA Control Chart for Quadratic Autoregressive Process
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Abstract
This research aims to study the approximation of the Average Run Length (ARL) by using the Numerical Integral Equation (NIE) methods including Gaussian Rule, Midpoint Rule, Trapezoidal Rule and Simpson's Rule on Modified Exponentially Weighted Moving Average control chart (Modified EWMA) in case of exponential white noise. In addition, the efficiency of Modified EWMA control chart is compared to Exponentially Weighted Moving Average control chart (EWMA). The performance measurement criteria of the control chart were measured in term of out-of-control Average Run Length (ARL1) and processing time (CPU Times). The results showed that the performance of all methods are hardly different. In addition, the performance of Modified EWMA control chart is better than EWMA control chart for all magnitudes of shift size. Moreover, the approximation ARL using NIE method can be utilized in a wide variety of real-world datasets to show the efficacy of the suggested method.
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