Enhanced Frameworks for Accurate ARL Estimation in Statistical Process Control Systems
Keywords:
Statistical process control, Average run length, Markov chain approach, Numerical integral equation, Explicit formulasAbstract
This study presents an enhanced framework for accurately estimating the Average Run Length (ARL) in Statistical Process Control (SPC) systems especially for control charts, which are essential for monitoring, maintaining, and improving process quality in industrial and economic applications. The ARL, a key performance metric in SPC, indicates the average number of samples taken before a control signal is triggered, with ARL₀representing false alarms and ARL₁indicating true detections. This paper reviews and compares four prominent ARL evaluation methods: Monte Carlo Simulation, Markov Chain Approach, Numerical Integral Equation, and Explicit Formulas. Each method’s strengths and limitations are discussed in terms of accuracy, and flexibility. The findings highlight the need for method selection based on the complexity of monitored processes, particularly in autocorrelation and non-normality are prevalent. Furthermore, integrating these methods with AI-driven optimization techniques - such as machine learning algorithms for data analysis and adaptive control - offers promising avenues for enhancing the precision and responsiveness of process monitoring in dynamic and complex environments.
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