article · FUDMA Journal of Sciences
Statistical process control (SPC) charts typically assume data independence, an assumption often violated by autocorrelated data, leading to inaccurate monitoring. This research introduces an Arithmetic Return Model (ARM) approach for SPC of autocorrelated data exhibiting Geometric Brownian Motion (GBM). The proposed ARM simplifies the autocorrelation problem by transforming an Autoregressive of order 1 (AR(1)) process. Findings indicate that ARM outperforms the existing Logarithmic Return Model (LRM) by removing autocorrelation faster and with less complexity. It also provides a better fit for process data and enables quicker detection of out-of-control signals in control charts, making it a more effective choice for monitoring such data.
Accurate statistical process control is vital for maintaining quality and efficiency in various systems. This research offers a more reliable and faster method for monitoring processes where data points are interconnected, leading to quicker identification of problems and better operational stability in industrial and other applications.
This research offers an improved method for statistical process control, particularly relevant for industrial settings where processes generate autocorrelated data, such as in manufacturing or chemical processing. Quality control engineers and process managers could use this Arithmetic Return Model to more accurately and quickly detect deviations in process parameters. The model has been tested with both simulated and real-world data, suggesting it is at an applied research stage with potential for practical implementation in industrial monitoring systems.
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Statistical process control charts operate with the two basic assumptions that the process data at different time points should be independent and identically normally distributed (i.i.n.d.).The assumption of independence is mostly violated which leads to wrong inferences made on the processes being monitored.This work aims at carrying out Statistical Process Control (SPC) of autocorrelated data exhibiting Geometric Brownian Motion (GBM): Arithmetic Return Model (ARM) approach.The proposed model proffers a simplified solution to the autocorrelation problem in SPC by transforming an Autoregressive of order 1 (AR (1)) process to ARM, this is because the GBM is the potential law which governs most positive time series, and has been confirmed to be AR(1) according to literature.Two sets of autocorrelated data which exhibit GBM properties; a simulated data and a furnace temperature data obtained from literature were subjected to SPC and monitoring.Findings from the work showed that the ARM performed better than the existing Logarithmic Return Model (LRM) in terms removal of autocorrelation faster with less sophistication, from 1.171261 to 2.86818 in the simulated data, and from 1.50446 to 1.7848 in the furnace temperature data.Also, the proposed model gave a better fitting of both process data, and faster detection ability for out of control signals in the control charts at λ=0.25, λ=0.5, λ=0.7 which makes the proposed ARM a better choice when dealing with SPC of autocorrelated data exhibiting the GBM.
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DOI: 10.33003/fjs-2025-0901-3185
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