Dual CUSUM Charts for Monitoring Autocorrelated AR (1) Processes Mean With s-Skipping Sampling Scheme

Abstract

In statistical process monitoring, it is often assumed that the sequential observations generated by processes are independent and identically distributed (iid). However, in real practice, these observations tend to exhibit an autocorrelation pattern. Thus, an autocorrelated process yields misleading results in terms of a high false alarm rate and slow detection of process changes if employing iid-based designed monitoring schemes. Therefore, in this article, we propose the dual cumulative sum (DCUSUM) and dual Crosier’s CUSUM (DCCUSUM) mean charts for monitoring the autocorrelated processes using a first-order autoregressive model. Monte Carlo simulations are extensively used to compute the performance measures: the average run length, standard deviation run length, extra quadratic loss, and relative average run length of the two-sided DCUSUM and DCCUSUM charts under both the zero-state and steady state cases. It is observed that as the level of autocorrelation increases, the performance of the studied charts deteriorates. Thus, a s-skipping sampling scheme is incorporated to reduce the negative effect of autocorrelation. To demonstrate the effect of autocorrelation and highlight implications further, a simulated dataset with a shift in the process mean is considered.

Keywords

• AR (1) model
• autocorrelation
• DCUSUM chart
• Monte-Carlo simulations
• s-skipping sampling
• statistical process control