A new double sampling scheme to monitor the process mean of autocorrelated observations using an AR(1) model with a skip sampling strategy

Abstract There are numerous academic researches on statistical process monitoring schemes that assume that sequential observations are independent and identically distributed (iid); however, in industrial processes, sequential data tends to exhibit serial correlation (i.e. autocorrelation). Implementing monitoring schemes designed for iid observations when in fact data is sampled from an autocorrelated process yields misleading results. In this paper, a side-sensitive double sampling (SSDS) scheme to monitor the mean of autocorrelated observations using a first-order autoregressive model is proposed. In order to reduce the negative effect of serial dependence, a sampling strategy that involves sampling of non-neighbouring observations (i.e., skipping s observations before sampling to form a subgroup, called in short, s-skip strategy) is incorporated into the computation of the probability values of the run-length distribution and the charting limits. The main findings of this study is that the proposed s-skip SSDS scheme yields a run-length distribution that has uniformly better average run-length (ARL) and expected ARL values as compared to the existing non-side-sensitive double sampling scheme, other well established Shewhart-type schemes (i.e. runs-rules and synthetic) using the s-skip strategy and the basic X ¯ scheme using mixed samples strategy. A real life example is used to illustrate the implementation.