One-sided runs-rules schemes to monitor autocorrelated time series data using a first-order autoregressive model with skip sampling strategies

摘要

In some industrial or health-related processes, it makes more practical sense to monitor either an increase only or a decrease only in the quality characteristic of interest. Consequently, in this paper, we propose four one-sided Shewhart X over bar charts supplemented with runs-rules to monitor the mean of autocorrelated normally distributed samples using a stationary first-order autoregressive model. To counteract the negative effect of autocorrelation, we implement a sampling strategy which involves sampling of non-neighboring observations to form rational subgroups. The Markov chain technique is used to derive zero-state and steady-state closed-form expressions of the specific shift performance metric, ie, average run-length (ARL). Moreover, we compute the expected ARL metric which evaluates each monitoring scheme based on all specified range of possible values of the shift parameter, or more specifically, from a global point of view and thus gives a different perspective from the specific shift ARL metric. We observed that the steady-state improved w-of-w and the improved 2-of-(H + 1) schemes yield a better overall performance than their corresponding basic counterparts for all different levels of autocorrelation. A real-life example is provided to illustrate the implementation of the monitoring schemes proposed here.