Shewhart-type monitoring schemes with supplementary w-of-w runs-rules to monitor the mean of autocorrelated samples

Abstract

The simplicity of the Shewhart charts makes it popular in practice; however, it is insensitive to detecting small shifts. In an effort to preserve its simplicity but increase its detection ability, in this paper, we propose two Shewhart-type charts supplemented with w-of-w runs-rules to monitor the mean of autocorrelated samples using a first-order autoregressive model. It is shown that the higher the level of autocorrelation, the poor the proposed schemes perform. Hence, we implement the skipping sampling strategy which involves sampling of nonconsecutive observations to form the rational subgroups to compute the corresponding sample means. The Markov chain approach is used to derive zero- and steady-state closed-form expressions of the average run-length (ARL). To supplement the specific shift performance metric, i.e. ARL, we compute the overall performance metric so that these schemes can also be evaluated from a global point of view. A real-life example is provided to illustrate the implementation of the monitoring schemes proposed here.