A combined mixed-s-skip sampling strategy to reduce the effect of autocorrelation on the X̄ scheme with and without measurement errors

Abstract

In order to reduce the effect of autocorrelation on the $\overline{X}$ monitoring scheme, a new sampling strategy is proposed to form rational subgroup samples of size n. It requires sampling to be done such that: (i) observations from two consecutive samples are merged, and (ii) some consecutive observations are skipped before sampling. This technique which is a generalized version of the mixed samples strategy is shown to yield a better reduction of the negative effect of autocorrelation when monitoring the mean of processes with and without measurement errors. For processes subjected to a combined effect of autocorrelation and measurement errors, the proposed sampling technique, together with multiple measurement strategy, yields an uniformly better zero-state run-length performance than its two main existing competitors for any autocorrelation level. However, in steady-state mode, it yields the best performance only when the monitoring process is subject to a high level of autocorrelation, for any given level of measurement errors. A real life example is used to illustrate the implementation of the proposed sampling strategy.

KEYWORDS:

• Autocorrelation
• measurement errors
• mixed samples strategy
• multiple measurements
• skipping sampling strategy
• steady-state
• zero-state

View correction statement:

Correction

Data availability statement

The data used in the application example is available from the papers by Costa and Castagliola [5] and Franco et al. [7].

Acknowledgements

The authors would like to gratefully acknowledge the three anonymous referees and the Associate Editor for taking their valuable time to thoroughly read and give suggestions to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article was originally published with errors, which have now been corrected in the online version. Please see Correction (http://dx.doi.org/10.1080/02664763.2020.1807783)