Combined effect of autocorrelation and measurement errors on the adaptive X¯ monitoring schemes

Abstract

For independent and identically distributed observations, and those with measurement errors only, the adaptive designs (i.e. variable sampling sizes (VSS), variable sampling intervals (VSI) and the latter two combined to form VSSI) have been thoroughly discussed. However, no research exists for processes under the combined effect of autocorrelation and measurement errors; thus, such adaptive Shewhart [Formula: see text] schemes are proposed. The Markov chain approach for adaptive designs are used to evaluate the run-length distribution properties with two special sampling strategies (i.e. s-skip and multiple measurements) incorporated to reduce the combined negative effect of autocorrelation and measurement inaccuracy. Using numerous run-length metrics, it is shown that the combination of the two sampling strategies with the VSSI design reduces this negative effect considerably and improves the detection ability of the [Formula: see text] scheme by a significant margin as compared with using the fixed sample size and sampling interval (FSSI), VSS and VSI designs. Autocorrelation level has a higher negative effect as compared with the measurement inaccuracy level. For high levels of autocorrelation ([Formula: see text]0.8), the s-skip strategy has little influence in reducing the negative effect; but the VSSI design maintains better performance than the other designs. Finally, a real-life example is used to illustrate its implementation.

The Measurement Errors and Their Effects on the Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables

“…For example, the measurement error reduces the performance of control charts to detect the Out-Of-Control (OOC) process. In recent years, some scholars have noticed and analyzed the influence of measurement errors on the performance of control charts (see Linna and Woodall [18], Cocchi and Scagliarini [19], Maravelakis [20], Abbasi [21], Maleki et al [22], Amiri et al [23], Liu et al [24], Sabahno et al [25], Shongwe and Malela-Majika [26], Thanwane et al [27], Maleki et al [28], and Munir et al [29]).…”