A combined variable sampling interval and double sampling control chart with auxiliary information for the process mean

Abstract

In recent years, the suitable use of auxiliary information technique in control charts has shown an improved run length performance compared to control charts that do not have this feature. This article proposes a combined variable sampling interval (VSI) and double sampling (DS) chart using the auxiliary information (AI) technique (called VSIDS-AI chart, hereafter). The plotting-statistic of the VSIDS-AI chart requires information from both the study and auxiliary variables to efficiently detect process mean shifts. The charting statistics, optimal design and performance assessment of the VSIDS-AI chart are discussed. The steady-state average time to signal (ssATS) and steady-state expected average time to signal (ssEATS) are considered as the performance measures. The ssATS and ssEATS results of the VSIDS-AI chart are compared with those of the DS AI, variable sample size and sampling interval AI, exponentially weighted moving average AI (EWMA-AI) and run sum AI (RS-AI) charts. The results of comparison show that the VSIDS-AI chart outperforms the charts under comparison for all shift sizes, except the EWMA-AI and RS-AI charts for small shift sizes. An illustrative example is provided to demonstrate the implementation of the VSIDS-AI chart.

Adaptive CUSUM and EWMA charts with auxiliary information and variable sampling intervals for monitoring the process mean

“…In this study, on the lines of Haq 20 and Abbasi and Haq, 21 following Ng et al 23 and Umar et al, 24 we enhance the sensitivities of the AIB-ACC and AIB-AE charts with the VSI feature when monitoring the process mean. The run length properties of these control charts are computed using the Monte Carlo simulations, namely the average run length (ARL), average time-to-signal (ATS), median run length (MRL), median time-to-signal (MTS), standard deviation of the run length (SDRL), and standard deviation of the time-to-signal (SDTS).…”

“…As expected, the AIB-E chart based on VSI is uniformly more sensitive than that based on FSI. In addition, Umar et al 24 proposed an AIB-combined VSI and double sampling (DS) chart for the process mean, where the new chart generally prevails over the AIB-DS, AIB-VSSI, AIB-E, and AIB run sum charts. More related works on the AIB charts may be seen in Riaz, 18 Riaz, 25 Haq and Khoo, 26 Riaz et al, 27 Haq, 14 Haq and Khoo, 28,29 Haq et al, 30 and in the references cited therein.…”

The effect of measurement errors on the performance of the homogenously weighted moving average X¯ monitoring scheme

“…Note that the EARL metric is used to investigate the performance of a scheme for a range of shifts. The EARL is mathematically defined by (see for example Shongwe et al, 2020a; Umar et al, 2019)…”

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

“…To evaluate the performance of the proposed schemes from an overall performance perspective, the expected ATS ( EATS ) and the expected SDTS ( ESDTS ) are used because users tend not to know beforehand what exact shift value(s) is targeted – see, for example, Khoo et al (2019) and Umar et al (2019). The EATS and ESDTS measure the performance of a monitoring scheme over a range of shift values, that is, δ min to δ max − which are the lower and the upper bound of δ , respectively.…”