A variable sample size run sum coefficient of variation chart

Abstract

A run sum chart with variable sample size (VSS) to detect shifts in the coefficient of variation (γ) is proposed. The run sum γ chart divides the chart into different regions with distinct scores assigned to these regions, and evaluates the process from the cumulative score. The proposed chart varies the sample size based on the cumulative score. A detailed description of the operation for the proposed chart is provided. Formulae to evaluate various performance measures are also derived. Furthermore, algorithms to optimize the chart are proposed. The chart significantly outperforms the run sum γ chart without the VSS feature in most cases. Besides the run sum γ chart, comparisons are also made against other γ charts. Finally, the implementation of the VSS run sum γ chart is shown on an illustrative example.

A variable sample size side-sensitive synthetic coefficient of variation chart

“…These scores need to be optimized to implement the chart. Hence, by letting the scores be ( S 1 , S 2 , S 3 , S 4 ) , the optimal ( S 1 * , S 2 * , S 3 * , S 4 * , n S * , n L * , W * , K * ) need to be obtained (Yeong et al, 2022), which results in higher computational complexity.…”

“…This approach separates the charting region into many states, with the transition probabilities dependent on whether the current Z i falls within the warning limits. Next, Yeong et al (2022) introduced the VSS feature into the run sum γ chart proposed in the work by Teoh et al (2017). The run sum γ chart separates the charting region into several regions, with scores assigned to these regions.…”

“…These scores are then accumulated based on positive and negative deviations from γ 0 , and an out-of-control signal is produced if the accumulated scores exceed a threshold. In the VSS run sum γ chart by Yeong et al (2022), larger sample sizes are adopted when the accumulated scores exceed a warning threshold; conversely, smaller samples are adopted. In both of the studies by Muhammad et al (2018) and Yeong et al (2022), the VSS feature was found to result in an improvement over their fixed sample size counterpart, where the number of samples required for detecting an out-of-control signal is reduced, without an associated increase in the average sample size.…”

Alternative Design of One-Sided Shewhart Control Charts for the Multivariate Coefficient of Variation

“…In these conditions, it is better to monitor the CV. Over the years, many intermediate and advanced CV charts have been discussed by using different strategies, such as exponentially weighted moving average (EWMA) (Zhang et al, 2014;Castagliola et al, 2011), CUSUM (Tran & Tran, 2016), synthetic (Calzada & Scariano, 2013;Chew et al, 2021), run rules (Castagliola et al, 2013), adaptive schemes (Khaw et al, 2017;Castagliola et al, 2015;Yeong et al, 2018) and variable sample size run sum (Yeong et al, 2022). Those proposed charts provided better performance in detecting small and moderate shifts.…”