One-sided 4-out-of-5 Run Rules Charts for the Multivariate Coefficient of Variation in the Finite Horizon Process

Quality improvement has been receiving great attention in industries. In recent years, the finite horizon process is commonly encountered in industries due to flexible manufacturing production. Past research works on finite horizon process monitoring are still limited. Because of this, one-sided 4-out-of-5 run rules charts are proposed to monitor the multivariate coefficient of variation in a finite horizon process. The performance measures of the proposed charts are derived using the Markov-chain approach. The proposed schemes can serve as a framework for practitioners who wish to perform process monitoring easily and efficiently. Numerical comparisons between the proposed and existing charts have been made, in terms of the truncated average run length and the expected truncated average run length criteria. The findings reveal that the proposed charts outperform the existing charts for detecting small and moderate process shifts in the finite horizon process.

Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart X ¯ Chart

In modern quality control applications, there often exist significant measurement errors because observations are measured quickly in time order. As a result, the errors influence the power of a control chart to detect a given change in the process parameter(s) of a quality characteristic. In this paper, by using a covariate error model, the properties of the Shewhart X ¯ chart integrated with run rules are investigated when errors exist in the measurement of quality characteristic. Two metrics, the average run length and 95% quantile of the run length, are adopted to evaluate the chart’s performance for different mean shifts and sample sizes. Numerous simulations are conducted, and the results indicate that the errors in the measurement significantly affect the performance of the run rule X ¯ chart, especially when the errors are large. To reduce this negative effect on the run rule X ¯ chart, measuring more times of each item in each subgroup and increasing the coefficient in the covariate error model are shown to be good choices for practitioners.

A Combined Upper-Sided Synthetic S2 Chart for Monitoring the Process Variance

In order to monitor the process variance, this paper proposes a combined upper-sided synthetic S2 chart for monitoring the process standard deviation of a normally distributed process. This combined upper-sided synthetic S2 chart comprises a synthetic chart and an upper-sided S2 chart. The design and performance of the proposed chart are presented, and the steady-state average run length comparisons show that the combined upper-sided synthetic S2 chart outperforms the standard synthetic S2 chart as well as several run rules S2 charts, especially for larger shifts in the process variance.