The variable sampling interval S -super-2 chart with known or unknown in-control variance

The chart has been known as a powerful tool to monitor the variability of the normal process. This paper considers the variable sampling interval (VSI) chart to improve the performance of the original chart. A VSI chart based on the average run length (ARL) unbiased and average time to signal (ATS) unbiased criteria is developed when the in-control variance is known. The performance of the proposed chart is investigated in terms of the mean and standard deviation of the RL and total time to signal. The impact of parameter estimation on the proposed VSI chart is also evaluated. The results show that the performance of the control chart is seriously different from the known parameter case when the parameter is estimated. Then, a new VSI chart with the desired in-control ARL and ATS is considered when the in-control variance is estimated. In evaluating the usefulness of the VSI feature, the VSI charts are compared with the fixed sampling interval (FSI) versions in terms of their statistical properties. The comparison results show that the VSI chart can detect the shifts in the process variance quicker than the corresponding FSI chart, regardless of whether the in-control variance is known or unknown. Finally, two examples are used to illustrate the proposed control chart.