The variable sampling interval run sum X‾ control chart

• Sampling intervals for VSI run sum X‾ chart are varied according to process quality.
• Optimization programs to minimize ATS1(δopt)ATS1(δopt) and AATS1(δopt)AATS1(δopt) for the VSI run sum X‾ chart are developed.
• The zero state and steady state VSI run sum X‾ chart’s performances are evaluated.
• The VSI run sum X‾ chart performs well compared with other competing charts.
• An example of application explains the construction of the VSI run sum X‾ chart.

Traditional control charts for process monitoring are based on taking samples from the process at fixed length sampling intervals. More recently, research works focused on the use of variable sampling intervals (VSIs), where the lengths of the sampling intervals are varied according to the process quality. A short sampling interval is considered when the process quality indicates a possible out-of-control situation while a long sampling interval is considered, otherwise. In this paper, the VSI run sum (RS) X‾ chart is proposed with its optimal scores and parameters determined using an optimization technique to minimize the out-of-control average time to signal (ATS) or the adjusted average time to signal (AATS). A Markov-chain method is used to evaluate both the ATS and AATS of the proposed chart, for the zero and steady state cases, respectively. Results show that the VSI RS X‾ chart is considerably more efficient than the basic RS X‾ chart. The VSI RS X‾ chart performs generally well compared with other competing charts, such as the standard X‾, synthetic X‾, exponentially weighted moving average (EWMA) X‾, VSI X‾ and VSI EWMA X‾ charts. The sensitivity of the VSI RS X‾ chart can be enhanced further by adding more scoring regions or a head-start feature. An illustrative example is presented to explain the implementation of the proposed VSI RS X‾ chart.