-Chart with runs and variable sampling intervals

Abstract

The -chart for monitoring a process mean takes samples from the process at fixed time intervals between each two samples. When used with tuns rules the chart signals if a single sample falls outside the control limits or if a run of a specified length occurs in a specified region. This paper considers the -chart with runs rules in which the sampling interval is allowed to vary depending on what is observed from the current sample and past samples. The variable sampling interval (VSI) chart with runs rules uses a long sampling interval if there is no indication of changes in the process mean, and a short sampling interval if there is an indication that the process mean may have shifted from the target value. The stronger the indication, the shorter the sampling interval to be used. If an indication is strong enough, the chart will give an out-of-control signal in the same way as a usual chart with runs rules. A Markov chain approach is used to evaluate the properties of the VSI chart such as the average time to signal and the average rrumber of samples to signal. Comparisons with the usual fixed sampling interval (PSI) chart with runs rules show that the VSI chart is more efficient.

Keywords:

• control chart
• variable time delay
• process control
• quality control
• warning limits
• Markov chain