Setbacks of Joint Location and Dispersion Control Charts
Keywords:
Joint chart, multiple charting, parameter estimation, average run length (ARL), median run length (MRL)Abstract
It is a common practice to monitor or control a process with control charts. The Shewhart - and
R- or S-charts are the most common in use for monitoring process location and dispersion respectively. The literature reveals that until lately, the tradition has been to apply the charts for location and dispersion independently, but now, some works considered them jointly. The use of three-sigma limits, estimated parameter, and multiple charting have been shown to affect the joint chart schemes
by deteriorating the performance. In the literature, works exist on joint charts for ¯ and R-charts when the process parameters are known and the process is in a state of control, on - and R-charts when the process parameters are unknown and the process is in a state of control and on ¯ and S-charts (here, S-chart has one-sided control limit) for both when the process parameters are known
and unknown and the process is in a state of control. For the works so mentioned, the in-control average run length was used as the sole index for measuring the charts performance. Similar works on such joint charts for both the in-control and out-of-control states with estimated parameters where the performance is evaluated in terms of the average run and the median run lengths lack in the literature and this work will fill the gap. Therefore, in this work, a joint and -charts will be extensively considered when the -chart is with both one-sided and two-sided control limits using the information from the unconditional run length (RL) cumulative distribution function (cdf) and its percentiles (mainly the median). New control limit constants will be provided to guarantee the desired in-control performance for the joint chart.
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