Abstract
Repetitive sampling has been found very popular in improving the control chart techniques for last couple of years. In repetitive sampling based control charts, there are two additional control limits inside the usual upper control limit (UCL) and lower control limit (LCL). If any subgroup crosses these limits but remain inside outer limits, it is deferred and replaced with another selection. Process is said to be out of control if any subgroup falls outside UCL/LCL. In this article, the technique has been modified by introducing a relation between outer and inner control limits in terms of a ratio and need of this modification has also been justified by highlighting a gap in the existing technique. By using Monte Carlo simulation, several results have been generated relevant to different sample sizes and introduced ratios. The results have been described with the help of average run length (ARL) tables that how the efficiency of control chart is effected by using different ratios. The modification in the technique also provides variety of alternatives within the scope of repetitive based control charts. All the discussed options have summarized to one table to see that how the control limits under this technique behave and impact on detecting shifts in the process average. The schemes have been interpreted in the light of above ratio and their comparison has been described under different sample sizes that facilitate the user to select most appropriate scheme for a desired process control. An example has been included by choosing one of the proposed schemes to show the application and performance of the proposed control chart in a manufacturing process.
Highlights
The statistical process control (SPC) techniques have been widely used in the industry for the monitoring of product and service
In the above mentioned review we find smallest ratios as 0.011, 0.04 and 0.07, these indicate very strict control charts where it is obvious that due to very large repetitive zone, number of subgroups might have deferred if these charts are applied to any process
In some of the cases the ratio has been even below 0.05. If this scheme is used in normal processes, it is expected that around 86% of the subgroups may need to be deferred and re-sampled since they fall in the repetitive zone of the control chart
Summary
The statistical process control (SPC) techniques have been widely used in the industry for the monitoring of product and service. The control chart has been found a best technique to monitor process variation whether quality characteristics is continuous or attribute. The process is said to be out-of-control if the plotting statistic value falls beyond the UCL or LCL. The Shewhart control charts are usually more efficient to detect larger shift in the manufacturing process. These charts are less capable to detect small shifts in the process and may mislead the process monitoring personnel. By exploring the subject of process control, extensive work is found to improve the efficiency of Shewhart control chart, see for example Koutras (2007). More details about the design and applications of control charts can be seen in Castagliola (2005), Chen et al (2005), Shu et al (2007), Yang et al (2011) and Ali et al (2016)
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