Proposed Synthetic And Group Runs Control Charts Based On Runs Rules And Double Sampling Np Methods X
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Date
2015-08
Authors
Chong, Zhi Lin
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Abstract
A control chart is an important tool to monitor one or more quality characteristics of interest in a production process. The classical Shewhart X control chart is the most widely used variables control chart in manufacturing and service
industries to monitor the mean of a process with continuous data, due to its simplicity to shop floor personnel. The Shewhart X control chart is very effective for detecting large shifts in the process mean. However, the Shewhart X chart is insensitive to small and moderate mean shifts. This is a major disadvantage of the Shewhart X
chart. Runs rules are commonly used to increase the sensitivity of the classical Shewhart X chart for detecting small and moderate process mean shifts. A more
recent and efficient runs rule is the revised m-of-k ( / − R mk) runs rule scheme for
continuous data. On the other hand, in process monitoring involving attribute data,
the double sampling (DS) np control chart is an effective chart to detect small and
moderate shifts in the fraction of nonconforming items from a process. Motivated by the need to improve performance of existing charts, we incorporate the synthetic and
group runs (GR) control charting procedure into the R − / mk runs rule scheme and DS np chart. The main objective of this thesis is to propose four new optimal designs of control charts by minimizing the out-of-control average run length ( 1 ARL ) of (i)
the synthetic R − / mk runs rule X chart, (ii) the GR R − / mk runs rule X chart,
(iii) the synthetic DS np chart, and (iv) the GR DS np chart. The 1 ARL results of the optimal charts show that the new charts perform better than their basic counterparts
while having comparable performance with some existing charts. In addition, optimization programs for the four proposed charts are provided in this thesis. These optimization programs enable practitioners to compute the optimal charting parameters instantaneously, for use in process monitoring.
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Mathematics