Nt1310 Unit 3 Assignment 1 Sign Control Chart
In this section we illustrate the sign control chart using a set of data from Montgomery \cite{(2)} on the inside diameters of piston rings manufactured by a forging process based on the SRS and RSS schemes. Forty samples, each of size 5, have been taken from this process. All samples are combined such that we have 200 measurements of the inside diameters of the piston rings. \\
This set of data is used by Haq et al. \cite{Haq} and \cite{Haq2} to explain the implementation of the proposed control charts based on different schemes of RSS. Mean and median of these populations are $74.004$ and $74.003$, respectively. First, we assume that the process is in-control and we draw 30 samples, each of size 12, from the 200 …show more content…
Then, for two sided control chart $ARL_0=157.54$, $\alpha_0=0.0063476$ and control limits are $\pm10$. To reach this value of $ARL_0$ in the case of RSS, let $UCL_{rss}=7$ and $\gamma=0.04648$. Sub-figures (a) and (b) in Figure \ref{redfig1} show the plot of the proposed control chart based on these 30 samples. \\
From these sub-figures, it is clear that the process is in-control state. Suppose that after the $30^{th}$ sample the process becomes out-of-control. For this purpose, we again draw 10 samples from 200 measurements and add 0.005 to all values within each sample that were obtained under SRS and RSS schemes. The values of their charting statistics have been computed for these 10 samples and plotted in sub-figures (C) and (D) in
Figure \ref{redfig1}. It is interesting to note that the SRS control chart detects the random shift at the $38^{th}$ sample, whereas the proposed RSS control chart detects it at the $35^{th}$ , $37^{th}$ and $38^{th}$ samples and at the $34^{th}$ sample is on the upper warning limit. Hence the RSS control chart detects the random shift in the process mean substantially quicker than the SRS control chart can
This set of data is used by Haq et al. \cite{Haq} and \cite{Haq2} to explain the implementation of the proposed control charts based on different schemes of RSS. Mean and median of these populations are $74.004$ and $74.003$, respectively. First, we assume that the process is in-control and we draw 30 samples, each of size 12, from the 200 …show more content…
Then, for two sided control chart $ARL_0=157.54$, $\alpha_0=0.0063476$ and control limits are $\pm10$. To reach this value of $ARL_0$ in the case of RSS, let $UCL_{rss}=7$ and $\gamma=0.04648$. Sub-figures (a) and (b) in Figure \ref{redfig1} show the plot of the proposed control chart based on these 30 samples. \\
From these sub-figures, it is clear that the process is in-control state. Suppose that after the $30^{th}$ sample the process becomes out-of-control. For this purpose, we again draw 10 samples from 200 measurements and add 0.005 to all values within each sample that were obtained under SRS and RSS schemes. The values of their charting statistics have been computed for these 10 samples and plotted in sub-figures (C) and (D) in
Figure \ref{redfig1}. It is interesting to note that the SRS control chart detects the random shift at the $38^{th}$ sample, whereas the proposed RSS control chart detects it at the $35^{th}$ , $37^{th}$ and $38^{th}$ samples and at the $34^{th}$ sample is on the upper warning limit. Hence the RSS control chart detects the random shift in the process mean substantially quicker than the SRS control chart can