Introduction

A manufacturing process test-run was ran. The process mean is 25 and the process standard deviation is 1.75. By dividing the square root of the sample size by the process standard deviation we can see that \(\sigma_{\bar{X}}=0.78\). By subtracting 3 times the standard deviation for the sampling distribution of means from the process mean we find that the LCL is 22.6521286 and by adding 3 times the standard deviation for the sampling distribution of means to the process mean we can find that the UCL is 27.3478714.

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Analysis 1

As you can see, starting at hour 6, there are four consecutive points that are farther than one standard deviation away from the mean on the same side, therefore, the process must be stopped at hour 9 because of the violation of Nelson’s rule.

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Analysis 2

As you can see, starting at hour 2, there are two out of three consecutive points(hour 2 and hour 4) that are over 2 standard deviations away from the mean and on the same side. Since, at just hour 4, the chart violates Nelson’s rule, the process must be halted there.

Analysis 3

Based on the control chart from day 3, I see no reason for the process to be halted. Looking at the chart, it does not seem to violate any of Nelson’s rules.

Works Cited

Project, The Ximera. “An Application of X-Bar Charts to Manufacturing.” Ximera, ximera.osu.edu/qcstats/QC_stats/STAT_QC-0250/main. Accessed 8 Nov. 2024.