Introduction

This report will take a look at a manufacturing process test-run based on control charts. There will be 3 days worth of data and each will contain 23 hours of data. An examination of each chart will be completed to determine at which hour the process should have been halted based on when one of Nelson’s Rules was violated.

The population mean is 25 with a standard deviation of 1.75 with a sample size of 5. Given this information, the standard deviation of the sampling distribution of means is computed by dividing the population standard deviation by the square root of the sample size which gives the result of: \[\sigma_{\bar{x}}=0.7826238\] In each graph below the central limit (CL) is the mean which is 25. The blue lines represent the +/- 1 standard deviation of the sampling distribution away from the mean. The red lines represent +/- 2 standard deviations of the sampling distribution away from the mean. The black lines represent the upper central limit (UCL) and the lower central limit (LCL) which are +/- 3 standard deviations of the sampling distribution away from the mean.

Day 1

On day 1 of manufacturing, the process should have been halted at hour 6. Nelson’s rule #3 was violated which says “four out of five consecutive points are on the same side of the center line above \(\mu + \sigma_{\bar{x}}\) or below \(\mu - \sigma_{\bar{x}}\)”. The green line is the first of four consecutive points that are above the \(\mu + \sigma_{\bar{x}}\) line.

Day 2

On day 2 of manufacturing, the process should have been halted at hour 2. Nelson’s rule #2 was violated which says “two out of three consecutive points are on the same side of the center line and above \(\mu + 2\sigma_{\bar{x}}\) or below \(\mu - 2\sigma_{\bar{x}}\)”. The green line is the first of 2 out of 3 consecutive points above the \(\mu + 2\sigma_{\bar{x}}\) line. This occurs again at hour 21 with 2 consecutive points below the \(\mu - 2\sigma_{\bar{x}}\) line.

Day 3

On day 3 of manufacturing there was never an instance where the process should have been halted. None of Nelson’s rules were broken therefore the manufacturing process went smoothly and there was no need to halt production.

Works Cited

Project, T. X. (n.d.-a). An application of X-bar charts to manufacturing. Ximera. https://ximera.osu.edu/qcstats/QC_stats/STAT_QC-0250/main