Report 1
Nana Amponsah
2025-11-18
Introduction
This report analyzes control charts from a three day manufacturing process to determine if the process went out of control.The process was allowed to run for 23 hours each day without interruption, other than the regular end of day maintenance during the last hour.
Population mean: \(\mu = 25\) Population standard deviation: \(\sigma = 1.75\) Sample size: \(n = 5\)
The standard deviation for the sampling distribution of means is: \[\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{1.75}{\sqrt{5}} = 0.7826\] The control limits are:
- UCL: \(\mu + 3\sigma_{\bar{x}} = 27.348\)
- LCL: \(\mu - 3\sigma_{\bar{x}} = 22.652\)
DAY1
The process for day 1 remained in control throughout the whole day.There were no violations of Nelson’s rules detected.
DAY2
The process for day 2 remained in control throughout the whole day.There were no violations of Nelson’s rules detected.
DAY3
The process for day 3 remained in control throughout the whole day.There were no violations of Nelson’s rules detected.
Work Cited
Project, The Ximera. “An Application of X-Bar Charts to Manufacturing.” Ximera, ximera.osu.edu/qcstats/QC_stats/STAT_QC-0250/main. Accessed 20 Nov. 2025.