Introduction

Manufacturing Company X has provided data for 3 days for running their machines for 23 hours each of day with one hour for break and general maintenance. They have stated the mean of their process is \(\mu\)= 25 with a standard deviation \(\sigma=1.75\). Each day I have a sample of (n)=5 at each out and the standard deviation of the sampling distribution of means is \(\sigma_{\bar{X}}=0.7826238\). The upper control limits (\(mu+3*sigma_xbar\)), noted as UCL will be 27.34787 and the lower control limits (\(mu-3*sigma_xbar\)), noted as LCL will be 22.65213. Below the control charts are listed with analysis.

Day 1 Report

On day of the selected samples, the control chart shows that the process should have been halted at the sixth hour of operation. This would be the recommend stop time due to the Nelson Rule 3 where four out of five consecutive points are on the same side of the center line and above \(\mu\)+\(\sigma_{\bar{X}}\).

##Day 2 Report

On day two of the data the selected samples show that the machines should have been halted at the second hour of operation. Between hours two and four of operation there are two points out of the three that are on the same side and above \(\mu\)+\(2\sigma_{\bar{X}}\).

Day 3 Report

For day 3 the machines had some variance but all samples that were pulled show the work ran within expectations and there was no need for halting the process.

Citations

Ohio State University. (n.d.). Control charts and statistical quality control. Ximera. Retrieved November 7, 2024, from https://ximera.osu.edu/qcstats/QC_stats/STAT_QC-0250/main