Report 1

Introduction

A manufacturing process was test-run and sampled over a period of three days. The process ran for 23 hours each day without any interruptions besides for one hour at the end of the day that was used for maintenance. The process should have a mean of 25 and a standard deviation of 1.75. The sampling distribution of means produced a standard deviation of \(\sigma_{\bar{x}} =\) 0.7826238. In this scenario, the lower limit is 22.6521286, and the upper limit is 27.3478714.

Day 1

In Day 1 of the test-run process, the process was in control until hour six. The process should have been halted by hour nine because of Nelson’s rules. The process saw four consecutive hours, hours six to nine, with points falling outside of one standard deviation above the expected mean of 25.

Day 2

In Day 2 of the test run process, the process should have been halted early on in the day. From hour two to hour four, we saw two out of three points fall two standard deviations above the expected mean of 25. This violates one of Nelson’s rules.

Day 3

In Day 3 of the manufacturing process, the process appears to be in control. Looking at the graph of Day 3 it doesn’t seem like there are any points that appear to fit the Nelson Rules when it comes to the manufacturing process.

Works Cited

“An application of X-bar charts to manufacturing”. Ximera. https://ximera.osu.edu/qcstats/QC_stats/STAT_QC-0250/main