A manufacturing process test was evaluated using control charts generated from three days of operational data. The process ran continuously for 23 hours each day, followed by a scheduled maintenance period during the last hour. Control chart analysis identified specific times when the process should have been paused to prevent defects or inefficiencies. Key findings include patterns and deviations from control limits, with justifications for each recommended stoppage.

NOTATION USED FOR THE STANDARD DEVIATION OF THE SAMPLING DISTRIBUTION OF MEANS:

\(\sigma=1.75\)

\(\mu=25\)

\(n=5\)

\[\sigma_{\bar{X}}= 0.7826238\]

\[LCL=22.65\] \[UCL=27.35\] For this report, I used control charts to analyze the manufacturing process and detect potential out-of-control behavior. I applied Nelson’s Rules, which include 8 criteria for identifying non-random patterns such as runs, trends, and excessive variation. These set of rules are used in manufacturing to determine when a process may be out-of-control.

Data Day 1:

Based on Nelson’s Rule number 3, if four out of five consecutive points fall on the same side of the center line and outside the control limits (\(\mu+\sigma_{\bar{X}}\) or below \(\mu-\sigma_{\bar{X}}\)), the process may be out of control. During day 1, since four consecutive points are above \(\mu+\sigma_{\bar{X}}\), the process should have been paused at hour 9 to prevent defects or inefficiencies.

Data Day 2:

Based on Nelson’s Rule, if 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 process may be out of control. During day 2, since two consecutive points are outside, the process should have been stopped at hour 4 to keep the process in control and prevent defects.

DATA DAY 3:

During day 3, there is no evidence indicating the need to stop the process, as it appears to be in control. Therefore, there is no need to take further action.

Works Cited:

“An Application of X-bar Charts to Manufacturing.” Ximera, https://ximera.osu.edu/qcstats/QC_stats/STAT_QC-0250/main . Accessed 7 Nov. 2024.