Introduction

This paper assesses a manufacturing process test-run. The process runs for 23 hours a day for three days straight and remains uninterrupted, except for the one hour maintenance that occurs at the end of each day. The main goal of this report is to identify when the process should be halted which can be done by creating control charts. Large deviations in these graphs will help determine whether or not the process has gotten unmanageable or out of control. The evaluation process is very important for a test run because the stability and quality can be monitored continuously.

For the manufacturing process, the known variables are the mean and standard deviation. \[\mu{}=25\] \[\sigma{}=1.75\]. The sample size that will be used is \[n=5\]

The standard deviation for the sampling distribution set of means is \(\sigma_{\bar{x}}=\) \(0.7826238\) which is found by dividing the standard deviation by the square root of the sample size.

The upper control limit is \[UCL = 27.3478714\]

This can be found by taking the mean and adding 3 times the sample standard deviation.

The lower control limit is \[LCL = 22.6521286\]

This can be found by taking the mean and subtracting 3 times the sample standard deviation.

Now, let’s look at the control charts…

Day 1

According to the control chart for Day 1 and Nelson’s rules, the process should be halted at hour 9 because Rule 3 is violated. Rule 3 states four out of five consecutive points are on the same side of the center line and above one standard deviation or below one standard deviation from the sample mean.

Day 2

According to the control chart for Day 2 and Nelson’s rules, the process should be halted at hour 4 because Rule 2 is violated. Rule 2 states two out of three consecutive points are on the same side of the center line and above 2 standard deviations or below 2 standard deviations from the sample mean.

Day 3

According to the control chart for Day 3 and Nelson’s rules, the process should not be halted because no rules are violated. The process seems to be in control and manageable for it to continue. There are no unusual patterns at this point in time. Therefore, the process is stable.

Sources

Ximera. An Application of X-bar Charts to Manufacturing, ximera.osu.edu/qcstats/QC_stats/STAT_QC-0250/main.