Introduction

This report evaluates the manufacturing process test-run based on generated control charts. The process was allowed to run for 23 hours a day for 3 days, generating different data for each day. This report also examines the control charts to determine when the process should have been halted. Each day’s data will be compared against the following information about the process: \[\mu=25\], \[\sigma=25\], \[n = 5\] where \(\mu\) is the population mean, \(\sigma\) is the population standard deviation, and \(n\) is the number of samples collected.

The standard deviation for the sampling distribution is \(\sigma_{\bar{X}} = 0.783\), which is computed using \(\sigma_{\bar{x}} = \sigma/\sqrt(n)\). To compute the upper and lower control limits for the process, the following formulas are used: \[UCL = \mu+3\sigma_{\bar{X}}\], \[LCL = \mu-3\sigma_{\bar{X}}\] Therefore, the upper and lower control limits are \(UCL = 27.348\) and \(LCL = 22.652\) respectively.

Day 1

The above graph describes the process running for day one. The black vertical line indicates the hour in which the process should have been stopped, which is at hour nine. The reason for this is because at that hour, rule three of the Nelson Rules applies. Rule three states that a manufacturing process should be stopped if four out of five consecutive points lie on the same side of the center line and are above \(\mu + \sigma_{\bar{X}}\) or below \(\mu - \sigma_{\bar{X}}\)

Day 2

Similarly, the above graph describes the process running for day two. The black vertical line indicates the hour in which the process should have been stopped, which is at hour four. The reason for this is because at that hour, rule two of the Nelson Rules applies. Rule two states that a manufacturing process should be stopped if two out of three consecutive points lie on the same side of the center line and are above \(\mu + 2\sigma_{\bar{X}}\) or below \(\mu - 2\sigma_{\bar{X}}\)

Day 3

The graph above represents the manufacturing process for day three. The process stays in control throughout its 23 hour run time, and so it did not need to be halted. This is because no Nelson Rule could be applied at any point in the process.

Source

“STAT QC-0250.” Ximera, The Ohio State University, https://ximera.osu.edu/qcstats/QC_stats/STAT_QC-0250/main. Accessed 31 Oct. 2024.