The report that I will be testing is a manufacturing test run based on diffrent control charts. The three diffrent data sets that will be used for the test run is sample1, sample2, and sample3. each set is made for a whole 23 hours and each hour will be tested i will examine at what hour the process should be halted. the population that is being used is 25 and a population standered devation of 1.75 along with the sample size which will be at 5. using the charts given is how I will decide what hour it should be halted.

\[\sigma_{\bar{x}}=1.75\]

Day one violates Nelson rule three which says “Rule three: Four out of five consecutive points are on the same side of the center line and above μ+σX¯ or below μ−σX¯” which you can see happen starting at hour six through hour ten where four of five dots are out of the zone.

Chart two violates rule five due to the six consecutive points that are ascending starting at hour thirteen and finishing at hour eighteen. this should be halted at hour eighteen when things get out of control rule five of nelsons rule claims “Rule five: Six consecutive points are ascending/decending.” which can be seen in this graph

This graph should not be halted it is in control it does not violate any of the nelson rules. if it does not violate any of the rules it is deemed in control and should keep processing

                                    Work Cited

Project, The Ximera. “An Application of X-Bar Charts to Manufacturing.” Ximera, ximera.osu.edu/qcstats/QC_stats/STAT_QC-0250/main. Accessed 20 Nov. 2025.