| Course | MT435 Operations Management |
|---|---|
| Unit | Unit 8 |
| Paper type | Control chart analysis |
| Length | About 930 words, 6 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | BS in Business Administration |
| Updated | October 2026 |
Free sample paper for MT435 Unit 8
A New Spray Tip Moved the Mean: An MT435 Unit 8 Control Chart Analysis of Topcoat Thickness
[Student Name]
Purdue University Global
MT435: Operations Management
Unit 8 Control Chart Analysis
[Instructor Name]
[Date]
Pacolet Bunk & Loft's readings are composite, built for the exercise; control chart constants are the standard values for subgroups of five, and the sources cited are real.
The Data
Each working day for five weeks, the booth operator measured dry-film thickness, in mils, at five marked points on a sample bed rail taken from the day's production. The finish specification is 3.0 to 5.0 mils. The 25 subgroups' means and ranges are listed below.
1. Days 1 to 8: means 4.02, 4.08, 3.98, 4.11, 4.05, 3.96, 4.09, 4.03; ranges 0.41, 0.52, 0.38, 0.47, 0.55, 0.43, 0.49, 0.36
2. Day 9: mean 4.06, range 1.25
3. Days 10 to 16: means 4.07, 4.00, 4.12, 3.99, 4.06, 4.04, 4.05; ranges 0.51, 0.44, 0.48, 0.40, 0.53, 0.46, 0.47
4. Days 17 to 25: means 4.24, 4.31, 4.49, 4.26, 4.33, 4.22, 4.30, 4.29, 4.47; ranges 0.58, 0.66, 0.71, 0.55, 0.62, 0.69, 0.57, 0.60, 0.68
Trial Limits
Across all 25 subgroups, the grand mean is 4.145 mils and the average range 0.552 mils. For subgroups of five, the standard constants are 0.577 for the mean chart and 0 and 2.114 for the range chart (Montgomery, 2020). The mean chart's limits are therefore 4.145 plus or minus 0.577 times 0.552: a lower limit of 3.826 and an upper limit of 4.464. For ranges, the upper limit is 1.168 mils, which is 2.114 multiplied by 0.552, and its lower limit is zero.
Reading the Range Chart First
Ranges come first here because the width of the mean chart's band is computed from the average range; if the ranges themselves are unstable, that band is too.
One range exceeds its limit. Day 9's range of 1.25 mils is above 1.168. The operator's log for that day records a partly clogged gun tip, cleared mid-shift; one reading was thin and another thick. That is an assignable cause.
Reading the Mean Chart
Two means exceed the upper limit: day 19 at 4.49 and day 25 at 4.47. More telling is the pattern from day 17 on. Every one of the nine means from day 17 to day 25 sits above the center line of 4.145, a run that random variation would rarely produce. If only chance were at work, nine consecutive means landing on the same side of the center would happen roughly once in 256 such stretches.
The maintenance log explains it. On day 17, the booth's worn spray tips were replaced with a larger tip size the supplier recommended for faster coverage. The larger tip lays down more coating per pass, and the operator did not adjust the gun's speed or the number of passes. The mean shifted up by about 0.28 mils.
The single high days on 19 and 25 were not the problem; they were the visible edge of a shift that began on day 17.
Revised Limits
Limits meant to judge future production should be built from a period when the process was in control. Removing day 9, which had an assignable cause, and days 17 to 25, which reflect a changed process, leaves fifteen clean early subgroups. Their mean is 4.043 mils and average range 0.460. Revised mean limits are 3.778 and 4.309, and the revised upper range limit is 0.972. Against these tighter limits, four of the nine subgroups from day 17 on exceed the upper limit and all nine sit well above the revised center line of 4.043, which confirms that the tip change created a new process.
Capability
Control and capability answer different questions, a distinction Slack and Brandon-Jones (2019) stress when they introduce process control: control asks whether the process is stable, capability whether a stable process meets the specification. The process standard deviation is estimated from the clean average range divided by 2.326, the constant for subgroups of five, about 0.198 mils.
Before the tip change, with a mean of 4.043, the process sat close to the middle of the 3.0 to 5.0 specification. Its Cpk, which compares the gap between the mean and whichever specification limit is closer with three standard deviations, was about 1.61, comfortably capable. After the change, with the mean near 4.323, the distance to the upper limit shrank to about 0.68 mils and Cpk fell to about 1.14. The process still meets the specification, but with far less margin, and the thicker coat uses more material and takes longer to cure.
Why Not Simply Adjust When a Point Is High
It is tempting to respond to each high reading by turning down the coating flow. That would have been the wrong response on days 1 to 16, when the process was stable and highs and lows were common-cause variation; adjusting for them would have added variation rather than removed it. It would also have missed the cause after day 17, a single change of tip size, which a chart reveals and day-by-day tinkering hides.
What the Analysis Recommends
The booth should either return to the previous tip size or reduce passes with the new tip until the mean returns to about 4.0 mils, then chart for another two weeks to confirm. The tip change should be added to the booth's change log as a process change that requires new control limits. Shewhart (1931) introduced the distinction this analysis turns on, between common-cause variation a process always shows and assignable causes that should be found and removed.
References
Montgomery, D. C. (2020). Introduction to statistical quality control (8th ed.). Wiley.
Shewhart, W. A. (1931). Economic control of quality of manufactured product. D. Van Nostrand.
Slack, N., & Brandon-Jones, A. (2019). Operations management (9th ed.). Pearson.
What the MT435 Unit 8 assignment asks for
The eighth unit asks students to build and interpret control charts for a process measurement. Instructors expect the data organized in subgroups, trial limits computed with the correct constants for the subgroup size and the range chart read before the mean chart, since the mean limits depend on the average range. Signals should be identified by the standard rules, points outside limits and runs on one side of center, and each traced to an assignable cause where the records allow. Revised limits should be built from subgroups free of assignable causes. Capability should be assessed separately from control, with Cpk against the specification. Interpretation counts more than arithmetic, and the paper should end with a corrective action and a plan to confirm it.
Inside the MT435 Unit 8 example
In this sample the data appear as subgroup means and ranges, with the specification. Trial limits are computed with the constants for subgroups of five. The range chart is read first and its one signal traced to the operator's log. The mean chart's two high points and nine-point run are read together and traced to a tip change in the maintenance log, under a highlighted line that the run, not the outliers, was the problem. Revised limits are built from fifteen clean subgroups. A capability section, citing Slack and Brandon-Jones, separates capability from control and computes Cpk before and after. A section explains why adjusting for single high points would have been wrong, and the recommendation, citing Shewhart, sets a correction and a confirming run.
Reading the MT435 Unit 8 grading rubric
Interpretation tends to outweigh arithmetic when control chart papers are graded, though wrong constants spoil both. Reading the mean chart before the range chart is a common slip, since mean limits rest on average range. Instructors watch for signals traced to causes rather than simply flagged. Rubrics reward recognizing a run on one side of center, not only points outside limits. Credit goes to revising limits from clean data and saying why. Keeping capability separate from control, and computing it correctly, shows understanding. A corrective action tied to the cause, with a plan to confirm it, completes the analysis. A data table, two labeled charts and a limits calculation that a grader can retrace support the interpretation.
MT435 Unit 8 help: mistakes that cost points
The most frequent weak control chart analysis computes limits correctly and then lists the points outside them with no explanation of cause. Another common error reads the mean chart first and ignores an unstable range. Students often use constants for the wrong subgroup size. Runs are frequently missed because no single point crosses a limit. Many papers revise limits by dropping only the points outside them, keeping a shifted period in the baseline. Capability is sometimes confused with control. Before submitting, check whether any stretch of seven or more means sits on one side of your center line. If one does, look for what changed when it began, because that change is usually the finding.
Get an MT435 Unit 8 example written to your instructions
Measurements from your Unit 8 data set, the subgroup size and any specification limits are the inputs, together with your instructions and rubric. The composite analysis sent back computes trial and revised limits, reads the range chart first, ties each signal to a cause and keeps capability separate. Free first custom sample in 24-48h. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
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MT435 Unit 8 questions, answered
Which control chart suits measurement data?
For measurements collected in small subgroups, usually two to ten readings, X-bar and R charts are the common choice in MT435. Larger subgroups often use X-bar and S charts, and single readings use an individuals chart. Your data set's structure normally decides it, and the prompt may name the chart. State the subgroup size, since the constants depend on it.
What counts as an out-of-control signal besides a point beyond a control limit?
Most courses teach a few run rules, such as a long run of points on one side of the center line, or a steady trend up or down. Your textbook's version of the rules applies. Patterns like these indicate a shift that single points may not reveal, and many assignments are built to see whether students notice them.
Should limits be recalculated after finding a problem?
Usually yes, once the cause is identified and removed. Drop the affected subgroups, recompute the centerline and both limits from what remains, and use the revised chart going forward. Explain which subgroups were removed and why. Recalculating without a known cause can hide real variation, so the reason matters as much as the arithmetic.
Where can I find a free MT435 Unit 8 sample paper?
You can read the complete MT435 Unit 8 analysis here, charting 125 topcoat thickness readings and tracing three signals to their causes.
What caused the shift in the MT435 Unit 8 sample?
A larger spray tip installed on day 17 laid down more coating per pass, moving the mean up about 0.28 mils and cutting Cpk from 1.61 to 1.14.