| Course | MT475 Quality Management |
|---|---|
| Unit | Unit 5 |
| Paper type | Process capability study |
| Length | About 840 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 MT475 Unit 5
Stable but Off Center: An MT475 Unit 5 Process Capability Study of Welded Skylight Frame Widths
[Student Name]
Purdue University Global
MT475: Quality Management
Unit 5 Process Capability Study
[Instructor Name]
[Date]
Overlook Skylight Company, its welder and every measurement are composite; the sources cited are real.
The Process and the Specification
Overlook Skylight Company's frame welder joins four vinyl extrusions into a rectangular skylight frame. The outside width of the standard 27-inch frame must be 27.500 inches, plus or minus 0.0625 inches, so that the frame fits its curb and flashing kit. Frames outside the specification must be remade; oversize frames are the more common problem, and they also feed the wrong-size remakes counted in Unit 2.
The Data
Over five weeks, a quality technician measured five consecutive frames every two hours on the day shift, producing 25 subgroups of five, 125 frames in all.
Stability First
Capability indices describe what a predictable process will produce. If the process is not stable, the indices mean nothing, because tomorrow's process may not resemble today's. Shewhart (1931) built control charts on the idea that only a process in statistical control can be predicted, so stability is checked first with X-bar and R charts (Montgomery, 2020).
The grand mean of all 125 widths is 27.5187 inches and the average subgroup range is 0.0404 inches. Using the standard chart constants for subgroups of five, the X-bar chart's limits run from 27.4954 to 27.5420 inches, and the range chart's upper limit is 0.0853 inches, with a lower limit of zero. All 25 subgroup means and ranges fall inside their limits, with no runs or trends. The process is stable, so capability can be assessed.
Estimating Variation
Short-term variation is estimated from the subgroup ranges. For five frames per subgroup the conversion factor is 2.326, so the average range of 0.0404 inches implies a standard deviation of about 0.01737 inches.
The Indices
Cp compares the width of the specification with the spread of the process: the tolerance, 0.125 inches, divided by six standard deviations, 0.1042 inches, gives 1.20. A Cp above 1.0 means the process could fit inside the specification if it were centered.
Cpk accounts for where the process is centered. It takes whichever specification limit lies nearer the process mean and asks how many three-standard-deviation steps fit between them. The distance to the upper limit, 27.5625 minus 27.5187, is 0.0438 inches, giving 0.84. The distance to the lower limit gives 1.56. Cpk is therefore 0.84, limited by the upper side.
Pp and Ppk use the overall standard deviation of all 125 measurements, about 0.0183 inches, instead of the within-subgroup estimate. They come to 1.14 and 0.80. Their closeness to Cp and Cpk confirms the stability finding: little variation arises between subgroups.
The welder is capable of the tolerance; it is aimed about a fiftieth of an inch too wide.
The Predicted Defect Rate
Assuming widths are roughly normal, a normal-curve calculation predicts about 5,800 parts per million above the upper specification limit, and almost none below the lower. The plant welds about 320,000 frames a year, so the current setting would produce roughly 1,850 oversize frames a year.
What Re-Centering Would Do
If the welder were re-centered on 27.500 inches, the process spread would be unchanged and Cpk would equal Cp, 1.20. Predicted defects would fall to about 160 per million on each side, about 320 per million in total, roughly 100 frames a year. Re-centering means adjusting the welder's stop positions and checking the result, work the maintenance technician estimates at half a shift. Kane (1986) introduced the capability indices partly to show managers exactly this distinction, between a process that is too variable and one that is merely off target.
Why the Welder Drifted Wide
The maintenance log offers a likely reason for the off-center aim. Eight months ago the welder's clamping jaws were replaced, and the stop positions were set from the old jaws' marks rather than measured against a master frame. A difference of about two-hundredths of an inch is small enough that no one noticed it at the welder, but large enough to push the process toward the upper limit. The finding matters for the control plan: stop positions should be verified with a master frame after any maintenance on the jaws.
Recommendation
Re-center the welder on 27.500 inches before considering any new equipment. A tighter welder, quoted at about $140,000, would reduce spread, but spread is not the problem, and buying it first would leave the aim exactly where it is. After re-centering, take another 25 subgroups to confirm the new mean and recompute the indices. If Cpk then reaches about 1.20, the remaining question is whether 1.20 is enough; many customers ask for 1.33, which would require reducing spread by about 10 percent.
Limits
The study covers the day shift only; night-shift frames may differ. The normal-curve prediction assumes a shape the tails may not follow. And the measuring gauge itself has not been studied for repeatability, which a short gauge study should check.
References
Kane, V. E. (1986). Process capability indices. Journal of Quality Technology, 18(1), 41-52. https://doi.org/10.1080/00224065.1986.11978984
Montgomery, D. C. (2020). Introduction to statistical quality control (8th ed.). Wiley.
Shewhart, W. A. (1931). Economic control of quality of manufactured product. Van Nostrand.
MT475 Unit 5 instructions, in plain terms
MT475 Unit 5 asks for a capability study of a measured characteristic against its specification. Confirm stability first with X-bar and R charts or similar, because capability indices describe only a predictable process. Estimate short-term variation from subgroup ranges and calculate Cp and Cpk, explaining what each shows: Cp the spread against the tolerance, Cpk the spread and the centering together. Many instructors also want Pp and Ppk from the overall standard deviation, and a comparison with Cp and Cpk. Predict the defect rate and translate it into units per year. If Cp and Cpk differ, consider what re-centering alone would achieve before recommending new equipment. Look for a cause of any off-center aim. Close with limits, such as an unstudied gauge. About five pages covering stability, indices, predicted defects and a recommendation is typical for this study.
Inside the MT475 Unit 5 example
Overlook's study opens with the welder, the specification and why oversize frames matter. The data section describes 125 frames in 25 subgroups. Stability comes first with Shewhart's logic and Montgomery's charts, and all points fall within limits. Variation is estimated from the ranges. Cp, Cpk, Pp and Ppk are calculated and explained, under a highlighted line that the welder is capable but aimed too wide. The predicted defect rate becomes about 1,850 frames a year. A section shows re-centering would raise Cpk to 1.20, citing Kane on separating spread from aim. A maintenance log entry about replaced clamping jaws explains the drift. The recommendation re-centers the welder instead of buying a $140,000 machine, with a confirmation study, and the limits mention night shift and an unstudied gauge.
MT475 Unit 5 rubric: what earns full points
Capability studies are marked on sequence, calculation and interpretation. Instructors credit studies that establish stability before computing indices, since capability means nothing for an unstable process. Correct estimation of short-term variation and clear calculation of Cp and Cpk are expected. Explaining the difference between the two indices in plain terms, as spread versus aim, is a frequent marking point. Comparing Cp and Cpk with Pp and Ppk shows understanding of short-term and overall variation. Translating parts per million into units per year makes the finding meaningful to a manager. Recommending the cheaper fix when the problem is centering is often rewarded as practical judgment. Identifying a plausible cause of the drift adds value. Honest limits about gauges, shifts and normality show critical awareness.
MT475 Unit 5 help: mistakes that cost points
The commonest Unit 5 weakness is calculating Cp and Cpk without first checking stability. Another frequent problem reports Cp as if it described actual performance, ignoring that an off-center process produces defects even with a good Cp. Students often stop at the indices without predicting defects or converting them to units. Recommendations tend to call for new equipment when the data show re-centering would solve the problem. Gauges are rarely questioned, though measurement error can inflate variation. Before submitting, compare your Cp and Cpk. If they differ by more than a few hundredths, ask where the process is aimed and what moving it to the target would achieve. Then check whether your recommendation addresses spread or aim, and make sure it matches what the indices show.
Get an MT475 Unit 5 example written to your instructions
Send the measurements and subgroup structure from your Unit 5 prompt, the specification limits and the rubric. A composite study comes back that confirms stability first, computes Cp, Cpk and, where asked, Pp and Ppk by script, predicts the defect rate and recommends the fix the indices point to. The opening custom sample is free, 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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MT475 Unit 5 questions, answered
How do Cp and Cpk differ?
Cp compares the width of the specification to the spread of the process and ignores where the process is centered. Cpk uses the distance from the process mean to the nearer specification limit, so it falls when the process drifts off center. When Cp is acceptable and Cpk is not, re-centering is usually the cheaper fix.
What Cpk value counts as capable?
Many textbooks and customers use 1.33 as a common minimum, with higher targets such as 1.67 for critical characteristics, and 1.0 as the point where the process just fits. Your course's threshold and any figure named in the case take precedence. State the benchmark you are using, since capable has no meaning without one.
Can capability be calculated from individual measurements?
Yes, though the method changes. Without subgroups, within-process sigma is usually estimated from the average moving range divided by 1.128, and the data should first pass an individuals chart for stability. Your prompt's data structure decides the method, and saying which sigma estimate you used lets a grader check the calculation.
Where can I find a free MT475 Unit 5 sample paper?
This page prints the full MT475 Unit 5 capability study of 125 welded skylight frames, with stability charts, four indices and a re-centering recommendation.
What would re-centering achieve in the MT475 Unit 5 sample?
Cpk would rise from 0.84 to 1.20 and predicted defects would fall from about 5,800 to about 320 per million, roughly 1,850 frames a year down to about 100.