| Course | MT475 Quality Management |
|---|---|
| Unit | Unit 4 |
| Paper type | Control chart analysis |
| Length | About 910 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 4
One Spike, One Suspicious Run, a Stable Rate Beneath: An MT475 Unit 4 Control Chart Analysis of Skylight Water Tests
[Student Name]
Purdue University Global
MT475: Quality Management
Unit 4 Control Chart Analysis
[Instructor Name]
[Date]
Overlook Skylight Company, its test data and every figure are composite; the sources cited are real.
The Data
Every skylight Overlook Skylight Company builds is water-tested before packing: sprayed under pressure for five minutes while an inspector checks the interior for leaks. Each unit passes or fails. Over 25 production days, 15,857 skylights were tested and 309 failed, an overall proportion of 1.95 percent. Daily volume ranged from 590 to 672 units.
Choosing the Chart
The choice of chart comes before any limit. Each skylight passes or fails, so the data are attributes, not measurements. The number tested varies from day to day. A p chart, which plots the proportion failing each day, suits attribute data with varying sample sizes, and its control limits are recalculated for each day's volume, because a proportion from 590 units varies more than one from 672 (Montgomery, 2020).
The Limits
The center line is the overall proportion, 1.95 percent. Each day gets its own pair of limits, placed three standard errors on either side of 1.95 percent, and the standard error shrinks as volume grows, because it divides the proportion's variance by the number of skylights tested that day. At 640 units, a typical day, the limits fall near 0.31 percent and 3.59 percent. At 590 units they widen to about 0.24 and 3.66; at 672 they narrow to about 0.35 and 3.55.
Signal One: Day 11
Day 11 tested 630 skylights and 33 failed, 5.24 percent, well above that day's upper limit of about 3.60 percent. A point beyond its limit points to a special cause, something different about that day; Shewhart (1931) designed three-standard-error limits so that such points would rarely occur by chance alone. The inspector's notes show that most of the day's failures leaked at the glass edge, not at frame corners. The insulated glass units used that day came from a single lot from one supplier, Coyle Glass, and Unit 7 traces the problem to that lot's thin secondary seal.
Signal Two: Days 17 Through 24
Days 17 through 24 all plot below the center line, eight in a row, averaging about 1.2 percent. Every one of those points sits within its limits. Yet a streak of eight on the same side of the center is itself a standard warning, because chance alone rarely produces it, and it usually means something in the process has moved (Montgomery, 2020).
A run below the center line looks like good news. It was not. The maintenance log shows the water test booth's pressure regulator was replaced on day 16, and a check on day 25 found the new regulator delivering about 20 percent less pressure than specified. Fewer skylights failed because the test had become gentler, not because the skylights had improved. The regulator was reset, and the units tested on those days were flagged for a sample retest.
The best eight days on the chart were the days the test was too gentle to find leaks.
Revised Limits
With both special causes found and removed, the chart is recalculated from the sixteen days with neither signal: 10,137 skylights tested and 214 failures, a center line of about 2.11 percent. At 640 units the revised limits fall near 0.41 and 3.81 percent. All sixteen days plot inside them with no runs.
The Verdict
Once the two causes are removed, the process is stable at about 2.1 percent. Stable means predictable: the plant can expect roughly two skylights in a hundred to fail the water test on any ordinary day, and the scatter of daily points inside the limits comes from the way the skylights are built and tested, not from anything that happened on a particular day. Deming (1986) called reacting to ordinary variation tampering and showed that it usually makes a process worse, so the chart's first use is to stop chasing ordinary days.
Its second use is to show that the stable rate is too high. A 2.1 percent water-test failure rate means about 3,400 leaking skylights a year caught at the plant, and some share of leaks the test misses reach customers' roofs. Reducing a stable rate requires changing the process itself, not reacting to individual days. Unit 10 proposes such a change, aimed at frame corners, where most stable-period failures occur.
What the Supervisors Should Do Differently
The chart changes daily practice in two ways. First, supervisors should stop holding meetings about any day that plots inside the limits; a day at 2.9 percent is unpleasant but ordinary under the current process. Second, any point outside the limits, or any run of eight on one side, should trigger an investigation within a shift, starting with the glass lots, the test booth and any maintenance done that day. Both signals in this sample were found by asking what had changed, and both causes would have been missed by a team that discussed every bad day equally.
Limits
The analysis rests on inspectors' pass and fail judgments, which may vary between people; a short study of inspector agreement would strengthen it. The revised center line depends on correctly identifying the special-cause days, and a cause not yet found could still be hidden in the sixteen days.
References
Deming, W. E. (1986). Out of the crisis. MIT Press.
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.
The Purdue Global MT475 Unit 4 instructions
The Unit 4 task in MT475 asks you to build and interpret a control chart for a real or supplied process. Justify the choice of chart before computing anything: attribute or measurement data, constant or varying samples. Show how the center line and limits are calculated, recalculating limits where sample sizes vary. Plot the data and look for points beyond the limits and for runs or trends. Investigate each signal and say what caused it, including signals that look favorable. Once special causes are removed, recalculate the limits and judge whether the remaining process is stable. Distinguish a stable process from an acceptable one, since a predictable rate can still be too high. Recommend what supervisors should do differently. About five pages with a data table, the chart, the limit calculation and two pages of interpretation is typical for this assignment.
Inside the MT475 Unit 4 example
Overlook's analysis begins with the water test and its pass or fail data. A section justifies the p chart with variable limits, citing Montgomery. The limits are calculated at three daily volumes. Day 11's spike is investigated through the inspector's notes and tied to a single glass lot, with Shewhart on why points beyond the limits signal special causes. The run of eight below the center line follows, and the maintenance log reveals a weak pressure regulator, under a highlighted line that the best days were the least trustworthy. Revised limits are calculated from the sixteen clean days. The verdict separates stable from acceptable, citing Deming on tampering, and estimates about 3,400 leaking skylights caught a year. A section tells supervisors when to investigate and when to leave a day alone, and the limits note inspector agreement.
Where the points sit in the MT475 Unit 4 rubric
Control chart analyses are graded on correct method and careful interpretation. Instructors credit a justified choice of chart, especially when sample sizes vary. Limits calculated correctly and shown are expected. Investigating signals with evidence, rather than labeling them, earns analysis marks. Recognizing that a favorable-looking run can also signal a problem, such as a measurement change, is often rewarded as unusually perceptive. Recalculating limits after removing special causes shows understanding of how charts are maintained. Distinguishing stability from acceptability is a frequent marking point, since students often treat in control as good enough. Practical guidance for supervisors shows the student knows what the chart is for. A clear chart with labeled limits, center line and signals helps the grader.
MT475 Unit 4 help: mistakes that cost points
The most frequent Unit 4 weakness is using fixed limits when sample sizes vary, which misjudges small and large days. Another is calling every high day a problem, reacting to common-cause variation. Students often ignore runs because no single point is outside the limits. Favorable signals are rarely investigated, though they can hide measurement failures. Some papers conclude the process is fine because it is in control, missing that a stable rate can be too high. Before submitting, list every point outside the limits and every run of seven or eight on one side, and write what caused each. If you cannot find a cause, say so rather than guessing. Then state the stable rate in plain words and ask whether a customer would accept it.
Get an MT475 Unit 4 example written to your instructions
Supply the Unit 4 dataset, including daily counts and sample sizes, plus the chart type if your prompt names one and the rubric. The composite analysis returned justifies the chart, computes limits by script, traces every signal to an assignable cause, revises the limits and judges whether the stable level is good enough. First custom sample 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 4 questions, answered
When should an MT475 analysis use a p chart instead of a c chart?
A p chart tracks the proportion of units that are defective, where each unit either passes or fails, such as windows failing a water test. A c chart counts defects on a unit or area of constant size, where one item can carry several flaws, such as blemishes per door. If the inspected area or quantity varies, a u chart replaces the c chart.
Why do the limits on a p chart change from day to day?
Because the standard error of a proportion depends on sample size. Days with more units inspected have tighter limits, and days with fewer have wider ones. Some textbooks allow a single set of limits based on average sample size when volumes differ little, but calculating each day's limits is more accurate and often expected in your course.
Is a run below the center line a good sign?
It is a signal that something changed, and the change needs explaining before anyone celebrates. It may be a real improvement, or it may be a measurement change: a new inspector, a shorter test, a gauge drifting. Most rules flag a run of seven to nine points on one side, depending on the textbook's version.
Where can I find a free MT475 Unit 4 sample paper?
The whole MT475 Unit 4 analysis is on this page, building a p chart of 25 days of skylight water tests and investigating two signals.
Why is the run below the center line a problem in the MT475 Unit 4 sample?
A replacement pressure regulator made the water test gentler, so fewer skylights failed because the test found fewer leaks, not because the skylights improved.