| Course | BU 421 Operations Management |
|---|---|
| Unit | Unit 7 |
| Paper type | Quality control chart record |
| Length | About 1,050 words, 6 pages |
| Format | APA 7 student paper |
| School | Herzing University |
| Program | BS in Business Management |
| Updated | September 2026 |
Free sample paper for BU 421 Unit 7
The Chart Caught It Five Hours Early: An Averages and Range Chart Record for Door Width at a Composite Cabinet Plant, With Limits Set From the Process
Student Name
Business, Herzing University
BU 421: Operations Management
Instructor Name
April 8, 2026
The Chart Caught It Five Hours Early: An Averages and Range Chart Record for Door Width at a Composite Cabinet Plant, With Limits Set From the Process
What Was Measured and How
This record charts the finished width of one door size, a 15-inch shaker door with a nominal width of 14.875 inches, at the door line of Tallgrass Cabinet Works, the composite Nebraska cabinet shop that runs through every unit of this course. Door width matters because two doors meeting over a cabinet opening must leave an even gap; a door a few thousandths too wide rubs its neighbor, and one too narrow leaves a visible gap. The design allows plus or minus 0.015 inches.
Every hour, an inspector took five consecutive doors from the wide-belt sander and measured each with a digital caliper to the nearest thousandth of an inch. The table records each reading as its deviation from 14.875 inches in thousandths, so a reading of 4 means 14.879 inches. Twenty subgroups were collected over 20 production hours, from the start of first shift on a Monday through the end of first shift on Tuesday. The subgroup size of five and the hourly interval were chosen together: five doors made in a row show the short-term spread, and an hour between samples is short enough to catch a shift before a full cart of doors is affected. The readings belong to the composite case.
| Subgroup | Readings (thousandths of an inch from nominal) | Average | Range |
|---|---|---|---|
| 1 | -2, -3, 2, -3, -3 | -1.8 | 5 |
| 2 | 0, 2, -3, -2, -2 | -1.0 | 5 |
| 3 | 5, 5, 5, 1, -4 | 2.4 | 9 |
| 4 | -4, -3, -1, -2, 4 | -1.2 | 8 |
| 5 | 3, 0, 1, -1, -6 | -0.6 | 9 |
| 6 | 0, -2, -1, -1, 3 | -0.2 | 5 |
| 7 | -2, 0, -5, 1, -2 | -1.6 | 6 |
| 8 | -3, 2, 1, 1, 2 | 0.6 | 5 |
| 9 | 4, 8, -1, 6, -4 | 2.6 | 12 |
| 10 | -2, -5, 1, -3, -1 | -2.0 | 6 |
| 11 | 3, 2, 0, 3, 3 | 2.2 | 3 |
| 12 | 4, 7, -6, 1, 0 | 1.2 | 13 |
| 13 | -5, -2, 0, 3, 6 | 0.4 | 11 |
| 14 | 4, 1, 3, 4, 4 | 3.2 | 3 |
| 15 | 4, 7, 5, 4, 1 | 4.2 | 6 |
| 16 | 6, 5, 3, 5, 1 | 4.0 | 5 |
| 17 | 3, 1, -2, 2, 1 | 1.0 | 5 |
| 18 | 4, 5, -1, 3, 5 | 3.2 | 6 |
| 19 | 8, 3, 2, 2, 4 | 3.8 | 6 |
| 20 | 7, 3, 9, 3, 2 | 4.8 | 7 |
Why an Averages Chart and a Range Chart
Door width is a measurement on a continuous scale, not a count of defects, so it calls for a variables chart rather than an attribute chart such as a p chart. With subgroups of five, the standard pair is a chart of subgroup averages, which watches the process center, and a chart of subgroup ranges, which watches its spread. Montgomery (2019) recommends the range for subgroups smaller than about ten, where it estimates spread nearly as well as the standard deviation and is easier to compute on the floor. Because the averages chart's limits are built from the average range, the range chart must be shown stable first; limits built on an unstable spread would mean nothing.
The Range Chart
Control limits were calculated from the first 13 subgroups, the hours before any change was suspected, and then used to judge every subgroup. The average range over those 13 subgroups is 7.46 thousandths. For subgroups of five, the constants are D3 equal to 0 and D4 equal to 2.114, so the lower limit is 0 and the upper limit is 2.114 times 7.46, or 15.77 thousandths. Plotted, all 20 ranges fall between 3 and 13, inside the limits, with no runs or trends. The spread of the process is stable, which permits the averages chart to be built on it.
The Averages Chart
The grand average of the first 13 subgroups is 0.08 thousandths, the chart's center line. The constant A2 for subgroups of five is 0.577, so the limits sit 0.577 times 7.46, or 4.30 thousandths, either side of the center: an upper limit of 4.38 and a lower limit of negative 4.23. One standard error of the average is a third of that distance, 1.43 thousandths, which places the one-sigma lines at 1.51 and negative 1.36 and the two-sigma lines at 2.95 and negative 2.79.
Plotted, subgroups 1 through 13 vary around the center line with no point beyond two sigma on the same side as another nearby point. From subgroup 14 onward the points sit higher: 3.2, 4.2, 4.0, 1.0, 3.2, 3.8 and 4.8. The last of these, subgroup 20, falls above the upper limit.
Limits were deliberately not calculated from all 20 subgroups. Had they been, the higher readings after hour 13 would have pulled the center line up to 1.26 and the upper limit to 5.15, and subgroup 20 would no longer have crossed it. Shewhart (1931) set limits from the process in a period of control for exactly this reason: a chart whose limits absorb a shift cannot detect it.
Reading the Pattern
The rules were applied in order, following the Western Electric Company (1956) handbook. Rule 1, a single point beyond a control limit, first fires at subgroup 20. Rule 2, two of three consecutive points beyond two sigma on the same side, fires earlier, at subgroup 15, since subgroups 14 and 15 both sit above 2.95. Rule 3, four of five consecutive points beyond one sigma on the same side, fires at subgroup 18. And subgroups 14 through 20 form a run of seven points above the center line. Every rule points the same way: the process center moved up by about 3.4 thousandths at the start of Tuesday's shift and stayed there.
The first signal came at hour 15, five hours before any point crossed a limit. Treated as a signal to investigate, it led the line lead to the crosscut saw that sizes door rails. The saw blade had been changed at the start of Tuesday's shift, and the stop block that sets rail length had been bumped about four thousandths of an inch in the process, making every door slightly wider. The stop was reset, and a stop-block check was added to the blade-change procedure. Subgroups 14 through 20 are excluded from any future recalculation of limits, since their cause is known and has been removed.
Why the Specification Stays Off the Chart
Not one door in the record fell outside the plus or minus 15 thousandths the design allows; the widest reading was 9. A chart with the specification drawn on it would have shown nothing wrong. The process spread, estimated as the average range divided by the constant d2 of 2.326, is about 3.21 thousandths. Before the shift, the capability index Cpk was about 1.55. After it, with the center at about 3.5 thousandths, Cpk fell to about 1.20, still acceptable but with much less margin. Control limits describe what the process does; specification limits describe what the customer needs. Keeping them apart let the plant correct a real change while every door was still good, which is the purpose of the chart. Heizer et al. (2020) make the same distinction between a process in control and a product within tolerance. Tallgrass Cabinet Works, its door line and every reading are composites created for this course.
References
Heizer, J., Render, B., & Munson, C. (2020). Operations management: Sustainability and supply chain management (13th ed.). Pearson.
Montgomery, D. C. (2019). Introduction to statistical quality control (8th ed.). Wiley.
Shewhart, W. A. (1931). Economic control of quality of manufactured product. D. Van Nostrand.
Western Electric Company. (1956). Statistical quality control handbook. Western Electric.
What the BU 421 Unit 7 instructions ask for
The seventh unit of BU 421 asks students to build and interpret control charts for a measured quality characteristic. Standard requirements include describing the process and the measurement, choosing a subgroup size and sampling frequency, calculating center lines and control limits for an averages chart and a range chart, plotting the data and interpreting any signals. Many versions add capability indices or a question about the difference between control limits and specification limits. Some supply the data; others ask students to create a realistic data set and explain it. Expect three to five pages with tables or charts in APA 7. The interpretation matters as much as the arithmetic, since a chart only helps when someone acts correctly on what it shows.
Inside the BU 421 Unit 7 example
The record opens with what was measured, how often and by whom, with 20 subgroups of five doors in a table. It explains why the averages chart is paired with a range chart and why the range chart is read first. The range chart section computes its center line and limits with the constants D3 and D4 named, and the averages chart then uses the average range and A2. A pattern section applies the run rules in order, finds the first signal at hour 15, and follows it to a saw stop bumped during a blade change. The corrected subgroups are handled openly. The final section explains why the specification is kept off the chart and estimates capability before and after the shift, showing a real change while every door remained within tolerance.
Reading the BU 421 Unit 7 rubric
Control chart rubrics at Herzing tend to give points for data and sampling design, correct limit calculations, interpretation of signals, corrective action, and presentation with APA sources. Sampling design earns credit when the subgroup size and frequency are justified. The calculation criterion expects constants named and applied to the right chart, since a range chart limit built with A2 is a sign of confusion. Interpretation scores highest when run rules, not just points outside limits, are used and the earliest signal is found. Corrective action earns full marks when a cause is traced and the process is documented after the fix. Many rubrics also reward a clear statement of why control limits differ from specification limits, a distinction the strongest papers make in their own words.
BU 421 Unit 7 help: mistakes that cost points
One of the most frequent errors on the control chart unit is drawing the specification limits on the chart as if they were control limits, which hides real process changes. Another is reading the averages chart before confirming that the range chart is stable. Students also recompute limits after every point, which lets a drifting process move its own limits. Some papers look only for points outside the limits and miss the runs and trends that signal a change earlier. Others spot a signal but never say what caused it or what was done. Finally, removing out-of-control subgroups without explanation looks like hiding data; the sample states which were excluded, why, and what the limits became after the cause was fixed.
Get a BU 421 Unit 7 example written to your instructions
Attach the Unit 7 instructions and rubric from your BU 421 classroom along with the subgroup data the assignment provides. We write a custom example that justifies the chart pair, reads the range chart first, names every constant, applies the run rules in order and separates control from specification. First custom sample free, back in 24 to 48 hours.
More BU 421 papers and business management samples
- BU 421 Unit 1: Competitive priorities brief
- BU 421 Unit 2: Process flow documentation
- BU 421 Unit 3: Capacity planning worksheet
- BU 421 Unit 4: Demand planning record
- BU 421 Unit 5: Inventory policy write-up
- BU 421 Unit 6: Waste reduction proposal
- BU 421 Unit 8: Supply chain scheduling file
- BU 380 Unit 7: Governance and obligations memo
- BU 106 Unit 7: Business ethics case
- BU 217 Unit 7: Real case analysis
- BU 231 Unit 7: Risk and mitigation paper
BU 421 Unit 7 questions, answered
Why should specification limits stay off the chart?
Because they answer a different question. Control limits describe what the process does, computed from its own variation, while specification limits describe what the customer will accept. Putting both on one chart invites the conclusion that a process is fine because it happens to sit inside the tolerance, which says nothing about whether it is stable or predictable.
What subgroup size should the record use?
Whatever the data or the instructions supply, stated plainly. Small subgroups taken often detect a shift sooner, larger ones give a more stable estimate of spread. What matters for the write-up is that the size is constant across the chart, since the constants used in the limit formulas depend on it and mixing sizes breaks every bound.
What do I do with a point outside the limits?
Investigate it in the write-up rather than deleting it. Name plausible special causes for the composite process, say what evidence would separate them, and state what would justify removing the point and recomputing the limits. A record that keeps an awkward point and reasons about it reads far better than one whose chart is suspiciously tidy.
Where can I find a free BU 421 Unit 7 sample paper?
The BU 421 Unit 7 quality control chart record above is free to read in full, with both charts' calculations, the run rule analysis and margin notes. If your data or quality characteristic are different, we prepare a free custom chart record around them, typically within 48 hours.
What subgroup size works for BU 421 Unit 7?
Five is common because the range chart constants are well established for it and small subgroups keep sampling quick. The sample uses subgroups of five doors taken each hour, and states that choice with its reason at the start of the record.