Black Belt · Control phase
Lesson 5 covered a Shewhart chart's anatomy: rational subgroups, sampling frequency, and the arithmetic behind a center line and control limits. This lesson asks the harder Black Belt question sitting on top of that arithmetic: once a project has closed, which chart should the process owner actually run, and what happens after it signals? Choosing a chart is a decision about which size of shift matters and how fast you need to know about it. Then, whatever chart is running, someone has to decide what an out-of-control signal means, weigh the cost of chasing false alarms against the cost of missing a real shift, and hand the process owner a control plan that survives the Black Belt's departure.
A standard Shewhart chart, whether an I-MR, Xbar-R, or attribute chart, judges each plotted point almost entirely on its own; a point only signals when it individually lands beyond the 3σ limits (or trips a run rule across a handful of neighboring points). That design makes Shewhart charts excellent at catching a single large, sudden shift, such as a jammed fastener gun putting an entire batch of trusses out of tolerance at once. It makes them slow, sometimes very slow, at catching a small, sustained shift, such as a rehab crew's average punch-list close-out time drifting from 4.0 to 4.5 days and staying there. A shift of half a sigma takes, on average, about 33 subgroups (Xbar chart, n = 5) or about 155 points (individuals chart) to trip a 3σ limit, even though the process has genuinely moved and the cumulative cost of that drift is real. CuSum and EWMA charts exist specifically to close that gap: both use the history of recent points, not just the latest one, and both detect a small sustained shift far faster than a Shewhart chart while remaining nearly as resistant to false alarms on a stable process.
The cumulative sum (CuSum) chart plots the running total of each point's deviation from a target value, so a process sitting exactly on target produces a cumulative sum that wanders near zero, while a process that has shifted produces a sum with a steady upward or downward slope that keeps growing point after point. The most common implementation, the tabular CuSum, accumulates two one-sided sums, one tracking upward drift and one downward, and resets each to zero whenever it goes negative. Two parameters control it: the reference value K, which is subtracted from each deviation before it is accumulated and effectively sets the size of shift the chart tolerates before it starts accumulating, and the decision interval H, the threshold the accumulated sum must cross to signal. A commonly used starting point is K set to half a sigma (0.5σ) and H set to four or five sigma (4σ to 5σ), which is tuned to detect a sustained shift of roughly one sigma quickly while keeping the false-alarm rate low on a stable process.
The exponentially weighted moving average (EWMA) chart plots a smoothed statistic that is a weighted combination of the current point and every prior EWMA value, so each new point pulls the statistic partway toward itself while older points continue to matter, just less and less as they recede into the past. The weighting parameter, lambda (λ), sets how much of that pull the newest point gets: a smaller lambda leans more heavily on history, smooths harder, and is more sensitive to a small, sustained shift, while a larger lambda leans more on the latest point and behaves more like an ordinary Shewhart chart, reacting faster to a large, sudden shift but slower to a small one. A commonly cited working range for lambda is roughly 0.05 to 0.25, with the EWMA chart's own control limits narrowing as lambda gets smaller. Because EWMA and CuSum both trade some large-shift sensitivity for small-shift sensitivity, many mature SPC programs run a Shewhart chart and an EWMA or CuSum chart on the same characteristic side by side, one tuned for catching a sudden break, the other for catching a slow drift.
Why this matters
Exam scenario questions in this area almost always describe the size and speed of a shift and ask which chart is appropriate. A large, abrupt shift points to a Shewhart chart; a small, sustained shift points to CuSum or EWMA. Getting that classification right is worth more than memorizing any single constant.
A permit-review process has a target turnaround of 10.0 days with a process sigma of 2.0 days. Using K = 0.5σ = 1.0 day and H = 5σ = 10.0 days, the upper one-sided sum accumulates as SH(i) = max(0, SH(i-1) + (x(i) - target - K)). Five consecutive weekly average turnarounds come in at 11.5, 12.0, 11.0, 12.5, and 13.0 days:
After week 5 the sum reaches 5.0, still below the decision interval H = 10.0, but the steady week-over-week climb already shows an upward shift building, well before any single week's average would come close to an ordinary 3σ Shewhart limit of 16.0 days.
A Shewhart chart is not limited to the single rule "one point beyond 3σ." The Western Electric rules, developed to make a control chart more sensitive without abandoning it for a CuSum or EWMA chart, add a set of pattern-based signals, each checked against zones drawn at 1σ, 2σ, and 3σ from the center line:
Lloyd Nelson later extended this same zone logic into eight rules, covering additional patterns such as a steady trend of consecutive rising or falling points, points alternating up and down, and points clustering too close to (or oscillating too far from) the center line, all evidence that something nonrandom is driving the process even when no single point crosses 3σ.
Every one of these rules trades sensitivity for false-alarm risk. Adding more run rules to a chart, or shrinking a CuSum's H or an EWMA's lambda, catches a real shift sooner, but it also raises the rate at which a perfectly stable process trips a false signal, sending someone to investigate a cause that was never there. Running many rules simultaneously compounds this: a chart checked against all eight Nelson rules at once will false-alarm noticeably more often than one checked against Rule 1 alone, simply because more independent chances to trigger exist. The Black Belt's job in designing a control strategy is to pick the combination of chart type, control limits, and run rules that matches the cost of a missed shift against the cost of chasing a false alarm for that specific characteristic, not to maximize sensitivity everywhere by default.
Detecting a problem with a control chart is never the strongest available control. In descending order of reliability, the control methods hierarchy generally runs: eliminate the opportunity for the defect entirely (change the process so the error cannot physically occur); mistake-proof it (Poka-Yoke, a physical or procedural device that prevents or immediately catches the error at the source); automate the detection and reaction; use a control chart or other statistical monitoring; and, weakest of all, rely on manual inspection or an operator's checklist after the fact. A Black Belt closing out a project performs a cost-benefit analysis across this hierarchy for each CTQ: mistake-proofing a permit-application intake form so a missing signature cannot be submitted costs more to build once but removes the defect at its source, while a control chart on rejection rates is cheaper to stand up but only ever detects a problem after some defects have already occurred and must be caught and corrected downstream.
A finished control plan is a document, not an intention, and a Black Belt is expected to be able to name every column a mature one contains: the process step being controlled; the CTQ characteristic being protected; its specification or target; the measurement method used to check it; the sample size and sampling frequency; the control method itself (a mistake-proofing device, a control chart, or an inspection); the reaction plan, spelling out exactly what an operator or process owner does the moment the control signals, such as who to notify, whether to stop the process, and how the affected output is contained; and the named owner responsible for keeping the plan alive. A control plan with no reaction plan is close to useless: a chart that signals but triggers no defined response is just a decoration, and a chart with a strong reaction plan but a poorly chosen control method will either miss real shifts or drown the process owner in false alarms.
| Column | Example entry (rehab punch-list close-out) |
|---|---|
| Process step | Final walkthrough sign-off |
| CTQ | Days from repair complete to close-out sign-off |
| Specification | ≤ 5 business days |
| Measurement method | Timestamp difference in the work-order system |
| Sample size / frequency | All closed work orders, reviewed weekly |
| Control method | EWMA chart, λ = 0.2, plus a mandatory checklist field |
| Reaction plan | Supervisor contacts crew lead within 1 business day of a signal; hold new assignments until root cause identified |
| Owner | Field Operations Supervisor |
A control plan only works once the process owner, not the Black Belt, is the one running it day to day. That means the handoff has to include more than the document: the process owner needs to understand why each control method was chosen, has to be trained to execute the reaction plan without calling the Black Belt every time, and has to have the authority and resources the reaction plan assumes, such as the ability to actually stop a defective batch. A project is not closed, by the standard set in Yellow Belt Lesson 1, until this transfer has happened and the gain has been shown to hold under the process owner's ongoing management, not just under the project team's close attention during the improve phase.
1. Why is an ordinary Shewhart chart comparatively slow to detect a small, sustained shift?
2. Which characteristic of a shift should push a Black Belt toward a CuSum or EWMA chart instead of a plain Shewhart chart?
3. In a tabular CuSum chart, what does the reference value K control?
4. What does the decision interval H represent in a CuSum chart?
5. A permit turnaround process has a target of 10.0 days, sigma of 2.0 days, K = 1.0 day, and H = 10.0 days. Over four weeks the upper CuSum reaches 0.5, 1.5, 4.0, and then 9.0. If the fifth week's average turnaround is 13.0 days, what is the new cumulative sum, and does it signal?
6. In an EWMA chart, what does a smaller value of the weighting parameter lambda (λ) do?
7. What is a commonly cited working range for the EWMA weighting parameter lambda?
8. Using this lesson's numbering, which Western Electric rule is violated by two out of three consecutive points falling beyond 2σ on the same side of the center line?
9. Eight consecutive points fall on the same side of the center line, all well within 1σ. Does this violate a Western Electric rule?
10. How do the Nelson rules relate to the Western Electric rules?
11. What is the main tradeoff of adding more run rules, or shrinking a CuSum's H or an EWMA's lambda, to increase sensitivity?
12. In the control methods hierarchy, why is mistake-proofing (Poka-Yoke) generally preferred over a control chart?
13. Which element of a control plan specifies exactly what an operator does the moment a control signals?
14. By this course's standard, when is a Six Sigma project's control plan actually complete?