Control Charts

01 · What a control chart can establish

What a control chart can establish

A control chart plots an appropriate process statistic in time order against a centre line and control limits derived from a reference process. It helps distinguish routine, common-cause variation from patterns unlikely under that reference. In Measure, use it to examine baseline behaviour and decide whether pooling the data is defensible. In Control, use an established reference to detect departures after the improved process has been demonstrated. The same chart family can support both activities, but estimating a baseline and monitoring against one are different tasks.

A signal asks for investigation; it does not identify the cause. A point inside the limits does not certify that an individual order meets customer requirements. Control limits describe expected process variation under stated assumptions. Specification limits describe what the customer or governing requirement permits. A stable process may consistently produce unacceptable outcomes, and a process with excellent average performance may still be unstable. Stability and suitability therefore require separate judgements.

02 · Choose the statistic and sampling logic

Choose the statistic and sampling logic

Choose the chart from the data-generating process rather than the shape of a convenient spreadsheet. For continuous observations collected singly, consider an individuals and moving-range chart after checking measurement quality, distribution and serial dependence. For small rational subgroups of continuous measurements, consider paired mean and range charts; for larger subgroups, mean and standard-deviation charts may be appropriate. Monitor spread as well as location.

For binary classification of units, a p chart monitors the fraction nonconforming and accommodates varying sample sizes with corresponding limits. An np chart monitors the number nonconforming when sample size is constant. For counts of nonconformities, a c chart assumes constant inspection opportunity; a u chart uses an exposure denominator that can vary. One parcel can have several label defects, but it can be classified as a single nonconforming parcel. These are different outcomes and require different counting logic.

Define sampling frequency, subgroup boundaries and exclusions in advance. Group observations representing comparable short-term conditions when using rational subgroups. Mixing several carrier services with different risks can create extra variation that a simple chart model does not explain. Conversely, averaging away each shift’s problems can hide important signals. Preserve enough context to investigate without retrospectively selecting only favourable observations.

03 · Worked example: calculate a p-chart baseline

Worked example: calculate a p-chart baseline

Fictional Northbank checks 100 randomly selected dispatches on each of 25 comparable operating days. A dispatch is nonconforming if its released carrier service differs from the authorised service. Inspectors apply the same definition and independently verify the release records. Across the 2,500 checked dispatches, 250 are nonconforming. The pooled estimate is p-bar = total nonconforming / total inspected = 250 / 2,500 = 0.10. For unequal samples, use this pooled calculation rather than an unweighted average of daily percentages.

For n = 100, the estimated standard error is square root of [0.10 × 0.90 / 100] = 0.03. Three-sigma limits are therefore UCL = 0.10 + 3 × 0.03 = 0.19 and LCL = 0.10 − 3 × 0.03 = 0.01. The centre line is 10%; limits are 1% and 19%. These are binomial-model limits, with independent classifications and approximately constant nonconformance probability within the reference population. The counts expected in each category are large enough for this illustrative normal approximation.

The team inspects the baseline for signals and operational context before adopting it. The numerical summary alone does not prove baseline stability. A documented abnormal day should not simply be deleted because it widens the limits; determine its cause and whether it belongs to the process that will be monitored. Record any justified exclusion and retain the original data.

04 · Read a signal and preserve the reference

Read a signal and preserve the reference

After the reference is accepted, Northbank plots daily proportions against fixed baseline estimates. A later sample has 22 nonconforming dispatches out of 100, or 22%. It exceeds the 19% upper limit and triggers the agreed response: protect affected releases, verify classification and inspect carrier-service configuration and recent changes. The investigation finds an outdated service table after a system deployment. This operational evidence supports a cause; the chart alone did not establish it.

Another day has zero nonconforming dispatches, below the 1% lower limit. That also deserves investigation. It might represent an effective improvement, an unusual order mix or a failed inspection method. Treat favourable signals as learning opportunities rather than automatically declaring success. Check that the outcome definition and sample selection remained intact.

Do not recalculate the centre line and limits after every new point. Such rolling adjustment can absorb a deterioration and erase the reference needed to detect it. After a deliberately changed process has accumulated sufficient representative evidence and its behaviour has been assessed, establish a new documented baseline. Keep the old phase visible, annotate the intervention and explain the reason for the new limits.

05 · Signals, false alarms and varying denominators

Signals, false alarms and varying denominators

Agree the signal rules before looking at monitoring results. A point beyond a three-sigma limit is a common rule. Additional run or trend rules can improve sensitivity to particular shifts, but using many rules together increases false-positive opportunities. State the chosen rule set and train responders on its meaning. Do not try every available rule until one labels an inconvenient week as special cause.

If Northbank inspects 400 dispatches on a later day, retaining the same p-bar gives a standard error of 0.015 and limits of 5.5% and 14.5%. More information yields narrower limits. Compare that day with limits appropriate to n = 400, not the 100-dispatch limits. If a computed lower limit is negative, use zero; if the upper limit exceeds one, use one. Very rare outcomes and small samples may need more suitable exact or specialised methods.

Clustering, serial dependence and heterogeneous case mix can undermine basic assumptions. A carrier outage can affect many parcels together, so independence is doubtful. Investigate stratification, revised subgroup logic or a model accommodating extra variation with statistical support. Do not widen limits arbitrarily until every point looks acceptable.

06 · Connect chart interpretation to action

Connect chart interpretation to action

For special-cause evidence, investigate the specific event and protect the customer where needed. For a stable but unacceptable process, improve the system: redesign release logic, reduce ambiguity or change equipment. Repeatedly adjusting the process in response to ordinary fluctuations can increase variation. This is why a response plan must distinguish statistical signals from target misses.

Northbank’s customer requirement is no wrong-service dispatches. A stable 10% baseline is therefore unacceptable even though most samples lie within its limits. The team redesigns service validation and uses monitoring to assess the new method; it does not reinterpret the 19% limit as permission to ship errors. Customer protection continues independently of chart status.

Useful chart records include statistic, unit, denominator, sampling method, reference period, limit method, rule set, data owner and response owner. Annotate interventions and verify that responders can access underlying records. Avoid connecting missing days as if they were observations or replacing missing values with zeros. The chart is a disciplined conversation with data, supported by process knowledge and explicit decisions.

Connections

Related methods and phase use

Placed under Control because of the outcome it supports. Use the method in other phases when its purpose and assumptions fit the work; the phase list is a guide to selection, not a compulsory sequence.

Sources

Professional foundations and further reading

• NIST: Proportions Control Charts
• NIST: Counts Control Charts
• NIST: Univariate and Multivariate Control Charts
• ASQ: Control Chart

The explanation and fictional teaching examples are written for LeanTrainingLab. Linked primary sources provide professional foundations; example values and local conventions are stated in the guide. The accepted toolset draws on Six Sigma+Lean Toolset, second edition (Lunau, editor; Springer, 2013). No book text or examples are reproduced here.