Does the method use the median of observations or moving ranges?

Both: the observation median sets the center, and the moving-range median determines the distance to the limits.

Can the moving ranges be calculated after sorting values?

No. The method uses consecutive observations in process order.

Does a point beyond a limit prove a defective product?

No. A control-chart signal concerns process behavior; product conformance is assessed against its requirements.

AI Glossary / Statistics and probability / Intermediate

Clifford's method

Definition

Clifford's method is a median-based procedure for calculating robust control limits for an individuals control chart. In the NIST glossary formulation, the center line is the median of the observations, and the limits are that median plus or minus 3.15 times the median moving range. The method reduces sensitivity to some extreme observations when establishing a process-monitoring baseline.

What it means

An individuals chart follows measurements in their original time order. Its moving ranges are absolute differences between consecutive values. Conventional limits often use the mean and average moving range, which can be influenced strongly by unusual readings. Clifford's method substitutes medians. Robust does not mean immune to bad data, changing conditions or dependence. The method remains a control-chart procedure whose usefulness depends on an appropriate baseline and monitoring context, not a general guarantee of statistical control.

How it works

Retain the chronological observation sequence. Calculate each adjacent moving range as the absolute difference between the current and previous observation, producing n - 1 ranges from n observations. Find the median observation and the median of those ranges. Multiply the median range by 3.15 and subtract or add the result to form lower and upper limits. Plot the original measurements against these limits and investigate signals in context. Establish a documented baseline and a rule for revising it. Recalculating limits automatically after every shift can normalize a deteriorating process rather than detect it.

Three practical examples

Process monitoring: establish an individuals-chart baseline when occasional extreme readings would strongly distort mean-based limits.
Measurement review: compare robust and conventional limits while investigating unusual observations and checking whether a stable reference period exists.
Automated quality dashboards: implement a clearly documented median-based limit calculation, preserving time order and avoiding silent changes to baseline definitions.

Think of it this way

Think of estimating the usual location and step-to-step movement of a process without letting one unusually large step dominate the ruler. The ruler can be less sensitive to that extreme value, but it still needs a sensible reference period and a process for investigating genuine changes.

Worked example

Take the illustrative time-ordered measurements 10, 11, 10, 12, 11, 10, 30, 11 and 10. Their median is 11. The eight moving ranges are 1, 1, 2, 1, 1, 20, 19 and 1. Sorted, these are 1, 1, 1, 1, 1, 2, 19 and 20, giving median moving range one. Clifford's limits are therefore 11 - 3.15 = 7.85 and 11 + 3.15 = 14.15. The observation 30 lies above the upper limit and warrants investigation. The two large ranges adjacent to 30 do not increase the median range in this particular dataset. Now incorrectly sort the observations before calculating ranges. The sorted values produce ranges 0, 0, 0, 1, 0, 0, 1 and 18, whose median is zero. The resulting collapsed limits would be an artifact of destroying time order. This tiny example demonstrates the calculation, not an adequate production baseline or proof that 30 is an invalid measurement.

Illustrative case study

Fictional case: Elm Manufacturing compares control-limit methods after an instrument occasionally produces extreme readings. The team calculates Clifford-style limits alongside its existing chart, checks original measurement records and examines autocorrelation. Engineers establish a reviewed baseline and retain genuine process changes rather than removing every point outside the limits. They document when recalculation is justified. This fictional case illustrates a monitoring workflow and makes no claim that the robust method is universally superior or that it prevents defects.

Common misconceptions and mistakes

The median moving range is not the median absolute deviation from the overall median; they use different quantities. The constant 3.15 belongs with the stated median-range construction and should not be substituted into an average-range formula casually. Control limits are not product specification limits or confidence intervals for the mean. Sorting the data invalidates the intended moving-range calculation. Strong autocorrelation, coarse measurement resolution or many ties can make adjacent ranges misleading or zero. Several shifts or extensive contamination can defeat the protection offered by medians. A signal identifies unusual behavior relative to the baseline, not its cause.

Business use

Businesses should treat Clifford's method as one documented option within statistical process control. Check that individual measurements and their timing are appropriate, that the baseline represents the intended process, and that the measurement system has adequate resolution. Preserve the raw sequence and investigation records. For AI-powered monitoring, verify that anomaly explanations are supported by operational evidence and that automatic updates do not conceal persistent drift. Compare methods using false-signal behavior and detection objectives relevant to the process rather than choosing whichever chart produces fewer alerts.

Check your understanding

Q: Why does the extreme value 30 not widen the limits in the worked example?

Answer: A: It creates two large adjacent ranges, but the middle of the eight-range distribution remains one. That illustrates the median's resistance in this specific arrangement, not complete immunity to unusual data.

Related terms

Individuals chart
Median
Control limits
moving range
robust estimation
control limit
process stability
autocorrelation and specification limit

Learn next

reproduce the example and compare it with mean-and-average-range limits. Change several consecutive observations to simulate a sustained shift and inspect how the medians respond. Then investigate how ties and serial correlation affect moving-range-based estimates before using them operationally.

Sources

Sources: NIST glossary, exact Clifford's method definition: https://www.itl.nist.gov/div898/handbook/glossary.htm ; NIST Engineering Statistics Handbook, individuals charts and adjacent moving ranges: https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc322.htm ; JMP, individuals and moving-range chart interpretation: https://www.jmp.com/en/statistics-knowledge-portal/quality-and-reliability-methods/control-charts/imr-chart .

Previous: Client-side persistent data Next: Clinical trial