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Run chart maker

Paste your measure in time order and see whether the improvement worked: the page draws the median, highlights shifts and trends and says in plain language whether the change is real or chance.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

CheckRevised 11/03/2026
Data
See what was read

One row per day, shift, lot or part, in time order. The last numeric column is the value; a text or date column becomes the axis label. Up to 100,000 values.

Center line and references

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—Patterns in the sequence
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Run chart

Shaded band = shift (6+ points on one side of the median); thick stroke = trend (5+ points going up or down).

How to read: the horizontal axis is time (point 1 = the oldest) and the vertical one is the value of the measure. The center line is the median: half the points are above it, half below. In a process that only varies by chance, the points cross the median often and there are no shaded bands or thick strokes; a band or stroke is a sign that something really changed in that stretch.

Tap the chart to see the values.

    Details: run counts and signals

    Next step

    Take this page’s results to another calculator with the fields already filled in.

    Tests with p-values (clustering, mixtures, trend, oscillation) →I-MR control chart (3σ limits) →Histogram of the same values →Before × after boxplot →Capability (Cpk) with LSL and USL →

    The calculation report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. The full report also includes the charts and interpretations, in color. In the print dialog, choose Save as PDF.

    Method, assumptions and references

    Equations used

    Center line: median of the points (position (N + 1)/2) or of the first N (baseline); optionally the mean
    Shift: ≥ 6 consecutive points on the same side (points on the line ignored); trend: ≥ 5 consecutive points going up or down (repeated equal values ignored)
    Runs: number of same-side stretches among the m useful points; expected range from the Provost and Murray table (m = 10 to 60); m > 60: μ = 1 + 2ab/m, σ² = 2ab(2ab − m)/[m²(m − 1)], a = ⌊m/2⌋, b = m − a, range ⌊μ − 1.645σ − 0.5⌋ to ⌈μ + 1.645σ + 0.5⌉

    Assumptions and limits

    • IHI rules (Provost and Murray): designed for the median and for independent points in time order. The "astronomical point" (4th rule) is judged by people who know the process and is not flagged automatically; points outside LSL/USL show in red.
    • Above 60 useful points the run range uses the normal approximation, tuned to match the published table in 85 of the 102 limits from 10 to 60.
    • A run chart has no control limits; for 3σ limits use the I-MR chart, and for p-values of the runs tests, the Multi-vari page. Above 3,000 points the drawing is simplified (flagged points are kept); the rules use all of them.

    Standards and technical documents

    • Provost, L. P.; Murray, S. K. The Health Care Data Guide: Learning from Data for Improvement. Jossey-Bass, 2011
    • Perla, R. J.; Provost, L. P.; Murray, S. K. The run chart: a simple analytical tool for learning from variation in healthcare processes. BMJ Quality & Safety 20:46–51, 2011
    • Swed, F. S.; Eisenhart, C. Tables for testing randomness of grouping in a sequence of alternatives. Annals of Mathematical Statistics 14:66–87, 1943
    • Montgomery, D. C. Introduction to Statistical Quality Control, 8th ed. Wiley, 2019

    U.S. regulations

    • ISO 9001:2015, 9.1.1: monitoring and measurement
    • ISO 9001:2015, 10.3: continual improvement

    Frequently asked questions

    How do I make a run chart?

    Record the measure the same way every time (per day, shift or lot), in the order it happened, and paste the column here; if you have dates, paste both columns. The page draws the connected points, the median as the center line and, if you enter them, the goal and limits.

    How do I read a run chart?

    Do not react to a single point. Look for patterns: 6 or more points in a row on the same side of the median (shift), 5 or more going up or down (trend), or the line crossing the median too few or too many times. These patterns rarely happen by chance and signal that something changed.

    Why use the median and not the mean?

    Because the shift and number-of-runs rules were built for the median: half the points lie on each side, so 6 in a row on one side by chance is unlikely. The median is also not pulled by an extreme value.

    What is the baseline?

    The median computed only from the points before the change (for example, the 18 days before the kaizen) and extended forward. Points after the improvement are then compared with the old performance; a shift below it shows the improvement worked.

    How many points do I need?

    The run count starts with 10 points off the median, and 20 or more is better. With fewer, the rules rarely fire and only big changes become visible.

    How is it different from a control chart?

    A run chart has no control limits and needs neither much data nor a distribution assumption: it is ideal to follow an improvement from day one. A control chart (I-MR, X̄-R) adds 3-sigma limits and is the tool to keep the process in control afterwards.

    What should I do when a signal appears?

    Find out what happened at the start of the highlighted stretch: a material change, an adjustment, a new operator or the improvement itself. If the change was intended and for the better, standardize it and recompute the median with the new points; if it was for the worse, address the cause.

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