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Updated
Histogram template
A histogram is a bar chart of how many readings fall into each of a row of equal ranges, called bins, so the shape of a process's variation shows at a glance: where it is centered, how widely it spreads, and whether it has one peak, two, or a long tail. Drawing the specification limits on it shows how many parts fall outside them. It is one of the seven basic quality tools. Page 1 of the PDF has the header fields, a table for 100 readings, a tally table for up to 12 bins, a box for the numbers that set the bins (n, largest, smallest, range, number of bins, bin width and first edge) and a grid to draw the bars and the limits. Page 2 has the steps for setting the bins, six common shapes and what each often means, and a worked example drawn to scale. The Excel version takes up to 125 readings, works out n, the largest, the smallest, the range, the mean and the standard deviation, sets the bins by the square root rule (with Sturges' rule shown for reference and optional overrides for the number of bins, the width and the first edge), counts each bin with its % and cumulative %, counts the readings below the LSL and above the USL, and draws the histogram with the readings outside the limits in red. It has a worked example sheet and a shapes sheet.
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When to use it
When to draw a histogram
- To see where a measured characteristic sits against its specification and how widely it spreads, before deciding whether to re-center the process or reduce its variation.
- As a first look before a capability study, to check that the readings have one peak and roughly a bell shape.
- When parts from two machines, cavities, shifts or material lots may be mixed: two peaks or a flat top show it.
- To check a supplier's parts against the specification: a side that ends in a sharp cliff often means the lot was sorted.
How to fill it in
- 1
Collect the readings
At least 50, ideally 100, from one period of normal running. Write them in the order taken and note the gauge and its resolution.
- 2
Find the range
Count the readings (n), find the largest and the smallest, and work out range = largest − smallest.
- 3
Set the bins
Number of bins = √n, rounded, as a starting point. Width = range ÷ number of bins, rounded up to a whole number of resolution steps. First edge = smallest − half the resolution, so no reading sits on an edge.
- 4
Tally and count
Put one stroke per reading in its bin, then count each bin. The counts must add up to n.
- 5
Draw it
One bar per bin, with no gaps, as high as its count. Draw the LSL, the USL and the target, and count the readings outside the limits.
- 6
Read the shape
Compare it with the common shapes on page 2, then check the likely cause at the process before acting.
Shapes
Common histogram shapes and what they often mean
A shape is a clue, not a verdict: check the cause at the process before acting on it.
| Shape | What it looks like | What it often means |
|---|---|---|
| Bell (normal) | One peak in the middle, tails falling off evenly on both sides | Usual variation only: check where it sits against the limits |
| Skewed | Peak off center, a long tail on one side | A natural limit on the short side (zero, a stop, flatness, runout), or a process adjusted from one side |
| Two peaks (bimodal) | Two humps with a dip between them | Two sets of data mixed: machines, cavities, shifts, operators or material lots. Split the readings by source |
| Cliff (cut off) | One side ends sharply | Parts sorted at inspection, readings past a limit not written down, or the end of the gauge's range |
| Plateau | A flat top over several bins | Several streams with slightly different means mixed, or a process drifting (tool wear) during the period |
| Isolated peak | A small group apart from the rest | A short abnormal event: a wrong setting, another material lot, a measuring error or a mix-up |
Bell (normal)
- What it looks like
- One peak in the middle, tails falling off evenly on both sides
- What it often means
- Usual variation only: check where it sits against the limits
Skewed
- What it looks like
- Peak off center, a long tail on one side
- What it often means
- A natural limit on the short side (zero, a stop, flatness, runout), or a process adjusted from one side
Two peaks (bimodal)
- What it looks like
- Two humps with a dip between them
- What it often means
- Two sets of data mixed: machines, cavities, shifts, operators or material lots. Split the readings by source
Cliff (cut off)
- What it looks like
- One side ends sharply
- What it often means
- Parts sorted at inspection, readings past a limit not written down, or the end of the gauge's range
Plateau
- What it looks like
- A flat top over several bins
- What it often means
- Several streams with slightly different means mixed, or a process drifting (tool wear) during the period
Isolated peak
- What it looks like
- A small group apart from the rest
- What it often means
- A short abnormal event: a wrong setting, another material lot, a measuring error or a mix-up
A filled-in example
Illustrative, not a benchmarkAn example: the diameter of a turned shaft, specification 25.00 ± 0.10 mm, 100 readings to 0.01 mm (illustrative numbers). The Excel version's Worked example sheet has all 100 readings.
- n = 100, largest 25.12 mm, smallest 24.94 mm, range 0.18 mm. Mean 25.030 mm, standard deviation 0.0338 mm.
- Bins: √100 = 10. Width 0.18 ÷ 10 = 0.018, rounded up to 0.02 mm. First edge 24.94 − 0.005 = 24.935 mm.
- Counts from 24.935 mm up, bin by bin: 1, 3, 12, 17, 22, 20, 17, 5, 2, 1.
- No reading below 24.90 mm and 2 above 25.10 mm (25.11 and 25.12): 2.0% out of specification.
One peak and close to a bell, so nothing points to mixed streams. But the process is centered 0.030 mm above nominal and its spread nearly fills the 0.20 mm tolerance, so the top tail runs past the USL. The action was to re-center the process on 25.00 mm, then draw a new histogram to check.
Common mistakes
Too few readings
With 20 or 30 readings the shape owes a lot to chance. Use at least 50, ideally 100.
Bins that do not suit the data
Too few bins hide the shape and too many make it ragged; a width that does not match the resolution gives a comb of alternating high and low bars. Start from √n and round the width to the resolution.
Mixing streams without noting it
Readings from two machines or cavities in one histogram can look like one wide process. Note where each reading came from and draw the groups apart when the shape looks odd.
Reading a histogram as a trend
It hides the order of the readings, so a drift looks like a wide spread. Use a control chart to see change over time.
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FAQ
Histogram template: common questions
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