Practical guide · Quality management
Histogram: what it is, how to build one and how to read it in manufacturing
Short answer
A histogram is a bar chart of measured values grouped into equal ranges called bins, where each bar's height is how many readings fell in that range. It shows the shape of variation: where it is centred, how wide it is and whether it crosses a specification limit.
A histogram groups measurements of one characteristic, such as a diameter or a fill weight, into equal-width bins and draws a bar for each, so the height is the number of readings in the range. Choose about the square root of the number of readings as the bin count, count the readings per bin, and draw the bars touching. Read the shape first, then the centre, then the spread against the spec limits.
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What a histogram is, and what it is not
A histogram turns a list of measurements into a picture of how they are spread. The horizontal axis is the measured value, cut into equal ranges. The vertical axis is the count of readings in each range. Unlike a plain list, it shows at a glance whether the values pile up around a centre, lean to one side, split into two groups or run over a spec limit.
| Chart | What the bars are | Order of the bars | Use it to |
|---|---|---|---|
| Histogram | Ranges of one measured value | Fixed, from low to high, bars touching | See the shape and spread of variation |
| Bar chart | Separate categories | Any | Compare category totals |
| [Pareto chart](/learn/pareto-chart) | Categories, usually defect types | Descending, with a cumulative line | Choose which problem to work on |
| [Control chart](/learn/control-chart) | Not bars: one point per sample, in time order | Time | See whether the process is stable over time |
A histogram has no time axis. It shows how the values are spread, not when they happened, so a process that drifts up and down can produce the same histogram as one that is steady. That is the main limit of the tool and the reason it is usually paired with a control chart.
How to build a histogram in six steps
- 1
Collect the readings
Measure one characteristic on parts made under one condition: one machine, one shift or one setup, not a mix. Aim for at least 50 readings; 100 or more gives a cleaner shape. Record them with the same gauge and resolution.
- 2
Find the range
Range = largest reading minus smallest reading.
- 3
Choose the number of bins
Start with the square root of the number of readings, rounded. 100 readings gives 10 bins, 50 gives 7. Too few bins hide a second peak and too many make the chart ragged, so adjust once you see it.
- 4
Work out the bin width
Width = range ÷ number of bins, rounded up to a tidy number that matches your gauge, such as 0.02 mm. Use the same width for every bin.
- 5
Set the bin edges and count
Start the first bin at or just below the smallest reading. State which edge is included (lower edge included, upper edge not is a common rule) so a reading on the edge is counted once. Tally each reading into its bin.
- 6
Draw the bars and add the spec limits
Bars touching, height = count. Mark the lower and upper spec limits and the target as vertical lines. The histogram template bins, counts and draws it in Excel.
Worked example: 100 shaft diameters (illustrative)
This example is made up. A shaft has a specification of 25.00 mm ± 0.10 mm, so the limits are 24.90 and 25.10. An operator measures 100 shafts from one machine. The smallest reading is 24.88 and the largest is 25.12, so the range is 0.24 mm. The square root of 100 is 10 bins; a width of 0.02 mm gives 12 bins across that range and a tidy edge at 25.00, so the team uses 12.
| Bin (mm) | Count | Bin (mm) | Count |
|---|---|---|---|
| 24.88 to under 24.90 | 2 | 25.00 to under 25.02 | 14 |
| 24.90 to under 24.92 | 4 | 25.02 to under 25.04 | 12 |
| 24.92 to under 24.94 | 7 | 25.04 to under 25.06 | 9 |
| 24.94 to under 24.96 | 11 | 25.06 to under 25.08 | 6 |
| 24.96 to under 24.98 | 14 | 25.08 to under 25.10 | 4 |
| 24.98 to under 25.00 | 15 | 25.10 to under 25.12 | 2 |
Check: 2 + 4 + 7 + 11 + 14 + 15 = 53 and 14 + 12 + 9 + 6 + 4 + 2 = 47, so 53 + 47 = 100. In shape order the counts run 2, 4, 7, 11, 14, 15, 14, 12, 9, 6, 4, 2.
Reading it: the shape is a single peak, roughly symmetric, so the readings look like one process and not a mix. The peak bin is 24.98 to 25.00, and the middle reading (the 50th) falls in the same bin, since 38 readings sit below it and 53 up to and including it. The centre is therefore close to the 25.00 target. The spread is the problem: the bar below 24.90 holds 2 readings and the bar at 25.10 and above holds 2 more, so 4 of 100 shafts, 4%, are out of specification, split evenly on both sides.
That points to the right action. The process is centred, so adjusting the machine setting would move one tail over the limit to fix the other. The spread has to come down, which means looking for what makes the diameter vary: tool wear, material, fixturing, the gauge. The fishbone is a good next step. Had the peak sat at 25.04 with one tail over the upper limit, the answer would have been the opposite: move the centre.
What the common shapes mean
| Shape | What it looks like | What it often means |
|---|---|---|
| Bell (normal) | One central peak, tails of similar length | One stable source of variation. The shape most capability formulas assume |
| Skewed right or left | Peak to one side, long tail on the other | A natural limit on one side, such as a flatness that cannot go below zero, or a process sorted or reworked at one edge |
| Two peaks (bimodal) | Two humps with a dip between | Two sources mixed: two machines, shifts, tools, cavities or material lots. Split the data and draw each |
| Plateau | Bars about equal height across a wide range | Several processes centred at different values mixed together |
| Cut-off edge | Bars stop abruptly at one value, often at a spec limit | Parts outside the limit were sorted out or reworked before measurement |
| Comb | Alternating tall and short bars | The gauge resolution is coarser than the bin width. Widen the bins or use a finer gauge |
| Isolated island | A small separate bar far from the rest | A mis-measurement, a different part or a one-off event. Find out what it was before dropping it |
Mistakes that mislead
| Mistake | What goes wrong | Do this instead |
|---|---|---|
| Mixing machines, shifts or setups | A bimodal or flat shape that describes no real process | One condition per histogram, then compare them side by side |
| Too few readings | The shape changes with the next ten parts | At least 50, preferably 100 or more |
| Bin widths that are unequal or too fine for the gauge | False peaks and a comb pattern | Equal widths no finer than the gauge resolution |
| Reading it as proof of stability | A drifting process looks like a wide, steady one | Plot the same data in time order on a control chart |
| Judging by eye whether it fits the spec | A close call goes unnoticed | Draw the spec limits and count what falls outside them |
| Ignoring a measurement problem | Gauge error widens the picture | Check the gauge with a gage R&R study first |
From histogram to capability and control
A histogram with spec limits drawn on it is a picture of capability. To put a number on it, once a control chart shows the process is stable, the capability indices Cp and Cpk compare the spread and centre with the limits. The process capability calculator and the Cpk study sheet do the arithmetic. Capability is only meaningful on a stable process, which is why the order is histogram, then control chart, then Cpk.
Definitions and notes
- The histogram is one of the seven basic quality tools, a bar chart of measured data grouped into equal-width classes (ASQ, "Histogram"). The square-root rule for the number of bins is one of several rules of thumb; Sturges' rule is another. Treat any of them as a starting point.
- The 100 shaft readings, their bins and the spec are made up for illustration. They are not from a real plant. The bin counts add to 100 and the out-of-spec share is 4 readings of 100.
- The 50-reading minimum is a common rule of thumb, not a standard.
Go deeper
This page is the short version. These guides cover each part in full.
- Statistical Process Control Basics in ManufacturingWhere the histogram sits among the SPC tools and how the tools are used together.
- Control Charts: Reading and Interpreting Manufacturing DataThe next step after a histogram: checking the same process over time.
- Process Capability (Cp and Cpk) ExplainedHow to turn a histogram against spec limits into capability numbers.
- Measurement System Analysis for ManufacturingWhy to trust the gauge before you trust the shape of the histogram.
All our articles on this subject are in the quality management topic.
Free templates and tools
- Histogram templateReadings, bins set by the square root rule, a tally and counts, the spec limits drawn and the share out of spec, with the common shapes explained.
- X-bar and R control chart template25 subgroups with means and ranges, control limits from A2, D3 and D4, signal flags, both charts and a reaction log.
- Process capability (Cpk) study sheet25 subgroups of readings with Cp, Cpk, Pp and Ppk worked out, control limits to check stability, and a histogram.
- Gage R&R study sheet10 parts, 2 or 3 appraisers, 2 or 3 trials: EV, AV, GRR, PV, %GRR and ndc by the average and range method.
- Scatter diagram templateUp to 50 pairs with a group code, r and R², the least squares line, the quadrant count and r for each group.
- Pareto chart templateA tally sheet, the Pareto by count and by cost with the cumulative line and the 80% cut, and a before and after comparison. Excel sorts and draws it.
- Histogram makerPaste measurements: the histogram with automatic or chosen bins, plus mean, median and standard deviation, as a PNG or SVG.
- Box plot makerPaste one or more groups of numbers: box plots with quartiles, IQR, whiskers and outliers by the 1.5 IQR rule, as a PNG or SVG.
- Process capability (Cp, Cpk) calculatorCp and Cpk against your specification limits, plus Pp and Ppk from pasted measurements, with a distribution chart.
- First pass yield (FPY) calculatorFirst pass yield at each step and rolled throughput yield (RTY) across the whole process.
- Scrap rate calculatorScrap rate, the cost of scrap per period and per year, and what reaching a target rate would save.
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FAQ
Questions about histogram
It is a bar chart of measured values from one characteristic, such as a diameter, grouped into equal ranges called bins. Each bar's height is the number of readings in that range. It shows the centre, spread and shape of the variation and how it sits against the specification limits.
A common starting point is the square root of the number of readings, so 100 readings gives about 10 bins. Too few bins hide a second peak and too many make the chart ragged. Use equal widths that are no finer than your gauge can read, and adjust once you see the shape.
Read the shape first: one peak, two peaks, skewed or cut off. Then the centre, which is where the peak sits compared with the target. Then the spread, which is how wide it is compared with the spec limits. A centred process that is too wide needs less variation, not an adjustment.
A histogram groups one continuous measurement into ordered ranges and draws the bars touching, so the order is fixed and the gaps carry meaning. A bar chart compares separate categories and the bars can be in any order. A Pareto chart is a bar chart sorted from largest to smallest.
Usually two sources of variation were mixed in one set of data, such as two machines, shifts, tools, cavities or material lots. Split the readings by source and draw a histogram for each. If each is a single peak, the difference between the sources is what to investigate.
Related guides and tools
- Free histogram maker: paste measurements and see the distribution
- Process capability calculator (Cp and Cpk) for the same measurements
- Free histogram template for plotting a sample by hand or in Excel
- Control charts: watch the same measurement over time instead of in one pile
- Free box plot maker: compare the spread of several samples
More method guides
- The 6 Ms of production
- Poka-yoke
- Model area 90-day plans
- Moving from Excel to one system
- Reducing machine downtime: a worked month
- Andon and jidoka
- Cycle time vs lead time, worked through
- Root cause analysis
- How many operators a line needs
- Reducing scrap and rework: a worked month
- Unsafe acts and unsafe conditions
- Just culture
- Stop-work authority
- Material review board (MRB)
- What is an NCR?
- Problem solving methods
- Quad chart
- OEE calculation
- Quality assurance vs quality control
- SOP meaning and format
- Job hazard analysis
- Near miss reporting
- Fishbone diagram
- Pareto chart
- Control chart
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