KEVOS® MAKEOS · Quality
Individuals Control Chart Check (Moving Range, Control Limits, Points Out of Control)
From these individual measurements taken one at a time, where are the control limits, and is any point outside them?
Individuals (X) control chart from up to twelve readings in time order: the mean, the moving ranges between consecutive readings and their average, the process standard deviation estimated from the average moving range, the upper and lower control limits, and which readings fall outside them, so you can see whether the process is in statistical control.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of readings used | readings | How many of the readings below to use, in time order (at least 3). |
| Readings in time order | ||
| Reading 1 | Measurement number 1 in the order it was taken. | |
| Reading 2 | Measurement number 2 in the order it was taken. | |
| Reading 3 | Measurement number 3 in the order it was taken. | |
| Reading 4 | Measurement number 4 in the order it was taken. | |
| Reading 5 | Measurement number 5 in the order it was taken. | |
| Reading 6 | Measurement number 6 in the order it was taken. | |
| Reading 7 | Measurement number 7 in the order it was taken. | |
| Reading 8 | Measurement number 8 in the order it was taken. | |
| Reading 9 | Measurement number 9 in the order it was taken. | |
| Reading 10 | Measurement number 10 in the order it was taken. | |
| Reading 11 | Measurement number 11 in the order it was taken. | |
| Reading 12 | Measurement number 12 in the order it was taken. | |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Number of readings used
- What it is
- How many of the readings listed below are used for the chart, taken from the first reading in time order.
- Units and format
- Enter a number in readings: readings. The form accepts 3 readings to 12 readings. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 readings as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Readings beyond this count are ignored.
- Get it right
- Use at least 12 for rough limits; recalculate with 20 to 25 readings when you have them.
Readings in time order
What this means: Reading 1
- What it is
- Measurement number 1 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.02 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 1 must come first in time, or the moving ranges mean nothing.
What this means: Reading 2
- What it is
- Measurement number 2 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.05 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 2 must come after reading 1 in time, or the moving ranges mean nothing.
What this means: Reading 3
- What it is
- Measurement number 3 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 9.98 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 3 must come after reading 2 in time, or the moving ranges mean nothing.
What this means: Reading 4
- What it is
- Measurement number 4 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.01 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 4 must come after reading 3 in time, or the moving ranges mean nothing.
What this means: Reading 5
- What it is
- Measurement number 5 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.04 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 5 must come after reading 4 in time, or the moving ranges mean nothing.
What this means: Reading 6
- What it is
- Measurement number 6 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 9.99 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 6 must come after reading 5 in time, or the moving ranges mean nothing.
What this means: Reading 7
- What it is
- Measurement number 7 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.03 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 7 must come after reading 6 in time, or the moving ranges mean nothing.
What this means: Reading 8
- What it is
- Measurement number 8 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 8 must come after reading 7 in time, or the moving ranges mean nothing.
What this means: Reading 9
- What it is
- Measurement number 9 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.06 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 9 must come after reading 8 in time, or the moving ranges mean nothing.
What this means: Reading 10
- What it is
- Measurement number 10 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 9.97 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 10 must come after reading 9 in time, or the moving ranges mean nothing.
What this means: Reading 11
- What it is
- Measurement number 11 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.02 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 11 must come after reading 10 in time, or the moving ranges mean nothing.
What this means: Reading 12
- What it is
- Measurement number 12 in the order the readings were taken, one value of the characteristic per sample, part or batch.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.01 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean, its moving ranges and so the control limits; a value far from the rest may fall outside them.
- Get it right
- Keep the time order: reading 12 must come after reading 11 in time, or the moving ranges mean nothing.
Method and formulas
- Moving range MRᵢ = |xᵢ − xᵢ₋₁| for consecutive readings; MR̄ = average of the moving ranges.
- Control limits = x̄ ± 3 MR̄ ÷ 1.128, where 1.128 is d₂ for ranges of two (NIST e-Handbook 6.3.2.2); estimated σ = MR̄ ÷ 1.128.
- Any reading above the upper or below the lower limit signals a special cause.
- Example: mean 10.015 with limits 9.8965 to 10.133; 0 reading(s) outside.
Limitations
- Twelve readings give only rough limits: recalculate them once 20 to 25 readings are available.
- Only the beyond-the-limits rule is applied; runs and trends (other detection rules) need the full chart.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Chart a characteristic measured once per batch or per shift
- Check a run of readings for a special cause
- Set control limits for a new process
Who it is for
- Quality engineers and technicians
- Process engineers
- Production supervisors
What you get
- Mean and average moving range
- Estimated standard deviation
- Upper and lower control limits
- Readings outside the limits
Interpreting the result
- Limits describe what the process does, not what the drawing allows: a process can be in control and still make parts out of tolerance.
References
- NIST/SEMATECH e-Handbook of Statistical Methods, 6.3.2.2 Individuals Control Charts — https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc322.htm
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Individuals and moving ranges
In Control Charts by the Numbers
What it covers: Charting one reading per period: the moving range estimate of σ, individuals limits, why an outlier can hide itself, setting a clean baseline, and the extra care that single readings need.
Method explained here · KEVOS® original book
Controlling the process
In Induction Hardening by the Numbers
What it covers: Keeping induction hardening the same part after part: monitoring each heat, charting case depth, control limits against specification limits, capability, and a chart that hid its signal.
Method explained here · Library collection
Statistical process control on the shop floor: control charts, real signals and when to leave a process alone
What it covers: Control charts separate the normal noise of a process from real change. How to choose a chart, set limits, read the signals and stop well-meant adjustments that make variation worse.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.