Process capability calculator
Work out whether a process can hold the tolerance (Cp and Cpk), with a plain explanation using your own figures. Check the assumptions before you act on the result.
Your figures
Result
- Cp
- 1.40 ratio
- Cpk
- 1.23 ratio
How it is worked out
Cp = (upper limit - lower limit) ÷ (6 x standard deviation); Cpk = smaller of (upper limit - mean) and (mean - lower limit) ÷ (3 x standard deviation)
cp = (upper_limit-lower_limit)/(6*std_dev)cpk = min(upper_limit-mean,mean-lower_limit)/(3*std_dev)
Check before you rely on it. Review data stability, normality and gauge repeatability with a qualified quality engineer. Have an accountant or the right specialist check any figure that affects tax, a legal duty, safety or a large purchase.
What it works out
The process capability calculator turns records from the business into a figure for this decision: whether a process can hold the tolerance (Cp and Cpk), with a plain explanation. Use it when the responsible quality inspector and production supervisor needs a consistent answer for this specific task. The answer uses only the values entered. Record the measurement period beside it.
What you need
| Input | Unit | Where to find it |
|---|---|---|
| Upper limit (example: 20.08) | units | Get upper limit from the inspection sheet, drawing or approved lot record. |
| Lower limit (example: 19.92) | units | Get lower limit from the inspection sheet, drawing or approved lot record. |
| Mean (example: 20.01) | units | Get mean from the inspection sheet, drawing or approved lot record. |
| Std dev (example: 0.02) | units | Get std dev from the inspection sheet, drawing or approved lot record. |
Use the same item, period and measurement unit for related inputs. If a figure comes from an estimate rather than an actual record, mark it as estimated. Keep your original figures beside the result.
The formula
In plain words, calculate cpk using the measured inputs below. The expressions are shown without hidden rounding so they can be checked by hand.
- cp:
cp = (upper_limit-lower_limit)/(6*std_dev). - cpk:
cpk = min(upper_limit-mean,mean-lower_limit)/(3*std_dev).
Formula basis from the supplied taxonomy: Cp = (upper limit - lower limit) ÷ (6 x standard deviation); Cpk = smaller of (upper limit - mean) and (mean - lower limit) ÷ (3 x standard deviation). Use measurements from one stable process and the drawing tolerance limits. Keep unit, mean and standard deviation consistent.
A worked example
Illustrative example: an auto-component supplier uses the figures in the table above. These are example inputs, not industry averages. For this example, the main figures are upper limit: 20.08, lower limit: 19.92, mean: 20.01, std dev: 0.02.
- Cp:
(upper_limit-lower_limit)/(6*std_dev). With the example figures,(20.08 - 19.92) / (6 * 0.019)gives 1.40. - Cpk:
min(upper_limit-mean,mean-lower_limit)/(3*std_dev). With the example figures,min(20.08 - 20.01, 20.01 - 19.92) / (3 * 0.019)gives 1.23.
How to act: Use the result to review the defect and rework record. Write down the input date and the assumption that could move most.
How to read the result
Example bands, change them for your business:
- Comfortable: Your result meets the target for this item or reporting period. Keep the calculation with its source records and review the defect and rework record.
- Watch: The result is close to your action limit, or it changed since the previous calculation. Recheck upper limit and lower limit using the original records.
- Act: The result breaks a limit already agreed by the manager or owner. Record the difference, name a responsible person, and agree a correction date. For an operational starting point, read [Too many rejections](/problems/too-many-rejections) and [Quality issue to closure](/processes/quality-issue-to-closure). Do not use these example bands as published industry benchmarks.
Copy it into a spreadsheet
Create a sheet with column A for the label and column B for the number or formula. The expressions work in Excel or Google Sheets. Keep input cells editable and result cells protected from typing.
| Cell | Label | Value or formula |
|---|---|---|
| B2 | upper limit | 20.080000 |
| B3 | lower limit | 19.920000 |
| B4 | mean | 20.010000 |
| B5 | std dev | 0.019000 |
| B7 | cp | =((B2-B3)/(6*B5)) |
| B8 | cpk | =(MIN((B2-B4),(B4-B3))/(3*B5)) |
For any formula containing a divisor, enter a value above zero. For any monetary output, format the cell in Indian rupees. Do not replace the cells with rounded figures until the final display.
What this calculator leaves out
- A low rejection number can hide missed inspections, late customer claims or incomplete records.
- Cp and Cpk assume meaningful measurement data and a reasonably stable process. Ask a quality engineer to review the distribution and measurement system.
- The formula does not check whether the records are complete. Use the same count, lot boundaries and units in both parts of the calculation. Keep rework separate from new output.
Common mistakes
- Mixing periods. Using upper limit from one month with lower limit from another produces a number that looks precise but is hard to act on.
- Trusting old figures. Recheck the relevant source record before reusing last month's saved inputs. Investigate the first repeated defect before accepting an average as normal.
- Treating an estimate as approval. Record which assumptions were entered by hand. Get the relevant owner, accountant or technician to check unusual values.
A number like this helps only if someone works it out again when things change.
Questions people ask
Where do I find the numbers for process capability calculator?
Get upper limit from the inspection sheet, drawing or approved lot record. Get lower limit from the inspection sheet, drawing or approved lot record. Keep all inputs from the same period.
Can I use this number to approve a purchase or payment?
Use it as a first check. Use the result to review the defect and rework record. Write down the input date and the assumption that could move most. If the result affects tax, legal duties, workplace safety or a major investment, obtain the appropriate review.
When should I calculate it again?
Recalculate when a meaningful input changes, and at the next regular review of the relevant register. Save the date and the input values so changes can be explained.