Pp Calculator
Compare specification width with long-term process spread.
What this calculator does
Same arithmetic as Cp with the overall standard deviation. The page states the difference explicitly so the two are not confused.
Inputs and what they mean
- Upper specification limit
- — number value.
- Lower specification limit
- — number value.
- Overall standard deviation
- — Overall (long-term) standard deviation of all the individual measurements, including the drift between subgroups..
How to use it
- Enter your own figures — the calculator never fills in a rate, price or benchmark for you.
- Press Calculate to see the result.
- Read the formula, variables, assumptions and source below the result before you rely on it.
Formula
Pp = (USL − LSL) ÷ (6σ_overall)
Worked example
Specification 9.5 to 10.5 with an overall sigma of 0.15
Long-term performance, before any allowance for centring.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
Results depend entirely on the figures you enter and are rounded for display. They are for general information and education, not professional advice.
Reference: National Institute of Standards and Technology — NIST/SEMATECH e-Handbook of Statistical Methods
Last reviewed:
Common questions
Formula, source and verification
Specification width divided by six overall standard deviations, computed from all the individual measurements.
The question it answers: How does the process perform over the long run, and what sigma level does its defect rate imply?
The formula
Pp = (USL − LSL) ÷ (6σ_overall)
- USL — Upper specification limit
- (measurement). Highest acceptable value.
- LSL — Lower specification limit
- (measurement). Lowest acceptable value.
- σ_overall — Overall standard deviation
- (measurement). Long-term variation of all individual measurements, including drift between subgroups.
Units: Specification and standard deviation in the same measurement unit; the index is dimensionless.
What kind of calculation this is
Deterministic formula. The same inputs always give the same answer. The maths is fixed and does not depend on judgement.
Method
Same arithmetic as Cp with the overall standard deviation. The page states the difference explicitly so the two are not confused.
Assumptions built into the result
- Statistical: The standard deviation supplied is an overall (long-term) estimate from all individual measurements.
Figures this calculator will never guess for you
- No benchmark, target or 'world class' value is supplied or implied; the result describes only the figures entered.
- Pp is never presented as interchangeable with Cp; the two use different standard deviations.
- No minimum acceptable Pp is stated.
Limitations
- Pp ignores centring; use Ppk when the mean is off centre.
- Interpretation assumes measurements that are approximately normal over the period.
- A performance index, an industry benchmark and a customer's required index are three different things.
Source and version
- Standard or reference
- Process performance index Pp — NIST/SEMATECH (NIST/SEMATECH e-Handbook of Statistical Methods, process capability indices: performance indices use the overall standard deviation in place of the within-subgroup estimate.)
- Published source
- National Institute of Standards and Technology — e-Handbook
- Formula version
- Version 1
- Verification
- Reviewed against the cited source on
- How much weight the source carries
- Standards or government
- Applies to
- Currency
- The result is a ratio or index, so it does not depend on currency.
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