Capability Calculation

Interactive Cp / Cpk process capability studio

Click to rename — the title is used in the PDF report too

Cp
1.50
Cpk
1.00
Show

How tight the process spread is versus the spec width. Ignores where the process is centered.

When Cp changes, keep

Same spread, but measured against the nearest spec limit — so centering matters.

Off-center direction
Cpk can never exceed Cp — value was clamped to Cp.

Scenarios

Calculate from measurement data
Report details (optional, printed on the PDF)
Centering shift k
–
0% = on target
Mean offset
–
in σ from target
Expected defects
–
parts per million
Expected yield
–
within specification
–

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How to improve

User guide — Cp, Cpk, Pp, Ppk

1. The four indices at a glance

All four compare the width of the specification with the width of the process. They differ in only two things: which standard deviation (σ) they use, and whether they care where the process mean sits.

Indexσ usedCentering counted?The question it answers
Cpσ within (short-term)NoHow good could the process be if it were perfectly centered?
Cpkσ within (short-term)YesHow good is the process where its mean sits today, if it stays stable?
Ppσ overall (long-term)NoHow wide was all the collected data compared with the tolerance?
Ppkσ overall (long-term)YesWhat did the customer actually receive during the sampling period?

Rule of thumb: Cp/Cpk = what the process is capable of, Pp/Ppk = how it actually performed. An index of 1.00 means the ±3σ spread exactly fills the available room.

2. Formulas

Cp  = (USL − LSL) / (6 · σwithin)
Cpu = (USL − x̄) / (3 · σwithin)   Cpl = (x̄ − LSL) / (3 · σwithin)
Cpk = min(Cpu, Cpl)
Pp  = (USL − LSL) / (6 · σoverall)
Ppu = (USL − x̄) / (3 · σoverall)  Ppl = (x̄ − LSL) / (3 · σoverall)
Ppk = min(Ppu, Ppl)

3. The two standard deviations

σ overall is the ordinary sample standard deviation of all values — the same number as STDEV.S in Excel:

σoverall = √( Σ(xᵢ − x̄)² / (n − 1) )

σ within only looks at the variation between parts made close together in time. The tool picks the method from the subgroup size:

Subgroup sizeMethodFormula
1Average moving range (I-MR)σ = MR̄ / 1.128
2 – 10Average range (X̄-R)σ = R̄ / d₂
11 – 50Average standard deviation (X̄-S)σ = s̄ / c₄

MR̄ is the average absolute difference between consecutive values; R̄ is the average of (max − min) of each subgroup. d₂ by subgroup size: 2 → 1.128 · 3 → 1.693 · 4 → 2.059 · 5 → 2.326 · 6 → 2.534 · 7 → 2.704 · 8 → 2.847 · 9 → 2.970 · 10 → 3.078.

If the process is stable the two σ are close. Shifts, drift, tool wear or batch-to-batch differences make σ overall larger than σ within — which is exactly why Ppk drops below Cpk.

4. Worked example

Press Load sample data then Calculate: 50 diameters in 10 subgroups of 5, LSL = 9.80, USL = 10.20.

x̄ = 10.02502   R̄ = 0.0969   σwithin = 0.0969 / 2.326 = 0.04166   σoverall = 0.04501
Cp  = (10.20 − 9.80) / (6 × 0.04166) = 1.60
Cpu = (10.20 − 10.02502) / (3 × 0.04166) = 1.40
Cpl = (10.02502 − 9.80) / (3 × 0.04166) = 1.80
Cpk = min(1.40, 1.80) = 1.40
Pp  = 0.40 / (6 × 0.04501) = 1.48
Ppk = (10.20 − 10.02502) / (3 × 0.04501) = 1.30

Reading it: the spread is good (Cp 1.60), the mean sits slightly high so the upper side is the weak one (Cpk 1.40), and over the whole period the result is a little lower again (Ppk 1.30).

5. Reading the result

Cpk / PpkStatus in this toolOut of spec, centered (PPM)One side only (PPM)
below 1.00Not capablemore than 2,700more than 1,350
1.00Marginal2,7001,350
1.33Capable6633
1.67Excellent0.540.27
2.00Excellent0.0020.001

These thresholds are common practice, not a law — your customer's requirement always wins (many automotive customers ask for 1.67 on a new process, for example). The small figures under Cp and Cpk are 95% confidence intervals: with few measurements the true value can be far from the estimate.

6. Entering your data correctly

  1. Specification limits. Type LSL and USL. If the characteristic has only one limit, leave the other box empty — do not type 0 unless 0 really is a limit on the drawing.
  2. Target is optional. Left empty, the midpoint of the tolerance is used.
  3. Subgroup size. Use 1 when you measured one part at a time. Use the number of parts taken together each time when you sampled in groups (5 parts every hour → 5).
  4. Enter the measurements in production order. Subgroups must follow each other. Never sort the data — sorted data makes σ within tiny and Cpk absurdly high.
  5. Cells works like a small spreadsheet: each row is one subgroup and the number of columns follows the subgroup size. Type values, move with the arrow keys, Enter or Tab, and paste a block copied from Excel or Google Sheets into any cell. A table pasted into empty cells sets the subgroup size to its number of columns; a header row, a text column and a 1, 2, 3 … row-number column are left out. Cells that cannot be read as numbers turn red and are ignored. If a row has fewer values than the subgroup size, its row number is marked: fill it or delete the row, because the values are grouped one after another.
  6. Text is a plain box for long lists (more than 3000 rows): one row per subgroup or one long column. Paste measurement values only there — no row numbers, dates or units — and use one decimal style in the whole list (10.01 or 10,01, not both).
  7. If your Excel sheet has one subgroup per column, transpose it first (Paste Special → Transpose) so each subgroup becomes a row.
  8. After Calculate, check the message “Analyzed n measurements”: n must equal the number of values you intended to enter.
How much data? Two values are enough to calculate, but not to conclude. Aim for 50–100 values (for example 25 subgroups of 4–5) taken over a period that includes normal changes of shift, material and setup.

7. Showing and hiding indices

The Show buttons beside the big numbers switch Cp, Cpk, Pp and Ppk on or off — on screen, in the tables and in the PDF report. Nothing is recalculated; hidden indices are simply not displayed.

8. Why another tool gives a different number

9. When the indices can be trusted

The calculations in this tool follow the AIAG SPC conventions and were checked against an independent statistics library on 68 data sets.