Process capability index

Data

Rowsrows (max 500)

No.	Data $x_i$	Delete row
1
2
3
4
5
6
7
8
9
10

Use the up and down arrows to move between cells. Enter moves to the next row, and adds one at the bottom. Pasting a range copied from Excel or a spreadsheet fills several rows at once.

Specification limits

Upper specification limit

S_U

Lower specification limit

S_L

Used to work out the process capability indices $C_p$ and $C_{pk}$ . Enter one only and it is treated as a one-sided specification; leave both empty and neither is calculated.

Result

Item	Symbol and formula	Value
Number of values	$n$	-
Sum	$\sum x_i$	-
Mean	$\bar{x}$ $\displaystyle = \frac{1}{n}\sum x_i$	-
Median	$\tilde{x}$	-
Minimum	$x_{min}$	-
Maximum	$x_{max}$	-
Range	$R$ $\displaystyle = x_{max} - x_{min}$	-
Sum of squared deviations	$S$ $\displaystyle = \sum (x_i - \bar{x})^2$	-
Population variance	$\sigma^2$ $\displaystyle = \frac{S}{n}$	-
Population standard deviation	$\sigma$ $\displaystyle = \sqrt{\frac{S}{n}}$	-
Sample variance	$s^2$ $\displaystyle = \frac{S}{n-1}$	-
Sample standard deviation	$s$ $\displaystyle = \sqrt{\frac{S}{n-1}}$	-
Process capability index	$C_p$ $\displaystyle = \frac{S_U - S_L}{6s}$	-
Process capability index (allowing for bias)	$C_{pk}$ $\displaystyle = \frac{\min(S_U - \bar{x},\ \bar{x} - S_L)}{3s}$	-

Press Calculate to see the values.

Notes

The sample standard deviation needs at least two values, so it is left blank when only one is entered.
Empty cells are treated as not entered and left out. Cells that cannot be read as a number are also left out, and their row numbers are shown in red.
The process capability index $C_p$ measures the spread against the width of the specification; $C_{pk}$ also accounts for how far the mean sits from its centre.
Enter one limit only and it is treated as a one-sided specification ( $\displaystyle \frac{S_U - \bar{x}}{3s}$ for an upper limit, $\displaystyle \frac{\bar{x} - S_L}{3s}$ for a lower one), where $C_p$ and $C_{pk}$ come out the same.
The process capability index assumes the data are normally distributed. It is usually read as follows.
- $C_{pk} \geqq 1.33$ : good
- $1.00 \leqq C_{pk} < 1.33$ : marginal
- $C_{pk} < 1.00$ : poor