# Process Capability Metrics

## You Don't Have to be a Statistician to Understand Process Capability Metrics like Cp and Cpk

QI Macros Histogram calculates several process capability analysis metrics. Descriptions and formulas for these metrics are described below.

**Cp and Cpk Process Capability Metrics****Pp and Ppk Process Performance Metrics**

**Other Process Metrics****Why did My Metrics Turn Red?**

## Other Process Capability Metrics

### Capability Ratio - Cr Formula

The Capability Ratio indicates what proportion of tolerance is occupied by the data.

**Cr** = 1/Cp

**Cp** = 1.33 ~ Cr = 0.75 (data fits 75% of tolerance)

### Cpm Formula

The Cpm is an uncommonly used Capability Index that can be used when you have a target value.

**Cpm** = (USL-LSL)/(6√(sigma2+(Xbar-Target)2)

### Cg and Cmk versus Cp and Cpk

Cg and Cmk are calculated the same as Cp and Cpk (respectively). QI Macros uses uses “Cp” and “Cpk” as the default names. And although the calculations are the same, the difference is in the methodology of measurement and how the data is collected.

**Cg**examines the equipment-related variation behavior of the measuring system at the location of application. 50 measurements (a minimum of 20) are effected under identical conditions (measurements carried out by the same operator on the same part) or standard and feature at a precisely defined point, and then the deviations of the indications from the nominal indication are recorded.**Cmk**is measured using 50 or more continuous samples produced on a machine, keeping all influences other than the machine parameters constant. Also, the “Cmk” refers to Machine Capability, instead of Process Capability (Cpk).

**Min-Max**

Min = Min(Xi)

Max = Max(Xi)

**Z Score**

Z scores help estimate the non-conforming PPM.

Z scores *standardize* +/-3*stdev values into +/-3.

**Zlower** = (Xbar-LSL)/stdev

**Zupper** = (USL-Xbar)/stdev

**Zbench**

Zbench = normsinv(1-(Expected PPM/1,000,000)) Zbench is the Z score for the Expected PPM

**ZTarget/Delta Z**

**ZT (target) = ΔZ**= |Xbar-Target|/(stdev)

Ztarget measures how far the average varies from the Target.

ZT < 0.5 is desired (less than 1/2 standard deviation from target)

The target is assumed to be the midpoint between the USL and LSL.

**Sample Size Calculator**

**Variable
Sample Size (SS)** = (ZStdev)/Confidence2

Where:

Z = 1.96 for 95% confidence level

Stdev = standard deviation (or 0.5 Default)

Confidence interval expressed as decimal (e.g., .05 = ±5%)

**Attribute**

Sample Size (SS)= (Z2p(1-p))/Confidence2

Sample Size (SS)

Where:

Z = 1.96 for 95% confidence level

p = percent defects (0-0.5 = 0-50%)

Confidence interval expressed as decimal (e.g., .05 = ±5%)

**Correction for Finite Population**

new sample size = SS/(1+ (SS-1)/population)

**Defects**

**defects** = number of points outside USL-LSL

**% Total Defects** = (defects100)/(Total points)

### Parts Per Million (PPM) and Expected PPM

**PPM** = % Total Defects*1000000

**Expected PPM** = (Normsdist(Zlower) + (1-Normsdist(Zupper)))1,000,000

- Expected PPM Short Term (ST), "Within" uses sigma estimator (Rbar/d2 or Sbar/c4)
- Expected PPM Long Term (LT), "Overall" uses standard deviation.

**Sigma**

If observed PPM > 0, it uses the observed value to calculate Sigma.

If observed PPM = 0, it uses Expected PPM to calculate Sigma.

If both are zero, it defaults to 6 sigma.

If there are no USL/LSL, it leaves it blank.

**Confidence Interval**

The Confidence Interval within QI Macros is set at 95%, however in the XmR templates and dashboard you can set it to your choosing (except for the XmR Short Run):

**Skewness**

A "Skewness" value refers to the degree of asymmetry of a distribution around its mean. Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values. Negative skewness indicates a distribution with an asymmetric tail extending toward more negative values.

## Why did My Metrics Turn Red?

**Cp**= If Cp > Cpk or Cpk > Ppk. Your process is unstable or data was sorted.**Cpk**= If Cp > Cpk or Cpk > Ppk. Your process is unstable or data was sorted.**Cr**= If Cr is greater than or equal to 1, value turns red. (Cp < 1.0), Cr < 1 then value is not red.**ZTarget/∆Z**= If ∆Z > 0.5, value turnes red. Target = (USL-LSL)/2.**Pp**= If Cp > Cpk or Cpk > Ppk. Your process is unstable or data was sorted.**Ppk**= If Cp > Cpk or Cpk > Ppk. Your process is unstable or data was sorted.

### Why Choose QI Macros to Perform Capability Analysis and Draw Histograms?

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- Works Right in Excel
- Calculates Cp Cpk Pp Ppk
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