Process Capability Metrics

Jay Arthur
888-468-1537
303-756-9144
KnowWare International, Inc.
DBA LifeStar
2253 S. Oneida
Ste 3D
Denver, CO 80224

We work with companies
that want to fire up their profits using
Lean Six Sigma

Copyright © 2011

• Cp and Cpk Process Capability Metrics
• Pp and Ppk Process Performance Metrics
  
• Other Process Metrics
  • Skewness (Excel's skew function)
  • Standard Deviation (Excel's stdev function)
  • Min and Max
  • Z score
  • Z bench
  • Z Target/Delta Z
  • % Defects
  • Parts Per Million and Expected Parts Per Million
  • Sigma

Other Process Metrics

Min-Max

Min = Min(X_i)
Max = Max(X_i)

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
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 10000
Expected PPM = (Normsdist(Zlower) + (1-Normsdist(Zupper)))1,000,000

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.

Other Resources

• Control chart formulas
• Download a free pdf of histogram formulas and sample calculations at histogram-manual-calcs.pdf

The histogram with Cp Cpk and other metrics is just one of the tools included in the QI Macros for Excel SPC Software for Excel.

Download the FREE 30-day Evaluation copy of the QI Macros Excel SPC Software for Six Sigma

Try QI Macros
FREE
For 30-Days

Or Buy It Now!