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.

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

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

Cpm can be used when you have a target value.

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
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) uses sigma estimator (Rbar/d2 or Sbar/c4)
  • Expected PPM Long Term (LT) 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):

confidence-interval

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 Choose QI Macros to Perform Capability Analysis and Draw Histograms?

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