Getting started with Six Sigma

A unit of product can be defectives if it contains one or more defects. A unit of product can have more than one opportunity to have defects.

Determine all the possible opportunities for problems

Pare the list down by excluding rare events, grouping similar defect types, and avoiding the trivial

Define opportunities consistently between different locations

Proportion Defective (p):

p = Number Of Defective Units / Total Number of Product Units

Yield ( Y1st-pass or Yfinal or RTY)

Y = 1 – p The Yield proportion can converted to a sigma value using the Z tables

Defects Per Unit – DPU, or u in SPC

DPU = Number Of Defects / Total Number Of Product Units The probability of getting ‘r’ defects in a sample having a given dpu rate can be predicted with the Poisson Distribution.

Defects Per Opportunity – DPO

DPO = no. of defects / (no. of units X no. of defect opportunities per unit)

Defects Per Million Opportunities (DPMO, or PPM)

DPMO = dpo x 1,000,000 Defects Per Million Opportunities or DPMO can be then converted to sigma & equivalent Cp values in the next page. The DPMO, DPM, Sample Size, CI Calculator will help you calculate the metrics.

If there are 10 defects among 160 invoices, and there are 7 opportunities for errors for every invoice, what is the dpmo? dpu = no. of defects / total no. of product units = 10/160 = .0625dpu dpo = no. of defects /(no. of units X no. of defect oppurtunities per unit) = 10/(160 X 7) = .0023dpodmpo = dpo x 1,000,000 = .0023 X 1,000,000 = 23,809dpmo What are the equivalent Sigma and CP values? See Sigma Table.

Converting Yield to sigma &Cp Metrics – Example 

Given: a proportion defective of 1%

Yield = 1 – p = .990

Z Table value for .990 = 2.32σ

Estimate process capability by adding 1.5 σ to reflect the ‘real-world’ shift in the process mean 2.32σ + 1.5σ = 3.82σ

This σ value can be converted to an equivalent CP by dividing it by 3σ : CP = 3.82σ/3σ = 1.27 Note: Cpk cannot be estimated by this method 

Sigma Table