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Six Sigma Capability Improvement - Defect Based Six Sigma Metrics - Example

If there are 9 defects among 150 invoices, and there are 8 opportunities for errors for every invoice, what is the dpmo?

dpu = no. of defects / total no. of product units = 9/150 = .06 dpu

dpo = no. of defects / (no. of units X no. of defect oppurtunities per unit)

= 9/(150 X 8) = .0075 dpo
dmpo = dpo x 1,000,000 = .0075 X 1,000,000 = 7,500 dpmo

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
     

Six Sigma Capability Improvement

Six Sigma Capability Improvement

Sigma Table

Yield dpmo Sigma (σ) Cp Equiv.
 COPQ (Cost of Poor Quality)
.840 160,000 2.50 0.83 40%
.870 130,000 2.63 0.88  
.900 100,000 2.78 0.93  
.930 70,000 2.97 0.99  
.935 65,000 3.01 1.00  
.940 60,000 3.05 1.02
.945 55,000 3.10 1.03 30%
.950 50,000 3.14 1.05
.955 45,000 3.20 1.06
.960 40,000 3.25 1.08
.965 35,000 3.31 1.10
.970 30,000 3.38 1.13
.975 25,000 3.46 1.15
.980 20,000 3.55 1.18 20%
.985 15,000 3.67 1.22
.990 10,000 3.82 1.27
.995 5,000 4.07 1.36
.998 2,000 4.37 1.46
.999 1,000 4.60 1.53 10%
.9995 500 4.79 1.60
.99975 250 4.98 1.66 5%
.9999 100 5.22 1.74
.99998 20 5.61 1.87
.9999966 3.4 6.00 2.00
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