When Can a Process Be Considered Six Sigma Compliant?
When Can a Process Be Considered Six Sigma Compliant?
Let’s answer the question. The correct answer for the questions is:
A process is considered Six Sigma compliant when it achieves a defect rate of no more than 3.4 defects per million opportunities (DPMO), accounting for a potential 1.5σ shift in the process mean.
When the process has less than or equal3.4 defects per million opportunities. Six Sigma is a data-driven methodology aimed at process improvement by reducing variability and defects.
Six Sigma
Six Sigma is a customer-focused quality model. It was first developed and used by Motorola. Six Sigma measures defects in DPMO (Defects Per Million Opportunities)
A process is considered to be in Six Sigma if it operates with a defect rate of 3.4 defects per million opportunities (DPMO). This corresponds to a process performance level of 99.99966% defect-free.
Six Sigma Performance Table
| Sigma Level | Defects Per Million Opportunities (DPMO) | Yield (Defect-Free Rate) |
|---|---|---|
| 3 Sigma | 66,807 | 93.32% |
| 4 Sigma | 6,210 | 99.38% |
| 5 Sigma | 233 | 99.9767% |
| 6 Sigma | 3.4 | 99.99966% |
Specification Limits
- Target mean: μ
- Standard deviation: σ
- Upper Specification Limit (USL): μ+6σ
- Lower Specification Limit (LSL): μ−6σ
For a centered process with mean μ and standard deviation σ:
Upper Specification Limit (USL)=μ+6σ,
Lower Specification Limit (LSL)=μ−6σ.
A process is Six Sigma compliant if its defect rate is ≤ 3.4 defects per million opportunities (DPMO) after accounting for a 1.5σ process mean shift.
Accounting for Mean Shift
Processes may drift over time. Six Sigma accounts for a 1.5σ shift in the mean:
μshifted=μ±1.5σ(typically μ+1.5σ)
Distance to Specification Limits After Shift
For μshifted=μ+1.5σ:
Distance to USL=USL−μshifted = (μ+6σ)−(μ+1.5σ)=4.5σ,
Distance to LSL=μshifted−LSL = (μ+1.5σ)−(μ−6σ)=7.5σ.
Defect Probability Calculation
Defects occur if X>USL or X<LSL. Using the standard normal distribution (Z-scores):
The probability of defects is:
Defects above USL:
P(X>USL)=Φ(−4.5)≈3.4×10−6 (3.4 DPMO).
Defects below LSL:
P(X<LSL)=Φ(−7.5)≈0.
where Φ(z) is the Cumulative Distribution Function (CDF) of the standard normal distribution.
Total Defect Rate
Φ(−4.5)≈3.4×10−6=3.4 DPMO,
Φ(−7.5)≈0.
Total defects:
3.4 DPMO
