OpenSpecEngineering

Open data for a field built on precision

Control-chart factors, capability-index relationships, and the process sigma / DPMO / yield conversions used in statistical process control and Six Sigma work.

Choosing a Control Chart

Shewhart Control Chart Constants

Process Sigma ↔ DPMO ↔ Yield

With the conventional Six Sigma ±1.5σ long-term shift applied (i.e. process sigma = ZLT + 1.5). A "6σ process" delivers 3.4 defects per million opportunities.

Process Sigma (σ)DPMOYield (%)
1.0691,46230.85
2.0308,53869.15
3.066,80793.32
3.522,75097.73
4.06,21099.379
4.51,35099.865
5.023399.9767
5.53299.99968
6.03.499.999660

Standard Normal z-values

Two-sided confidenceOne-sided areaz
80%0.901.282
90%0.951.645
95%0.9751.960
95.45%0.97722.000
98%0.992.326
99%0.9952.576
99.73%0.998653.000

Capability Indices

IndexFormulaMeaning
CpUSL − LSL6σwithinPotential capability, centred
Cpkmin [ USL − μ3σwithin , μ − LSL3σwithin ]Actual capability
Pp, PpkSame forms, using the overall (long-term) standard deviationLong-term performance
CpmUSL − LSL6√(σ2 + (μ − T)2)Taguchi index, penalises off-target
CpkInterpretation
< 1.00Not capable — producing out-of-spec product
1.00 – 1.33Marginally capable — tight control needed
1.33 – 1.67Capable (common minimum for ongoing production)
≥ 1.67Highly capable (≥ 2.0 often required for new / critical processes)

DMAIC

PhasePurpose
DefineProject charter, scope, customer CTQs, and the problem statement.
MeasureValidate the measurement system, baseline current performance, map the process.
AnalyzeIdentify and verify the root causes / key process inputs (X's).
ImproveDevelop, pilot, and confirm solutions that address the verified causes.
ControlControl plan, SPC, mistake-proofing, and handoff to the process owner.