DPU, RTY, CoPQ, DPMO & Sigma Level

DPU, RTY, CoPQ, DPMO & Sigma Level (CSSGB BoK II.E.1 — Analyze)

Quick Answer: DPU = defects ÷ units. RTY multiplies successive process yields to estimate end-to-end first-pass success. CoPQ monetizes failure and poor quality. DPMO = (defects ÷ (units × opportunities)) × 1,000,000 and converts to a sigma level. Capability indices compare variation to specs. Green Belts calculate these metrics, trend them, and use them to prioritize and validate improvements.

BoK II.E.1 is at the Analyze level: compute metrics from given numbers, interpret what they mean for the business, and avoid confusing defects with defectives or short-term with long-term sigma.

Why Process Performance Metrics Matter

Champions fund projects that move business results. Process performance metrics translate process pain into numbers leaders understand—defect load, yield loss, quality cost, and sigma capability. They also let teams compare before/after states with a common language.

Defects, Defectives, Opportunities

• A defect is a single nonconformance to a requirement (scratch, missing field, late milestone).
• A defective is a unit that has one or more defects (a bad unit).
• An opportunity is a chance for a defect to occur—defined consistently (e.g., each critical characteristic on a part, each data field on a form).

Never mix definitions mid-project. If Measure defines five CTQ opportunities per order, Control must use the same five when computing DPMO.

DPU — Defects Per Unit

$\text{DPU} = \frac{\text{Total number of defects}}{\text{Total number of units}}$

DPU can exceed 1.0 when units often have multiple defects.

Worked example (DPU)

Inspection of 200 circuit boards finds 46 defects (some boards had several issues).

$\text{DPU} = \frac{46}{200} = 0.23$

Interpretation: on average, 0.23 defects per board. If 38 boards were defective, the defective rate is 38/200 = 19%, which is not the same as DPU.

Throughput Yield and Rolled Throughput Yield (RTY)

Throughput yield (TY) at a step is the proportion of units that pass that step without rework or scrap (first-pass yield for the step).

Rolled throughput yield (RTY) for a multi-step process is the product of the step yields when steps are sequential and independent in the yield sense:

$\text{RTY} = Y_1 \times Y_2 \times \cdots \times Y_n$

When average DPU for a process (or step) is known and defects follow a Poisson model, a common approximation is:

$Y \approx e^{-\text{DPU}}$

Worked example (RTY)

A three-step process has first-pass yields:

• Step 1: 95% (0.95)
• Step 2: 90% (0.90)
• Step 3: 98% (0.98)

$\text{RTY} = 0.95 \times 0.90 \times 0.98 = 0.8379 \approx 83.8\%$

Even though each step looks “pretty good,” only about 84% of units traverse all three steps defect-free on the first pass. Hidden factory rework is the rest. For 1,000 starts, roughly 162 units experience at least one failure path—strong justification for a project.

Exam tip: Multiplying yields (RTY) is stricter than averaging them. Average yield (0.95+0.90+0.98)/3 = 94.3% overstates end-to-end performance.

Cost of Poor Quality (CoPQ)

CoPQ (and the broader cost of quality model) monetizes quality-related costs. Classic categories:

Many deployments treat failure costs (internal + external) as the primary CoPQ target for DMAIC projects; prevention and appraisal investments often rise short-term to drive failure costs down long-term.

Simple CoPQ framing example

Monthly: scrap $40,000; rework labor $25,000; warranty $18,000; expedited freight for quality escapes $7,000.

$\text{Monthly CoPQ (failure)} = 40{,}000 + 25{,}000 + 18{,}000 + 7{,}000 = \$90{,}000$

Annualized ≈ $1.08M. A project that cuts failure CoPQ 30% with verified Control is a clear business case—tie charter savings to these line items, not vague “efficiency.”

DPMO and Sigma Level

Defects Per Million Opportunities (DPMO):

$\text{DPMO} = \left(\frac{\text{Number of defects}}{\text{Number of units} \times \text{Opportunities per unit}}\right) \times 1{,}000{,}000$

DPMO enables comparison across products with different complexity.

Worked example (DPMO)

• Units inspected: 1,000
• Opportunities per unit: 5 (five critical fields or characteristics)
• Defects found: 25

Total opportunities = 1,000 × 5 = 5,000

$\text{DPMO} = \frac{25}{5{,}000} \times 1{,}000{,}000 = 5{,}000$

Sigma level (conceptual mapping)

Sigma level links process performance to DPMO using the normal distribution (often with a 1.5σ shift convention in Six Sigma tables for long-term performance). Memorize landmark pairs for the exam:

A DPMO of 5,000 sits near the ~4σ region on common tables—far from world-class 6σ (~3.4 DPMO). Report both DPMO and sigma; leaders often recognize “four sigma” faster than “five thousand DPMO.”

Yield-to-sigma shortcuts on the exam: high first-pass yield does not automatically mean high sigma if opportunities are many and defects are undercounted. Always honor the opportunity definition.

Capability Indices — Overview (Link to Measure)

Process performance metrics above count defects and costs. Capability indices compare the process distribution to specification limits (details deepen in BoK III.F):

Rough intuition: higher Cpk means fewer defects relative to specs if the process is stable and approximately normal. DPMO/sigma from attribute counts and Cpk from continuous data should tell a consistent story; investigate when they do not (wrong opportunities, unstable process, non-normal data, measurement error).

Using Metrics to Drive Decisions

1. Baseline in Measure: DPU, RTY, DPMO/sigma, and CoPQ before changes.
2. Prioritize: High CoPQ + low RTY steps often beat vanity metrics.
3. Validate Improve: Show statistically and practically better DPU/DPMO/RTY—and dollar impact.
4. Control: Dashboard the few metrics that detect backsliding; link to control plans.
5. Avoid gaming: Changing opportunity counts or inspection rigor to “improve” DPMO without real process change is not Six Sigma.

Exam checklist: defects ≠ defectives; DPU can exceed 1; RTY multiplies step yields; DPMO needs opportunities; CoPQ must map to real cost buckets; sigma tables often assume the 1.5σ shift—read the stem for which convention is implied.