Coverage-effectiveness interaction
Doubling coverage does not double detection if effectiveness changes with speed, fatigue, or automation thresholds. Validate both inputs at the planned operating point.
Probability
Defect Rate Expected Value Calculator
Estimate detected and escaped defects, inspection cost, expected quality cost, and savings versus no inspection for a stated production plan.
QUALITY-COST EXPECTATION
Trace an inspection plan from expected defects to expected cost
Coverage and detection effectiveness are modeled separately. The page preserves expected physical flows before attaching costs, then compares the plan with a no-inspection baseline at the same assumed defect rate.
Total expected quality cost-
Expected savings vs no inspection-
Expected detected defects-
Expected escaped defects-
No-inspection baseline-
Cost per produced unit-
LIVE DECISION RECORD
Expected defect flow and cost ledger
Physical quantities and cost components reconcile to the live plan total and no-inspection comparison.
| Ledger component | Expected quantity | Unit cost | Expected cost | Flow role |
|---|
CURRENT CALCULATION PROCESS
Formula, current substitution, intermediate values, and reconciliation
Defects=Np; detected=Npce; escaped=Np-detected; total=Nc*ci + detected*cd + escaped*ce
| Symbol | Meaning and unit | Current value |
|---|---|---|
| N | Production units | 10000 |
| p | Defect rate, percent | 2 |
| c | Inspection coverage, percent | 80 |
| e | Detection effectiveness, percent | 90 |
| ci | Inspection cost per inspected unit | 0.15 |
| cd | Internal cost per detected defect | 8 |
| ce | Cost per escaped defect | 80 |
Waiting for valid inputs.
FIVE-STEP COST WORKFLOW
Keep physical expectations ahead of money
- Set one production horizon and an evidence-backed defect-rate scenario.
- Enter inspection coverage and separately estimate true detection effectiveness.
- Use incremental inspection cost and average costs on a consistent accounting basis.
- Review detected plus escaped defects before reading total cost.
- Compare with the no-inspection baseline and retain each component, not only net savings.
FIVE EXPECTED-VALUE FUNDAMENTALS
What the ledger assumes
- Expected defects
- Production volume multiplied by the assumed defect probability.
- Coverage
- Fraction of all units receiving the inspection step.
- Effectiveness
- Conditional detection rate among inspected defective units.
- Escape
- An expected defective unit not detected by this plan.
- Baseline
- All expected defects receive escape cost when inspection coverage is zero.
DEFAULT SUBSTITUTION
Reconcile 200 expected defects through the inspection path
Defects=10,000 x 0.02=200; detected=200 x 0.80 x 0.90=144; escaped=56
Inspection costs `8,000 x $0.15 = $1,200`; internal disposition costs `144 x $8 = $1,152`; escapes cost `56 x $80 = $4,480`. Total expected cost is $6,832 versus a $16,000 no-inspection baseline, for $9,168 expected savings.
THREE DEEPER MODULES
Find the assumption controlling value
Escape-cost governance
Use frequency-weighted average downstream cost, not one memorable catastrophic claim. Keep safety or regulatory severity in a separate risk analysis.
Prevention comparison
Inspection sorts output but does not lower modeled p. A prevention project changes the source rate and should be evaluated by rerunning the entire flow with evidence for the new p.
TWO COST CASES
A value-adding screen and an empty screen
High escape consequence
At $80 per escape, broad effective inspection can avoid enough downstream cost to exceed inspection and internal disposition expense in expectation.
Zero coverage
No units are inspected, so detected defects and inspection cost are zero. All 200 expected defects escape and the plan total exactly equals the no-inspection baseline.
QUALITY-COST GLOSSARY
Six terms in the ledger
- Inspection coverage
- Inspected units divided by produced units.
- Detection effectiveness
- Detected divided by inspected defective units.
- Internal failure cost
- Disposition cost before escape.
- External failure cost
- Average downstream cost after escape.
- Expected savings
- Baseline minus modeled plan cost.
- Cost per unit
- Total expected quality cost divided by production volume.
LIMITS AND EVIDENCE
Linear averages omit severity tails
- The defect rate is constant and inspected units are representative.
- Coverage and effectiveness multiply independently in the expected flow.
- Costs are linear averages with no fixed setup, capacity, delay, or rework loop.
- Safety, recall, legal, and brand-tail consequences need dedicated risk review.
- Expected value does not guarantee the realized cost of one period.
Retain: volume plan, defect-rate study, coverage logs, detection validation, cost-account sources, baseline definition, and exported flow ledger.
RELIABLE SOURCES
Primary statistical context
QUALITY EXPECTED VALUE FAQ
Questions about flow, costs, and baselines
Why distinguish coverage from detection effectiveness?
Coverage is the share of units inspected. Effectiveness is the chance an inspected defective unit is actually detected. Multiplying them gives the fraction of expected defects captured.
Is the result a guaranteed cost?
No. It is a probability-weighted planning value. Actual defect counts and severities vary, and the model assumes linear average costs.
What belongs in escaped-defect cost?
Use a documented expected amount on the same basis as internal cost, potentially including return, field service, logistics, credit, and expected contractual impact. Avoid mixing worst case with average cost.
Can expected savings be negative?
Yes. Dense inspection or low escape consequences can make the modeled plan more expensive than no inspection. A negative result is a decision signal, not a calculation error.
Does zero coverage make effectiveness irrelevant?
Yes. With no units inspected, no defects are detected by this plan regardless of entered effectiveness, and all expected defects remain escaped.
Does the model include prevention and process improvement?
No. It compares one inspection plan with no inspection at the same assumed defect rate. Prevention effects require a separate causal model.
IMPORTANT COST NOTE
Do not compress a tail risk into one average
Use this page for repeatable planning economics. Keep high-severity safety, compliance, and contractual events visible in a separate scenario or risk register.