Rare events can still dominate value
A small annual probability can produce a material expected loss when direct damage, outage duration, or loss per hour is large. Keep probability and consequence evidence separate.
Reliability
Component Failure Expected Value Calculator
Compare probability-weighted failure loss with mitigation cost and break-even risk reduction.
ECONOMIC SCREEN
Compare control cost with avoided expected failure loss
For maintenance and reliability teams screening one mitigation over a stated horizon while keeping consequence, probability, and control evidence separate.
Net savings-
Failure consequence-
Baseline expected loss-
Control-inclusive cost-
Break-even reduction-
CURRENT DECISION RECORD
Expected-loss decision ledger
Every row is regenerated from the active inputs and carried into Copy, TXT, and the page-specific PDF payload.
| Stage | Factor A | Factor B | Current value |
|---|
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate values, and reconciliation
EV0=p(Cdirect+hL)Y; EV1=p(1-r)(Cdirect+hL)Y+M
Waiting for valid inputs.
HOW TO USE
Five steps from consequence to break-even
- Define one failure consequence.
- Enter annual probability and evaluation years.
- Separate direct loss from downtime loss.
- Enter control cost and probability reduction.
- Use net savings and break-even reduction together.
EXPECTED-VALUE FUNDAMENTALS
Five concepts behind the economic comparison
- Failure consequence
- The monetary impact if the modeled failure occurs once, combining direct loss with downtime hours times loss per hour.
- Expected loss
- Probability-weighted average loss across many equivalent exposures; it is neither the most likely invoice nor a maximum loss.
- Residual probability
- The baseline annual probability multiplied by one minus the modeled relative risk reduction.
- Control-inclusive cost
- Residual expected loss over the horizon plus the entered mitigation cost.
- Break-even reduction
- The relative probability reduction at which avoided expected loss exactly equals mitigation cost.
DEEP ECONOMIC ANALYSIS
Separate consequence, horizon, and control value
The horizon defines the comparison
This model adds annual expected loss linearly across the entered years. Changing exposure, escalation, discounting, or repeated control costs requires a cash-flow model.
Avoided loss is not automatically savings
Risk reduction first removes expected loss; mitigation cost must then be subtracted. A technically effective control can still have negative modeled net value.
WORKED DECISION CASES
A preventive-control case and a zero-risk boundary
Preventive replacement for a production motor
A 4% annual failure chance, 25000 direct loss, 12 downtime hours at 1800 per hour, and five-year horizon create a baseline expected loss. A 6000 replacement program with 60% risk reduction is evaluated against the avoided portion, not against the full consequence.
Zero baseline risk boundary
If entered failure probability is zero, baseline and residual expected losses are zero. No finite probability reduction can repay a positive mitigation through this modeled failure alone, so break-even reduction is not finite.
EVIDENCE RECORD
Preserve the basis of every monetary input
Retain the failure definition, annual exposure, probability data period, repair quotation, damaged-item scope, downtime log, loss-per-hour method, mitigation quotation, implementation timing, reduction study, model owner, and review date. Evidence for consequence and evidence for probability should remain separately traceable.
MODEL LIMITS
What this expected-value screen excludes
- One failure mode, one consequence basis, and a constant annual probability.
- Annual expected losses add linearly with no discounting, inflation, escalation, or exposure growth.
- Parameter uncertainty and correlation with other failure modes are not propagated.
- The control changes failure probability only; consequence and operating exposure remain fixed.
EXPECTED-VALUE GLOSSARY
Six distinct economic-risk terms
- Annual probability
- Chance of the modeled failure in one year.
- Direct loss
- Repair, replacement, or damage entered directly.
- Downtime loss
- Hours multiplied by loss per hour.
- Risk reduction
- Relative decrease in probability.
- Residual risk
- Probability remaining after control.
- Net value
- Baseline expected loss minus control-inclusive cost.
FREQUENTLY ASKED QUESTIONS
Questions specific to probability-weighted loss
Is expected loss the most likely amount I will pay?
No. It is the probability-weighted average across many equivalent exposures. A real outcome may be zero loss or the full entered consequence.
Can I enter negative losses to represent a benefit?
No. Keep benefits in a separate benefit model so failure consequences, avoided losses, and positive operating gains remain auditable.
Does mitigation cost repeat every year?
This page treats mitigation cost as one total cost for the entered horizon. Recurring inspections, subscriptions, or replacements require their full horizon cost.
Are taxes, inflation, and discounting included?
No. The page compares undiscounted amounts in one currency basis. Use a discounted cash-flow analysis when timing materially affects the decision.
Can I add expected losses from several failure modes?
Only after checking shared causes, overlapping downtime, and duplicated consequence. Simple addition can overstate loss when modes are dependent or mutually exclusive.
What if the control reduction is uncertain?
Run documented low, central, and high reduction cases based on evidence. Preserve each result instead of reporting only the favorable assumption.
RELIABLE SOURCES
Reliability evidence references
IMPORTANT DECISION LIMIT
Economic value does not set safety acceptability
A positive or negative net value does not override legal duties, hazard controls, minimum maintenance requirements, or safety-critical design criteria. Use this result only as one documented economic screen.