Repair leverage
When MTBF is already long, reducing MTTR may recover more hours per dollar than another modest reliability improvement because every failure still consumes restoration time.
Probability
System Availability Expected Value Calculator
Convert MTBF, MTTR, planned downtime, and hourly economics into expected up hours, down hours, operational availability, and net value for one planning horizon.
REPAIRABLE-SYSTEM VALUE MODEL
Translate availability mechanics into an economic planning expectation
This model separates corrective-failure cycling from scheduled stops, conserves every hour in the entered horizon, and attaches explicit value and cost rates to the resulting time states.
Expected net value -
Operational availability -
Expected up hours -
Expected down hours -
Inherent availability -
Expected downtime cost -
LIVE DECISION RECORD
Availability and value reconciliation
Every row preserves its own basis, unit, intermediate value, and planning meaning.
| Layer | Starting value | Adjustment | Unit / rate | Current result | Interpretation |
|---|
CURRENT CALCULATION PROCESS
Formula, current substitution, intermediate values, and reconciliation
A_i = MTBF / (MTBF + MTTR); E[U] = (H - D_p)A_i; E[D] = H - E[U]; E[V] = E[U]v_u - E[D]c_d
| Symbol | Meaning and unit | Current value |
|---|---|---|
| mtbfHours | Mean time between failures (hours) - Positive operating hours between corrective failures. | 720 |
| mttrHours | Mean time to repair (hours) - Corrective restoration time; zero is allowed as an ideal boundary. | 6 |
| plannedDowntimeHours | Planned downtime (hours) - Scheduled maintenance already committed inside the horizon. | 12 |
| horizonHours | Planning horizon (hours) - Total calendar hours under the decision. | 2160 |
| valuePerUpHour | Value per available hour - Gross contribution or service value in one consistent currency. | 850 |
| costPerDownHour | Cost per unavailable hour - Incremental loss, penalty, or recovery cost per down hour. | 1250 |
Waiting for valid inputs.
WHO THIS MODEL SERVES
A scoped decision aid, not a universal forecast
Primary audience: Reliability engineers, maintenance planners, service owners, and finance partners screening one repairable asset.
Decision boundary: Use it to compare horizon-level expected value under stable MTBF/MTTR assumptions; do not use it as a timestamped outage forecast or a life-distribution model.
HOW TO USE THE EXPECTATION
Build an auditable horizon case in five steps
- Choose a calendar horizon that matches the budget, SLA, or maintenance decision.
- Enter MTBF and MTTR from the same asset population and operating regime.
- Record scheduled downtime separately, including committed inspections or upgrades.
- Use one documented currency basis for available-hour value and unavailable-hour cost.
- Read the time reconciliation before net value, then retain the current TXT or PDF with the source period.
AVAILABILITY FUNDAMENTALS
Five distinctions that keep the estimate defensible
- Inherent availability
- MTBF divided by MTBF plus MTTR; it isolates corrective maintenance under an idealized support environment.
- Operational availability
- Expected up hours divided by all calendar hours, so entered planned downtime remains visible.
- Expectation, not schedule
- Expected hours average possible histories and need not be whole outage events.
- Consistent observation basis
- MTBF and MTTR must refer to compatible definitions, units, and asset conditions.
- Economic boundary
- Up-hour value and down-hour cost are decision assumptions, not properties of the reliability distribution.
MODEL AND DEFAULT SUBSTITUTION
Read the time model before monetizing it
A_i = MTBF/(MTBF+MTTR); E[U]=(H-D_p)A_i; E[D]=H-E[U]
With the defaults, A_i=720/(720+6)=0.9917355. Schedulable time is 2,160-12=2,148 hours; expected up time is 2,130.248 hours and expected down time is 29.752 hours. The live model applies 850 per up hour and 1,250 per down hour without intermediate rounding.
DEEPER AVAILABILITY ANALYSIS
Three questions behind the headline value
Planned versus unplanned accountability
Keeping scheduled hours separate lets a review distinguish maintenance policy from random corrective performance instead of hiding both in one percentage.
Asymmetric economics
A down hour can cost more than an up hour earns. The net result therefore depends on both time probability and consequence severity.
WORKED DECISION CASES
Two operating contexts with different conclusions
Packaging line quarter
A line with 720-hour MTBF, 6-hour MTTR, and 12 scheduled hours has about 29.75 expected down hours in a 2,160-hour quarter. The ledger shows whether a spares proposal recovers corrective hours or merely moves planned work.
Zero-repair ideal boundary
Setting MTTR to zero makes inherent availability 100%. If planned downtime remains 12 hours, operational availability is still 99.444%. This catches the error of calling an asset operationally perfect because repair is instantaneous.
TERMS FOR THE REVIEW RECORD
Six terms used by the calculation
- MTBF
- Mean operating time between repairable failures.
- MTTR
- Mean corrective restoration duration.
- Planned downtime
- Calendar time intentionally unavailable for scheduled work.
- Inherent availability
- Corrective-cycle availability before planned stops and logistics delays.
- Operational availability
- Expected available time divided by total calendar time.
- Expected net value
- Probability-weighted up-state value less down-state cost.
EVIDENCE RETENTION
Keep the inputs traceable to the operating period
Retain failure-work-order extracts, restoration timestamps, the planned-maintenance calendar, horizon definition, and finance source for each hourly rate. Label censored or excluded incidents and preserve the current exported record with the decision date.
LIMITS AND EXCLUSIONS
What this expectation deliberately leaves outside
- Constant average failure and repair behavior is assumed throughout the horizon.
- Logistics, detection, and administrative delays are excluded unless embedded in MTTR.
- Planned and corrective downtime are treated as non-overlapping.
- Hourly value and cost are linear; startup losses, tiered penalties, and recovery ramps are not modeled.
- The output is a planning estimate, not a warranty, SLA certification, or safety case.
RELIABLE SOURCES
Primary references for availability definitions
EXPECTED-VALUE FAQ
Questions specific to repairable-system value
Why is planned downtime excluded before applying inherent availability?
The MTBF/MTTR ratio describes corrective-failure cycling. Scheduled maintenance is entered separately so its hours are not silently treated as random repair time.
Can MTTR be zero?
Yes, as a mathematical best-case boundary. It produces 100% inherent availability, while planned downtime can still reduce operational availability.
Should value per up hour use revenue or contribution margin?
Use the basis relevant to the decision and document it. Contribution margin is usually safer when variable costs continue during production.
Why can expected down hours be fractional?
Expected value averages possible operating histories. It is a planning quantity, not a prediction that one outage lasts that exact fraction.
Does this include multiple simultaneous failures?
No. It treats one repairable system through aggregate MTBF and MTTR. Redundant-unit states belong in the outcome-table model.
When should I avoid this estimate?
Avoid it when failure rate changes materially with age, repairs are highly skewed, planned work overlaps failures, or downtime economics are nonlinear.
IMPORTANT AVAILABILITY NOTE
Validate the data-generating regime before committing capital
This calculator is a screening and documentation aid. Reliability, safety, contractual, and investment decisions require system-specific engineering review and evidence that the entered averages represent the future operating regime.