Vose SoftwareModelRisk example · Manufacturing
Reliability and Availability of a Production Line
How often will the line stop, what does it cost, and is a standby machine worth it? Failures and repairs through a year.
From the model’s saved run
How much will the line stand still?
Downtime in a year of scheduled production, and what it costs.
| Measure | Unit | 5th pct | Median | 95th pct | Mean |
|---|---|---|---|---|---|
| Line downtime | hours | 75.8 | 102.3 | 136.4 | 103.7 |
| Contribution lost | US$k | 91.0 | 122.8 | 163.7 | 124.5 |
| Measure | Unit | Value |
|---|---|---|
| Availability, average year | 98.27% | |
| Availability, 1 year in 20 (5th percentile) | 97.73% |
S-curve (cumulative probability) of Without standby, With a standby capper from the saved simulation.
Histogram of Line downtime from the saved simulation.
The business question
A food company's packaging line fills, caps, labels and packs 2,400 jars an hour, and every hour it stands still costs about US$1,200 of contribution. The four machines run in series, so a stop anywhere stops the line. The filler's last 30 failures were logged. For the other machines the maintenance team knows their typical times between failures and repair times.
The engineers want to know how much the line will stand still next year, which machine is to blame, and whether a standby capper — switched in within a quarter of an hour whenever the capper fails — is worth its US$30,000 a year.
- Who it is for
- Maintenance and reliability engineers, production managers, operations finance.
- Main outputs
- The line's downtime and availability, and the contribution lost · each machine's failures and downtime · the hours and money a standby capper saves, and the chance that it pays for itself.
How the model works
Four sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The production hours scheduled in the year and the contribution lost per hour stopped. For each machine the Weibull shape and scale of its running time between failures and the mean and spread of its repair time; the standby capper's switch-over time and cost.
Data sheet
The running hours between the filler's last 30 failures.
Failures sheet
The filler's Weibull is fitted to its records with parameter uncertainty (VoseWeibullFitP). Each machine then fails again and again through the year: running time to the next failure from its Weibull, repair time from its Lognormal. Failures inside the scheduled hours are counted and their repairs added up. The standby capper replaces each capper repair by the switch-over time.
Results sheet
The line's downtime, availability and lost contribution; each machine's share; the hours, money and chance of profit of the standby capper.
ModelRisk techniques
Find similar models
- Product
- Type
- Application
- Uses
The results in detail
Which machine stops the line?
Average failures and downtime in a year, by machine.
| Machine | MTBF hours | Failures a year | Downtime hours a year | Share of downtime | Repair hours, mean |
|---|---|---|---|---|---|
| Filler | 401 | 14.8 | 22.1 | 21% | 1.5 |
| Capper | 277 | 21.5 | 42.9 | 41% | 2.0 |
| Labeller | 482 | 12.4 | 10.0 | 10% | 0.8 |
| Case packer | 800 | 7.1 | 28.7 | 28% | 4.0 |
Is a standby capper worth it?
The same failures, with each capper repair replaced by a quarter-hour switch.
| Measure | Unit | Value |
|---|---|---|
| Line downtime a year, without the standby | hours | 103.7 |
| …with the standby | hours | 66.1 |
| Hours saved | hours | 37.6 |
| Saving net of the standby's cost, average | US$k | 15.1 |
| Saving net of cost, 1 year in 20 (5th percentile) | US$k | −6.3 |
| Chance that the standby pays for itself | 83.8% |
How to read these results
- The line stands still about 104 hours in an average year — 98.3% availability — and about 137 hours in a bad year (1 in 20). At US$1,200 an hour that is about US$125,000 of lost contribution a year, and up to about US$164,000.
- The capper causes about 41% of the downtime: it fails most often, about 22 times a year, and its repairs are long and variable. The case packer fails rarely but takes four hours to repair on average (28%). The labeller's frequent short stops matter least.
- A standby capper turns each capper repair into a quarter-hour switch. It saves about 38 hours a year — about US$15,000 a year after its cost — and pays for itself in about 84% of years. In a quiet year for the capper it does not.
- The filler's reliability rests on only 30 records, so its Weibull parameters are uncertain: the model draws plausible ones in every iteration (VoseWeibullFitP with uncertainty). Its shape of about 1.7 says the filler wears out, so preventive maintenance could cut its failures (see MF-08).
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
The line 2 inputs
| Assumption | Unit | Value |
|---|---|---|
| Scheduled production hoursTwo shifts, five days a week. | hours a year | 6,000 |
| Contribution lost per hour stopped2,400 jars an hour × US$0.50. | US$ thousand | 1.2 |
Machines 16 inputs
Running time between failures (Weibull) and time to repair (Lognormal).
| Assumption | Unit | Value | Uncertainty |
|---|---|---|---|
| Filler: Weibull shape (fitted)Fitted to its failure records on the Data sheet (Failures sheet). | 1.73 | Calculated | |
| Filler: Weibull scale (fitted) | hours | 450 | Calculated |
| Filler: average repairShape and scale fitted to its failure records (Data sheet). | hours | 1.5 | Fixed |
| Filler: repair standard deviation | hours | 1.2 | Fixed |
| Capper: Weibull shapeTorque heads jam; some repairs wait for parts. | 1.30 | Fixed | |
| Capper: Weibull scale | hours | 300 | Fixed |
| Capper: average repair | hours | 2.0 | Fixed |
| Capper: repair standard deviation | hours | 2.5 | Fixed |
| Labeller: Weibull shapeMostly quick resets. | 1.10 | Fixed | |
| Labeller: Weibull scale | hours | 500 | Fixed |
| Labeller: average repair | hours | 0.8 | Fixed |
| Labeller: repair standard deviation | hours | 0.6 | Fixed |
| Case packer: Weibull shapeRare but long stops. | 1.80 | Fixed | |
| Case packer: Weibull scale | hours | 900 | Fixed |
| Case packer: average repair | hours | 4.0 | Fixed |
| Case packer: repair standard deviation | hours | 3.0 | Fixed |
Standby capper 2 inputs
Switched in whenever the capper fails.
| Assumption | Unit | Value |
|---|---|---|
| Time to switch overInstead of waiting for the repair. | hours | 0.25 |
| Cost of the standby capperLease and upkeep. | US$ thousand a year | 30 |
Units and conventions
- Time
- Hours of running or of repair.
- Money
- US$ thousand.
- Weibull
- Shape below 1: failures mostly early; 1: at random; above 1: wear-out.
- Availability
- Running hours ÷ scheduled hours.
Key assumptions and limitations
- Series
- Any machine down stops the line; stops of different machines do not overlap.
- Ageing
- Each machine is counted as running through all the scheduled hours — a slight overstatement of failures when availability is high (here about 2%).
- Repairs
- A repaired machine is as good as new; repair times are independent.
- Data
- The line and all figures are invented for this example.
How to use it
- Enter your scheduled hours and the contribution lost per hour.
- Enter each machine's failure and repair data, or paste a machine's failure records on the Data sheet.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Improve first the machine with the largest share of downtime; test options like the standby capper.
Simulate this model with ModelRisk’s classic engine: it does not run in Turbo mode yet.
ModelRisk functions used
- VoseWeibull
- Running time between failures.
- VoseWeibullFitP
- The filler's Weibull parameters fitted to its records, with parameter uncertainty (array).
- VoseLognormal
- Repair time, by its mean and standard deviation.
- VoseSimMean, VoseSimPercentile, VoseSimProbability
- Statistics of the simulation on the Results sheet.
Further reading
- Monte Carlo simulation explained (Vose guide)
- O'Connor, P. D. T. & Kleyner, A. (2012). Practical Reliability Engineering, 5th edition. Wiley.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley — renewal processes.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
Related example models
- ModelRiskOptimizer★★★★★Spare Parts and Maintenance Strategy Chosen by the OptimizerWhich replacement age and how many spare kits cost least while keeping the downtime promised to a customer?Bearing lives simulated on every spindle; the replacement age and spare kits chosen together by the Optimizer within a limit on downtime.
- ModelRiskOptimizer★★★★★Inventory Policy Chosen by the OptimizerWhich reorder point and order quantity cost least while keeping the service the customers were promised?Demand over a random lead time as an aggregate; the reorder point and order quantity chosen together by the Optimizer for a service target.
- ModelRisk★★★★★Inventory Policy under Uncertain Demand and Lead TimeWhen should we reorder?Demand during a random lead time as an aggregate, the service level of each reorder point, and its cost.
An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.