ModelRisk Optimizer example · Manufacturing

Spare Parts and Maintenance Strategy Chosen by the Optimizer

Which replacement age and how many spare kits cost least while keeping the downtime promised to a customer?

Complexity: ★★★★★
Free Excel workbook (MF-10)
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From the model’s saved run

The Optimizer’s plan against the starting plan

The two plans, and how each performs over the same simulated two years.

Decision	Unit	Starting plan	Optimizer’s plan	Change
Replacement age of a bearing	hours	3,500	2,250	−1,250
Spare kits held	kits	3	3	0

Measure	Unit	Starting plan	Optimizer’s plan	Change
Two-year cost, mean	US$k	176.9	205.0	28.1
Two-year cost, 90th percentile	US$k	226.8	235.8	9.0
Failures in service, mean	failures	4.3	2.4	−1.9	✔ better
Planned replacements, mean	bearings	20.7	37.9	17.2
Chance that any failure finds no kit	of futures	2.1%	0.2%	−2.0%	✔ better
Machine-hours lost, mean	hours	52.1	28.4	−23.7	✔ better
Chance of losing more than 48 hours	of futures	42.1%	8.7%	−33.4%	✔ better
Accepted chance of losing more (the promise)	of futures	10.0%	10.0%

Machine-hours lost: the hours failures stop the machines, plus the waits for a kit; all eight machines, two years.

Two-year cost — cumulative probability

S-curve (cumulative probability) of Starting plan, Optimizer’s plan from the saved simulation.

The business question

A machine shop's eight spindles all got new bearings in this year's shutdown. A bearing that fails in service costs about US$21,000 and stops its machine for 12 hours, or 48 if no spare kit is on the shelf. MF-08 found replacing at 3,500 hours with three kits cheapest.

Now the shop has promised a customer limited downtime, so the Optimizer chooses the age and the kits together.

Who it is for: Maintenance and reliability engineers, plant managers, spare-parts and MRO planners.
Main outputs: The Optimizer's replacement age and spare kits against a starting plan (MF-08's cheapest option: replace at 3,500 hours, three kits) · for both plans: the two-year cost, failures, planned replacements, the chance that any failure finds no kit, the machine-hours lost and the chance of losing more than promised · the distributions of the cost and of the hours lost.

What the Optimizer decides

The Optimizer changes the blue cells. The starting plan is MF-08's cheapest option: replace each bearing at 3,500 hours and hold three spare kits.

Decision	Unit	Starting plan	Optimizer’s plan	Lowest	Highest
Replacement age of a bearing	hours	3,500	2,250	2,000	6,000
Spare kits held	kits	3	3	0	8

Goal: Minimise the mean two-year cost
Limit: Chance of losing more than promised at most 10%

The Optimizer’s run: Vertex Detector, 150 plans tried, each on 10,000 samples, in 47.8 seconds.

How the model works

Four sheets after this one, read from left to right. Each one feeds the next.

Inputs sheet
Operating hours a year; the bearing's Weibull shape and scale; the cost of a kit, the labour, the damage and the downtime of a failure. The resupply time of a kit and the cost of holding one; the machine-hours lost that the promise allows, and the accepted chance of losing more.
Decisions sheet
The two cells the Optimizer changes — the replacement age and the spare kits held — with their bounds, the starting plan they are compared with, the goal (the least mean two-year cost) and the limit (the chance of losing more machine-hours than promised).
Spindles sheet
VoseWeibull draws the lives of ten successive bearings on each spindle. In each plan a bearing comes out at the replacement age or when it fails, and the next one starts. Failures, planned replacements, failures that find no kit, the machine-hours lost and the two-year cost are outputs.
Results sheet
Both plans on the same simulated lives: the two-year cost, failures, the chance of running out of kits, the machine-hours lost and the chance of losing more than promised; where the cost goes; the distributions of the cost and of the hours lost.

ModelRisk techniques

ModelRisk Optimizer: replacement age in steps and whole spare kits
Downtime promise as a probability limit
Weibull bearing lives VoseWeibull
Both strategies on the same bearing lives

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The results in detail

Where the two-year cost goes

Mean cost of each part, US$k: what earlier replacement buys and what it costs.

Machine-hours lost in the two years — cumulative probability

S-curve (cumulative probability) of Starting plan, Optimizer’s plan, Hours the promise allows from the saved simulation.

Measure	Unit	Starting plan	Optimizer’s plan	Change
Planned replacements	US$k	82.7	151.7	68.9
Failures in service	US$k	89.6	49.5	−40.0	✔ better
Waiting for a kit	US$k	0.9	0.1	−0.8	✔ better
Holding the spare kits	US$k	3.8	3.8	–
Total: the mean two-year cost		176.9	205.0	28.1

Each part: its mean number in the two years × its cost (Spindles sheet); holding: kits × the cost of holding one.

How to read these results

The starting plan — MF-08's cheapest option, replacing each bearing at 3,500 hours with three spare kits — loses more than 48 machine-hours in about two futures in five: far more often than the one in ten the shop has accepted.
The Optimizer replaces each bearing much earlier, at 2,250 hours, and keeps the three spare kits. Failures in service fall by about half, so a failure rarely finds the shelf empty: two kits would cost about the same, but three lose less time. The chance of losing more than 48 hours falls to just under one in ten.
Keeping the promise costs about US$28,000 more over the two years, some 16%: about 38 planned replacements instead of 21 buy about two fewer failures. At 2,500 hours the plan would cost about US$20,000 less, but lose more than 48 hours in about one future in seven.
The cost does not fall smoothly with the age. Only the two years are costed, so it jumps where one more round of replacements fits into them: a spindle without a failure gets five new bearings at 2,250 hours, four at 2,500. The Optimizer searches the list of ages, so it finds such steps.
Try 72 hours on the Inputs sheet and run the Optimizer again: it then settles near 3,250 hours with four spare kits, and the cost falls a little below the starting plan's.

Run the Optimizer yourself. Open the workbook, open the Optimizer from the ModelRisk ribbon (the saved task opens with it) and press Start; then simulate to compare the plans.

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Inputs and assumptions

Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.

The spindles 1 input

Eight machining centres, all with new spindle bearings after this year's shutdown.

Assumption	Unit	Value
Operating hours a yearTwo shifts, five days a week.	hours	6,000

Bearing life 2 inputs

A Weibull distribution of operating hours to failure.

Assumption	Unit	Value
Weibull shapeAbove 1: the bearings wear out — the older, the likelier to fail.		2.50
Weibull scale63% of bearings fail by this age; fitted to the shop's records.	hours	7,000

Costs 6 inputs

Assumption	Unit	Value
Bearing kit	US$k	2.5
Labour to replace the bearingsPlanned or not.	US$k	1.5
A failure: damage to the shaft and housing	US$k	5.0
A failure: hours the machine standsStrip, rebuild and test the spindle.	hours	12
Contribution lost per hour a machine stands	US$k	1.00
No kit on the shelf: extra hours waitingFor an expedited kit from the maker.	hours	36

Spare kits 2 inputs

How many to hold is a decision (Decisions sheet).

Assumption	Unit	Value
Resupply time of a kitOrdered as soon as a failure uses one.	weeks	8
Cost of holding a kitCapital, storage and obsolescence.	per year	25%

Downtime promised 2 inputs

The limit the Optimizer must respect.

Assumption	Unit	Value
Machine-hours lost that the promise allowsIn the two years, all eight machines: four failures, or one that waits for a kit.	hours	48
Accepted chance of losing moreAt most one future in ten may lose more machine-hours than the promise allows.	of futures	10%

Units and conventions

Hours: Operating hours since this year's shutdown: 6,000 a year, 12,000 in the two years.
Money: US$ thousand (US$k), not discounted over the two years.
Replacement age: Each bearing comes out when it reaches this age or when it fails, whichever comes first.
Stock-out: A failure that finds no spare kit on the shelf. Every kit used by a failure is reordered at once and arrives one resupply time later.
Machine-hours lost: The hours a failure stops its machine, plus the wait for an expedited kit when none is on the shelf. Planned replacements lose none.

Key assumptions and limitations

Bearings: Lives independent and Weibull; a new bearing is as good as new; all eight start new after the shutdown.
Planned work: Done in weekend maintenance windows: no lost production; its kits are ordered ahead and never wait.
Spare kits: One kit reordered for each failure; a failure that finds no kit waits for an expedited one.
Two years: Only the two years are costed. The cost jumps where one more round of replacements fits into them, and the age of the bearings left in service at the end is not charged.
Optimizer: Each plan the Optimizer tries is judged on the same 10,000 simulated two-year periods (common random numbers, seed 1) as the simulation on the Results sheet, so plans are compared fairly and the limit the Optimizer met holds on the Results sheet too.
Data: The shop and all figures are invented for this example.

How to use it

Enter your operating hours, the bearing's Weibull life (fitted to your failure records, see MF-03), your costs and your downtime promise on the Inputs sheet.
On the ModelRisk ribbon, open the Optimizer: the task is saved in this workbook. Press Start; each plan it tries is simulated in full, so a run takes a while. When it finishes, apply the best solution: the replacement age and spare kits on the Decisions sheet change.
Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set) to compare the new plan with the starting plan on the Results sheet.
To watch the search from the beginning, copy the starting plan onto the Optimizer’s plan first.

ModelRisk functions used

ModelRisk Optimizer: Chooses the replacement age and the spare kits: least mean two-year cost, with the chance of losing more machine-hours than promised at most the accepted chance.
VoseWeibull: The life of each bearing, in operating hours.
VoseOutput: Failures, planned replacements, stock-outs, machine-hours lost and the cost of both plans, recorded at every sample.
VoseSimMean, VoseSimPercentile, VoseSimProbability: Statistics of both plans on the Results sheet.

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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.