Consider the traction converter cabinet of a rail vehicle: the power electronics that take the line supply and drive the motors, maintained in a depot road with the vehicle out of service. Seven replaceable items, 123 failures per 10⁶ hours between them. Every value is an illustrative teaching figure; the arithmetic is MIL-HDBK-472's.
The maintenance concept, settled first: repair by replacement at item level, by a depot technician with the vehicle stationary and the cabinet accessible from one side, complete when the converter has passed its power-on check.
The task times
Each repair broken into its elemental activities, in minutes:
| Item | λ | loc | iso | disas | inter | reas | align | check | Total |
|---|---|---|---|---|---|---|---|---|---|
| A · Cooling fan unit | 40 | 4 | 3 | 6 | 8 | 6 | 0 | 5 | 32 |
| B · Gate driver card | 22 | 4 | 14 | 10 | 6 | 10 | 4 | 12 | 60 |
| C · Control card | 18 | 4 | 9 | 8 | 5 | 8 | 18 | 15 | 67 |
| D · Power module stack | 15 | 4 | 8 | 34 | 26 | 32 | 6 | 18 | 128 |
| E · Line contactor | 12 | 4 | 7 | 12 | 9 | 12 | 5 | 8 | 57 |
| F · DC-link capacitor bank | 9 | 4 | 6 | 22 | 14 | 20 | 0 | 10 | 76 |
| G · Current sensor | 7 | 4 | 26 | 9 | 5 | 9 | 7 | 11 | 71 |
Three rows are worth reading before any arithmetic. The fan is the most frequent failure and the quickest repair, because it was designed to be swapped. The power module is a two-hour job dominated by getting at it and putting it back. And the current sensor has a 26-minute isolation time, four times anyone else's, which is not a mechanical property at all: it is the ambiguity group the testability analysis would have found.
The mean, weighted properly
Mct = Σ λᵢ tᵢ ÷ Σ λᵢ = 7,591 ÷ 123 = 61.7 minutes = 1.03 hours
The unweighted average of those seven totals is 70.1 minutes, which is the number a spreadsheet gives and no technician experiences. The difference is the fan: the most common repair is also the shortest, and the weighting is what notices.
The distribution, and the number the contract wants
Fitting on the logarithms, weighted the same way:
μ = 4.0203, σ = 0.4481
| Quantity | Value |
|---|---|
Median, e^μ | 55.7 min |
Mean, e^(μ + σ²/2) | 61.6 min |
Mmax at 90 per cent | 99.0 min |
Mmax at 95 per cent | 116.4 min |
The fitted mean of 61.6 against the weighted arithmetic mean of 61.7 is the internal check that the lognormal is describing this mix honestly. And the 95th percentile is nearly twice the mean, which is the number a depot slot has to be sized on.
Where the time actually goes
Two sorts of the same table, and they say different things.
By item, weighted by λ·t, the ranking is not the failure-rate ranking:
| Item | Share of the technician's year | Failure-rate rank |
|---|---|---|
| D · power module stack | 25.3% | 4 of 7 |
| B · gate driver card | 17.4% | 2 |
| A · cooling fan unit | 16.9% | 1 |
| C · control card | 15.9% | 3 |
| E · line contactor | 9.0% | 5 |
| F · DC-link capacitors | 9.0% | 6 |
| G · current sensor | 6.5% | 7 |
The power module fails a third as often as the fan and consumes half again as much of the year.
By activity, summed across the cabinet and weighted:
| Activity | Weighted mean | Share |
|---|---|---|
| Disassembly | 12.3 min | 20.0% |
| Reassembly | 12.0 min | 19.4% |
| Checkout | 10.3 min | 16.7% |
| Interchange | 9.8 min | 15.8% |
| Isolation | 8.4 min | 13.6% |
| Alignment | 5.0 min | 8.0% |
| Localisation | 4.0 min | 6.5% |
Access is 39.4 per cent of the time and diagnosis is 20.1. That is the finding, and it belongs to whoever designs the enclosure.
What a perfect diagnostic would be worth
Suppose the testability work succeeds completely: every fault isolated to one item in five minutes, including the current sensor's 26.
Mct: 61.7 → 57.7 minutes, a 6.5 per cent cut · Mmax(95): 116.4 → 106.1 minutes
Worth having, and smaller than most people expect. Diagnosis is a fifth of the technician's time on this cabinet, so perfecting it cannot buy more than a fifth, and it buys a third of that because most isolation times were already short. Halving the power module's disassembly and reassembly, 66 minutes of its 128, would be worth considerably more, and that is a decision about fasteners and clearances taken while the cabinet is still a drawing.
What it means for availability
At 123 per 10⁶ hours the cabinet's MTBF is 8,130 hours, so at Mct = 1.03 h:
A = 8,130 ÷ (8,130 + 1.03) = 0.999873, about 66 minutes of downtime a year
and with the isolation fix, 62 minutes. Four minutes a year, which is the honest scale of the availability argument and a reminder of what this analysis is really for: it is a design tool for the maintenance burden, not an availability lever. The availability case for this vehicle is dominated by what happens before the technician arrives, not by what happens afterwards.