Exercise set

Clinical Equipment Fleet Maintenance and Availability Exercises

Worked clinical-equipment exercises for acceptance, PM capacity, availability, loaners, recalls, spares, batteries and release gates.

Branch: Biomedical Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises practise clinical equipment fleet management as an engineering availability problem. They cover acceptance readiness, preventive maintenance capacity, inherent and operational availability, loaner pools, electrical safety screening, recall closure, replacement review, PM backlog recovery, risk-weighted triage, service response, critical spares, transport batteries, utilization, lifecycle cost and release gates.

The focus is narrower than general healthcare technology management. A fleet page should answer whether installed clinical assets can safely remain in service with enough maintenance capacity, test evidence, spare coverage, recall control and downtime resilience.

How to Use These Exercises

For each calculation, define:

the device family, fleet size, location and clinical dependency;
the maintenance, safety, recall, battery or spare-part control being tested;
the downtime definition used by clinicians, not only by technicians;
the threshold that triggers release, restriction, escalation or replacement review;
the records needed to prove that the same asset configuration was checked.

The common mistake is treating a high administrative completion percentage as a release decision. Clinical engineering evidence must be device-level evidence when patient care depends on that device.

Release Evidence Notes

Fleet readiness evidence should be traceable to asset identifiers, locations, accessories, software versions, service records, safety-test results, battery state and clinical ownership.

Availability evidence should state the downtime basis. Hands-on repair time, parts delay, cleaning release, clinical handoff and documentation closure can produce very different availability values.

Maintenance evidence should include capacity and backlog. A PM program is weak when the annual plan looks feasible but overdue critical assets accumulate faster than the team can recover.

Spare and loaner evidence should be tied to real failure demand. A spare that is on hand but already committed to an open work order does not protect the next failure.

Engineering Boundary Notes

These calculations are simplified training exercises. Real clinical engineering decisions also require manufacturer instructions, local procedures, competent-person review, applicable standards, risk management, infection control, cybersecurity review, clinical governance and regulatory obligations.

A pass in one calculation does not release a device by itself. A fleet can pass PM capacity and still fail because a recall is open, the battery reserve is weak, leakage current is out of limit or clinical users have not accepted the downtime plan.

Scenario Map

Scenario	Exercises	Primary calculation	Engineering decision
Readiness and maintenance	1-6, 11-12	acceptance completion, PM capacity, safety screening, recall closure and backlog recovery	Decide whether the fleet can remain in routine service.
Availability and downtime	3-4, 10, 13, 16	MTBF, MTTR, loaners, operational availability and service response	Decide whether clinical downtime is covered.
Spares, batteries and lifecycle	7-9, 14-18	utilization, repair ratio, reorder point, battery runtime, lifecycle cost and release gates	Decide whether the fleet needs mitigation, replacement or restricted use.

Exercise 1: Acceptance Readiness Before Clinical Use

A hospital receives:

N=42

infusion pumps. Before clinical release, each pump requires asset registration, electrical safety test, functional check, accessory check and user-location assignment. The release file shows:

Gate	Completed
asset registration	$42$
electrical safety	$39$
functional check	$40$
accessory check	$38$
user-location assignment	$41$

The local release rule requires every gate to be complete for every pump. Calculate the limiting completion percentage and decide whether the fleet can be released.

Solution

The limiting gate is accessory check:

N_{min}=38

The limiting completion percentage is:

C_{lim}=\dfrac{38}{42}=0.9048=90.5\%

The number of pumps that cannot be fully released is at least:

N_{hold}=42-38=4

The fleet cannot be released as a complete clinical fleet because one gate is below $100\%$ .

Engineering Comment

Acceptance readiness is an all-gate decision. A pump with a completed asset record but missing accessory evidence can still fail at the bedside because the configured system was not actually checked.

Plausibility Check

Four missing accessory checks out of $42$ pumps gives a little under $10\%$ incomplete, so $90.5\%$ limiting completion is plausible.

Exercise 2: Preventive Maintenance Workload Capacity

A fleet contains:

N=180

patient monitors. Each monitor requires one preventive maintenance event every six months. Each event takes:

t_{PM}=38\ \text{min}

Two technicians each have:

H=92\ \text{available PM h/month}

after emergency work and documentation. Calculate monthly PM demand and capacity margin.

Solution

Annual PM events:

E_y=2N=360\ \text{events/year}

Monthly events:

E_m=\dfrac{360}{12}=30\ \text{events/month}

Monthly PM labor demand:

L_m=30\dfrac{38}{60}=19.0\ \text{h/month}

Monthly available PM labor:

L_c=2(92)=184\ \text{h/month}

Capacity margin:

M=L_c-L_m=184-19=165\ \text{h/month}

The team has enough capacity for this PM workload.

Engineering Comment

The arithmetic looks comfortable, but a real PM plan also depends on access windows, cleaning state, clinical holds, calibration fixtures, spare accessories and technician competence.

Plausibility Check

Thirty short PM events per month should be well below two full technicians. A large positive margin is expected.

Exercise 3: Fleet Availability from MTBF and MTTR

A ventilator fleet has:

MTBF=5200\ \text{h},\qquad MTTR=9\ \text{h}

Estimate inherent availability.

Solution

Inherent availability is:

A_i=\dfrac{MTBF}{MTBF+MTTR}

Substitute:

A_i=\dfrac{5200}{5200+9}=0.99827

Therefore:

A_i=99.83\%

Engineering Comment

Inherent availability excludes logistics delay. If a failed ventilator waits three days for a part, clinicians experience much lower operational availability than this value suggests.

Plausibility Check

The repair time is tiny compared with $5200$ hours, so the availability should be close to $100\%$ .

Exercise 4: Loaner Pool for Downtime Coverage

A ward uses:

N=72

syringe pumps. Historical peak-week records show that:

6.0\%

of the fleet is unavailable for PM, repair, cleaning or battery replacement. The ward wants:

3

additional pumps as surge margin. Estimate the minimum loaner pool.

Solution

Expected unavailable pumps:

N_u=0.06(72)=4.32

Round up for whole devices:

N_{cover}=5

Add surge margin:

N_{loaner}=5+3=8

The minimum loaner pool is:

8\ \text{pumps}

Engineering Comment

Loaners must include compatible accessories, charged batteries, cleaning release and location tracking. A physical pump that cannot be configured for the ward does not provide real downtime coverage.

Plausibility Check

Eight loaners are about $11.1\%$ of the $72$ -pump fleet, which is plausible for peak-week coverage.

Exercise 5: Electrical Safety Screening

A patient-connected device is tested after repair. The project screening limits are:

I_{leak}\le 100\ \mu\text{A},\qquad R_{iso}\ge 50\ \text{M}\Omega

The measured values are:

I_{leak}=84\ \mu\text{A},\qquad R_{iso}=62\ \text{M}\Omega

Calculate the leakage-current margin and insulation-resistance margin.

Solution

Leakage-current margin:

M_I=100-84=16\ \mu\text{A}

Percentage margin relative to the limit:

M_{I,\%}=\dfrac{16}{100}=16.0\%

Insulation-resistance margin:

M_R=62-50=12\ \text{M}\Omega

Percentage margin relative to the minimum:

M_{R,\%}=\dfrac{12}{50}=24.0\%

Both simplified screens pass.

Engineering Comment

This does not replace the applicable safety standard or manufacturer procedure. It only shows how a project-level screen can be converted into a release margin.

Plausibility Check

The measured leakage is below the maximum, and the measured insulation resistance is above the minimum, so both positive margins are expected.

Exercise 6: Recall Closure Rate

A safety notice affects:

N=126

devices. After two weeks the team has located $118$ devices, corrected $104$ devices and verified documentation for $99$ devices. Calculate the documented closure percentage.

Solution

The release evidence is limited by verified documentation:

N_c=99

Closure percentage:

C=\dfrac{99}{126}=0.7857=78.6\%

Open documented closures:

N_o=126-99=27

Documented closure is $78.6\%$ , with $27$ devices still not closed in the release record.

Engineering Comment

Recall management is not only correction count. The clinical engineering file must show the affected asset, location, correction evidence, quarantine rule and owner for remaining exceptions.

Plausibility Check

About one quarter of the devices are still not documented as closed, so a result near $79\%$ is reasonable.

Exercise 7: Utilization-Adjusted PM Interval

A transport monitor has a nominal PM interval of:

T_0=12\ \text{months}

The high-use service line operates at:

u=1.35

times the reference utilization. The local rule scales the interval inversely with utilization:

T=\dfrac{T_0}{u}

Calculate the adjusted PM interval.

Solution

Substitute:

T=\dfrac{12}{1.35}=8.89\ \text{months}

Rounded to a practical schedule:

T\approx 9\ \text{months}

Engineering Comment

Utilization scaling is only a local planning model. Battery wear, connector damage, transport vibration, cleaning chemistry and failure history may justify a shorter interval.

Plausibility Check

Higher utilization should shorten the interval. A $35\%$ utilization increase moving $12$ months to about $9$ months is plausible.

Exercise 8: Incident Evidence Completeness

A review of:

N=18

clinical equipment incidents requires five evidence fields: asset ID, patient-care context, user statement, service finding and corrective action. The audit finds:

Evidence field	Records complete
asset ID	$18$
patient-care context	$15$
user statement	$14$
service finding	$16$
corrective action	$13$

Calculate the weakest-field completeness and the number of records blocking closure.

Solution

The weakest field is corrective action:

N_{min}=13

Completeness:

C=\dfrac{13}{18}=0.722=72.2\%

Records blocking full closure:

N_b=18-13=5

The incident package is not release-ready.

Engineering Comment

Incident evidence is a learning system. Without corrective action, the record may document harm or near miss but fail to reduce recurrence.

Plausibility Check

Five incomplete corrective-action records out of $18$ is a large gap, so completeness near $72\%$ is plausible.

Exercise 9: Replacement Review from Repair Cost Ratio

An analyzer costs:

C_{new}=96000\ \text{USD}

to replace. During the last year, repair cost was:

C_r=27600\ \text{USD}

The local review threshold is:

25\%

of replacement cost. Calculate the repair cost ratio and decide whether replacement review is triggered.

Solution

Repair cost ratio:

R_c=\dfrac{27600}{96000}=0.2875

Therefore:

R_c=28.8\%

Threshold margin:

M=28.8\%-25.0\%=3.8\ \text{percentage points}

Replacement review is triggered.

Engineering Comment

The ratio does not automatically justify purchase. The review should include downtime, parts support, quality-control failures, user complaints, reagent compatibility, cybersecurity support and transition risk.

Plausibility Check

$24000$ would be exactly $25\%$ of $96000$ , and the observed cost is higher, so the trigger should be exceeded.

Exercise 10: Operational Availability With Logistics Delay

An ultrasound fleet has:

MTBF=4100\ \text{h}

Hands-on repair time is:

8\ \text{h}

Parts delay, cleaning release and clinical handoff add:

34\ \text{h}

Calculate operational availability.

Solution

Total downtime per failure:

DT=8+34=42\ \text{h}

Operational availability:

A_o=\dfrac{4100}{4100+42}=0.9899

Therefore:

A_o=98.99\%

Engineering Comment

Operational availability uses downtime that matters to clinical users. It makes spare parts, cleaning release and handoff visible instead of hiding them outside MTTR.

Plausibility Check

Forty-two hours is about $1\%$ of $4100$ hours, so availability just under $99\%$ is plausible.

Exercise 11: Preventive Maintenance Backlog Burn-Down

A fleet has:

B_0=84

overdue PM events. New PM events become due at:

18\ \text{events/week}

The team can complete:

30\ \text{events/week}

for the next recovery period. Estimate the net backlog burn-down rate and weeks to clear the backlog.

Solution

Net burn-down rate:

r=30-18=12\ \text{events/week}

Weeks to clear:

t=\dfrac{84}{12}=7\ \text{weeks}

The backlog clears in about:

7\ \text{weeks}

if access and staffing remain unchanged.

Engineering Comment

Backlog plans should prioritize clinical criticality, not only age. A low-risk device overdue by four weeks may be less urgent than a life-support device overdue by one week.

Plausibility Check

At twelve net events per week, eight weeks would clear $96$ events, so seven weeks for $84$ events is exact.

Exercise 12: Risk-Weighted PM Backlog Triage

Three overdue groups have the following values:

Group	Count	Criticality weight	Weeks overdue
A	$12$	$5$	$3$
B	$28$	$2$	$5$
C	$9$	$4$	$2$

Use:

S=NwT

where $N$ is count, $w$ is criticality weight and $T$ is weeks overdue. Rank the groups.

Solution

Group A:

S_A=12(5)(3)=180

Group B:

S_B=28(2)(5)=280

Group C:

S_C=9(4)(2)=72

The ranking is:

B>A>C

Engineering Comment

This score is a triage aid, not a substitute for clinical judgement. A single high-dependency asset may outrank a larger group when no backup exists.

Plausibility Check

Group B has many devices and high overdue time, so it reasonably becomes the largest weighted backlog.

Exercise 13: Service-Response Downtime Exposure

A critical fleet has:

N=18,\qquad MTBF=3600\ \text{h}

Each month has:

720\ \text{h}

The current service contract produces $8$ h response, $6$ h repair and $4$ h release time per failure. A proposed cheaper contract changes response time to $44$ h while repair and release remain unchanged. The downtime exposure limit is:

90\ \text{device-h/month}

Estimate monthly failures and compare both contracts.

Solution

Expected monthly failures:

\lambda_m=\dfrac{18(720)}{3600}=3.6\ \text{failures/month}

Current downtime per failure:

DT_c=8+6+4=18\ \text{h}

Current exposure:

E_c=3.6(18)=64.8\ \text{device-h/month}

Proposed downtime per failure:

DT_p=44+6+4=54\ \text{h}

Proposed exposure:

E_p=3.6(54)=194.4\ \text{device-h/month}

The current contract passes the $90$ device-hour limit. The proposed contract fails.

Engineering Comment

Contract review is an availability decision. A lower price can be unsafe if slower response consumes the clinical downtime budget.

Plausibility Check

The proposed response adds $36$ h per failure. At $3.6$ failures per month, that adds $129.6$ device-hours, matching the exposure jump.

Exercise 14: Critical Spare-Part Reorder Point

A ventilator fleet uses a critical module at an average rate of:

3.75\ \text{modules/month}

Supplier lead time is:

2\ \text{months}

Safety stock is:

4\ \text{modules}

Current on-hand stock is $9$ modules, but $2$ modules are already committed to open repairs. The target is to order up to $14$ modules. Calculate reorder point, effective stock, shortfall and order quantity.

Solution

Lead-time demand:

D_L=3.75(2)=7.5\ \text{modules}

Reorder point:

ROP=D_L+SS=7.5+4=11.5

Round up:

ROP=12\ \text{modules}

Effective stock:

S_e=9-2=7\ \text{modules}

Shortfall:

\Delta=12-7=5\ \text{modules}

Order quantity to target:

Q=14-7=7\ \text{modules}

The fleet should reorder.

Engineering Comment

Committed stock is not protective stock. A spare already assigned to an open repair cannot protect the next failure before replenishment arrives.

Plausibility Check

Two months of demand is about $8$ modules, and safety stock raises the reorder point to about $12$ , so an effective stock of $7$ should trigger an order.

Exercise 15: Transport Device Battery Runtime and Reserve Gate

A transport monitor has end-of-life usable battery energy:

E_{EOL}=210\ \text{Wh}

The battery is at:

SOC=0.82

The clinical load is:

P=68\ \text{W}

The transport requires $1.8$ h and the local reserve requirement is $0.5$ h. Decide whether the monitor can be dispatched.

Solution

Available energy:

E_a=210(0.82)=172.2\ \text{Wh}

Runtime:

t_r=\dfrac{172.2}{68}=2.53\ \text{h}

Required runtime:

t_{req}=1.8+0.5=2.3\ \text{h}

Reserve margin:

M=2.53-2.30=0.23\ \text{h}=14\ \text{min}

The battery runtime passes the simplified dispatch gate.

Engineering Comment

The reserve is narrow. A real dispatch check should include battery age, alarms, accessories, ambient temperature, charging history and backup power options.

Plausibility Check

About $172$ Wh divided by about $70$ W should give roughly $2.5$ h, so the calculation is credible.

Exercise 16: Utilization and Spare Coverage for Peak Demand

A department owns:

N=54

monitors. Peak census requires:

N_d=47

monitors in use. The expected unavailable fraction during the peak week is:

u=8\%

Calculate expected available devices and reserve margin.

Solution

Expected unavailable devices:

N_u=0.08(54)=4.32

Expected available devices:

N_a=54-4.32=49.68

Reserve margin:

M=49.68-47=2.68\ \text{devices}

Rounded conservatively, the department has about two devices of margin.

Engineering Comment

Average availability is not a guarantee. If unavailable devices cluster in the same location or accessory type, the clinical reserve may disappear.

Plausibility Check

An $8\%$ loss from $54$ is a little over four devices, leaving just under fifty available. Demand of $47$ leaves a small margin.

Exercise 17: Lifecycle Cost per Available Device

A device fleet has annual ownership cost:

C_y=342000\ \text{USD/year}

The fleet has $38$ devices and expected operational availability:

A_o=0.972

Calculate the annual cost per expected available device.

Solution

Expected available devices:

N_a=38(0.972)=36.936

Annual cost per expected available device:

C_a=\dfrac{342000}{36.936}=9259\ \text{USD/device-year}

Rounded:

C_a\approx 9260\ \text{USD/device-year}

Engineering Comment

This metric is useful for replacement planning because it penalizes fleets that are expensive and frequently unavailable. It should still be balanced against clinical need and transition risk.

Plausibility Check

If all $38$ devices were available, cost would be $9000$ per device-year. Lower availability should raise the value slightly, which it does.

Exercise 18: Fleet Release Gate

A release review for a high-dependency fleet assigns weights to five gates:

Gate	Weight	Result
PM current	$0.25$	$0.96$
electrical safety complete	$0.20$	$1.00$
recall closure	$0.20$	$0.94$
loaner and spare readiness	$0.20$	$0.88$
battery reserve evidence	$0.15$	$0.91$

The fleet release threshold is:

S\ge 0.94

and no gate may be below:

0.90

Calculate the weighted score and decision.

Solution

Weighted score:

\begin{aligned} S&=0.25(0.96)+0.20(1.00)+0.20(0.94)+0.20(0.88)+0.15(0.91)\\ &=0.240+0.200+0.188+0.176+0.1365\\ &=0.9405 \end{aligned}

The weighted score is:

S=94.05\%

The weighted score passes, but the loaner and spare gate is:

0.88<0.90

The fleet is held or restricted until loaner and spare readiness is corrected.

Engineering Comment

Weighted scoring should not hide a critical weak gate. A high total score is not enough when the missing control is directly tied to patient-care continuity.

Plausibility Check

The score is just above $94\%$ , but one gate clearly violates the floor. A hold decision is consistent with the stated rule.

Validation Package Checklist

Asset list includes device ID, model, location, owner, software version, accessory set and service status.
PM capacity is calculated from real available labor, not nominal staffing.
Availability definitions separate inherent repair time from logistics-inclusive clinical downtime.
Loaner and spare pools account for committed devices, cleaning state, accessories and peak demand.
Electrical safety and battery checks use the applicable procedure before release.
Recall closure is documented at asset level, including exceptions and quarantine status.
Replacement review includes repair cost, downtime, parts support, cybersecurity support and clinical transition risk.
Release decisions preserve weak-gate holds instead of relying only on aggregate percentages.

Common Release Mistakes

Counting a device as ready because it exists in inventory while accessories, battery, safety or software evidence is missing.
Using MTBF and MTTR without including parts delay, cleaning release and clinical handoff.
Sizing loaners from average downtime while ignoring peak weeks and common-mode failures.
Treating a recall correction as closed before documentation proves the affected installed asset was corrected.
Counting committed spare parts as available spare parts.
Accepting a cheaper service contract without calculating monthly device-hour exposure.
Dispatching transport equipment from nominal battery capacity instead of end-of-life usable energy and current state of charge.
Allowing a weighted score to override a failed high-criticality gate.

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