Exercise set

Supplier Performance Lead Time, Disruption, and Release Evidence Exercises

Solved supplier-performance exercises for measured lead time, delivery service, outage coverage, dual sourcing, quality release and recovery gates.

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

These exercises practise supplier-release decisions: measured lead time, delivery promise performance, outage coverage, dual-source recovery, supplier capacity, backlog burn-down, quality release, incoming inspection, ramp readiness, expedite dependence and supplier release gates.

The goal is to decide whether a supplier can support a released plan with evidence, not promises. A supplier may meet ship date but miss production need if quality release, transport, inspection, documentation, packaging or recovery capacity fails.

Assume simplified screening data unless an exercise states otherwise. Real supplier release should also check approved source status, process change control, capacity evidence, quality history, inspection status, route risk, customs delay, alternate-source qualification, engineering deviation and shortage escalation.

Release Evidence Notes

Supplier evidence should separate quoted lead time, confirmed order date, actual ship date, delivery date, receiving timestamp and quality-release timestamp. The boundary must match the release decision.

Performance evidence should include mean, tail and on-time percentage. A supplier with acceptable average lead time can still fail because late deliveries are frequent or severe.

Disruption evidence should show available stock, alternate-source capacity, ramp timing, recovery backlog and quality approval state. Expedites are not a stable release plan unless their capacity and risk are explicit.

Supplier release should connect quantity, timing, quality and documentation. A part is not released to production until the supplied material is approved, traceable and usable at the correct revision.

Engineering Boundary Notes

This page covers supplier performance and supplier-release evidence. Inventory policy belongs in the inventory-policy exercise set. Kanban, unit load, inspection delay and line-side execution belong in the material replenishment exercise set.

If the issue is supplier-change qualification deliverables rather than recurring performance math, use the supplier-change qualification project.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Lead time and delivery service	1-5	measured lead time, on-time rate, tail delay and z margin	Use measured lead time or restrict release.
Disruption and recovery	6-10	outage coverage, alternate capacity, backlog burn-down and ramp	Approve, escalate or throttle demand.
Quality and release evidence	11-15	PPM, inspection yield, documentation closure and deviation exposure	Release, hold or requalify material.
Supplier gate	16-18	expedite dependence, capacity margin and hard gates	Release, restrict or reject supplier plan.

Exercise 1: Mean Measured Lead Time

A supplier promises:

L_p=8\ \text{days}

Measured lead times are:

8,\ 9,\ 8,\ 11,\ 10,\ 9\ \text{days}

Find the mean.

Solution

Mean lead time:

\bar{L}=\dfrac{8+9+8+11+10+9}{6}=\dfrac{55}{6}=9.17\ \text{days}

Engineering Comment

Planning should use measured performance until supplier recovery evidence proves the promise is reliable.

Plausibility Check

Four values exceed eight days, so the mean should exceed the promise.

Exercise 2: On-Time Delivery Rate

Using the same six deliveries, count deliveries at or below:

8\ \text{days}

Find on-time percentage.

Solution

Two deliveries meet promise:

8,\ 8

On-time rate:

P=\dfrac{2}{6}=0.333=33.3\%

Engineering Comment

The promise is not credible as a planning input. A low on-time rate should trigger recovery action or a larger planning buffer.

Plausibility Check

Only two of six meet the promised lead time, so one third is expected.

Exercise 3: Lead-Time Delay Margin

Required production need date allows:

L_{max}=10\ \text{days}

Measured mean lead time is:

9.17\ \text{days}

Find mean margin.

Solution

Margin:

M=10-9.17=0.83\ \text{days}

Engineering Comment

The average margin is less than one day. Tail delivery performance and inspection delay may consume it.

Plausibility Check

The mean is slightly below the maximum, leaving a small positive margin.

Exercise 4: Lead-Time Z Screen

Measured lead time has:

\mu=9.17\ \text{days},\qquad \sigma=1.17\ \text{days}

Need date allows:

L_{max}=10\ \text{days}

Find z margin.

Solution

Use:

z=\dfrac{L_{max}-\mu}{\sigma}

Thus:

z=\dfrac{10-9.17}{1.17}=0.71

Engineering Comment

A z margin below one is weak for a constrained supplier. The release plan should not rely on average lead time alone.

Plausibility Check

The margin is less than one standard deviation, so z below one is expected.

Exercise 5: Late-Delivery Tail Estimate

For:

z=0.71

use a one-sided normal tail of:

23.9\%

Estimate probability of missing the need date.

Solution

The tail probability is:

P(L>10)\approx23.9\%

Engineering Comment

Nearly one in four late deliveries is not a stable release basis for constrained production.

Plausibility Check

A z margin below one should produce a large tail probability.

Exercise 6: Supplier Outage Coverage

Quality-cleared safety stock is:

SS=3600\ \text{units}

Demand is:

d=700\ \text{units/week}

Supplier outage is expected to last:

4\ \text{weeks}

Check coverage.

Solution

Outage demand:

D_o=700(4)=2800

Remaining stock:

S_r=3600-2800=800

The outage is covered.

Engineering Comment

This assumes the stock is usable and not allocated. If quality or revision status is wrong, the coverage is false.

Plausibility Check

Four weeks consumes less than the available stock.

Exercise 7: Maximum Covered Outage

Using:

SS=3600,\qquad d=700\ \text{units/week}

find maximum covered outage duration.

Solution

Coverage duration:

T_{max}=\dfrac{3600}{700}=5.14\ \text{weeks}

Engineering Comment

The plan has only about one extra week beyond the four-week outage assumption. Monitor recovery date closely.

Plausibility Check

Seven hundred units per week consumes thirty-five hundred units in five weeks, so $5.14$ weeks is plausible.

Exercise 8: Dual-Source Recovery Capacity

Normal demand is:

D=5000\ \text{units/week}

Primary supplier can deliver:

4200\ \text{units/week}

Alternate supplier can deliver:

1100\ \text{units/week}

after ramp. Find reserve.

Solution

Combined capacity:

C=4200+1100=5300

Reserve:

R=C-D=5300-5000=300\ \text{units/week}

Engineering Comment

The reserve is small. Any quality hold, transport delay or yield loss can erase recovery margin.

Plausibility Check

Combined capacity is slightly above demand, so reserve is positive but modest.

Exercise 9: Recovery Backlog Burn-Down

Supplier backlog is:

B=2400\ \text{units}

Weekly capacity above demand is:

R=300\ \text{units/week}

Find recovery time.

Solution

Time:

T=\dfrac{B}{R}=\dfrac{2400}{300}=8\ \text{weeks}

Engineering Comment

An eight-week recovery may be too slow for a launch or shutdown window. Demand throttling or more alternate capacity may be needed.

Plausibility Check

Three hundred units per week clears twenty-four hundred units in eight weeks.

Exercise 10: Ramp Gap

Alternate supplier ramp takes:

1\ \text{week}

Demand during ramp is:

5000\ \text{units}

Primary supplier delivers:

4200\ \text{units}

Find ramp-week gap.

Solution

Gap:

G=5000-4200=800\ \text{units}

Engineering Comment

Steady recovery capacity after ramp does not protect the ramp week. Buffer stock or demand smoothing must cover the gap.

Plausibility Check

Primary capacity is eight hundred units below demand.

Exercise 11: Supplier Quality PPM

Incoming lots total:

N=85000\ \text{units}

Defects found:

d=34

Calculate PPM.

Solution

PPM:

PPM=\dfrac{d}{N}(10^6)=\dfrac{34}{85000}(10^6)=400

Engineering Comment

PPM should be separated by defect type and severity. A low count of critical defects can still block release.

Plausibility Check

Thirty-four defects in eighty-five thousand units is four defects per ten thousand, or four hundred per million.

Exercise 12: Incoming Inspection Yield

An incoming inspection samples:

400

units and rejects:

12

Find inspection yield.

Solution

Accepted units:

N_a=400-12=388

Yield:

Y=\dfrac{388}{400}=0.970=97.0\%

Engineering Comment

Inspection yield is not supplier process capability. It is release evidence for the inspected lots and inspection method.

Plausibility Check

Twelve rejects in four hundred is three percent rejected, so yield is ninety-seven percent.

Exercise 13: Documentation Closure

A supplier release package requires:

N=18

documents. Approved documents:

N_a=17

The rule requires all documents. Check release.

Solution

Closure:

C=\dfrac{17}{18}=94.4\%

The hard gate fails because:

94.4\%<100\%

Engineering Comment

Missing certificates, deviations or inspection plans can block release even when material is present.

Plausibility Check

One missing document makes completion high but not complete.

Exercise 14: Capacity Claim Margin

A supplier claims capacity:

C_c=6200\ \text{units/week}

Demonstrated validated capacity is:

C_v=5400\ \text{units/week}

Demand is:

D=5000\ \text{units/week}

Find validated reserve.

Solution

Validated reserve:

R_v=C_v-D=5400-5000=400\ \text{units/week}

Claimed reserve would be:

R_c=6200-5000=1200\ \text{units/week}

Engineering Comment

Release should use demonstrated capacity, not unvalidated supplier claims.

Plausibility Check

The validated reserve is much smaller than the claimed reserve because validated capacity is lower.

Exercise 15: Deviation Exposure

A supplier deviation applies to:

N_d=3200

units. Daily production demand is:

d=800\ \text{units/day}

Find days of production exposed to the deviation.

Solution

Exposure:

T=\dfrac{N_d}{d}=\dfrac{3200}{800}=4\ \text{days}

Engineering Comment

Deviation release should state affected quantity, serial range, risk controls and expiry. Four production days is not negligible.

Plausibility Check

Eight hundred units per day consumes thirty-two hundred units in four days.

Exercise 16: Expedite Dependence

A recovery plan needs:

5000\ \text{units/week}

Normal validated supply is:

4400\ \text{units/week}

Expedites provide:

700\ \text{units/week}

Find expedite share of weekly supply.

Solution

Total supply:

S=4400+700=5100

Expedite share:

E=\dfrac{700}{5100}=0.137=13.7\%

Engineering Comment

High expedite dependence may be acceptable for a short recovery but weak for normal release.

Plausibility Check

Seven hundred out of just over five thousand is a little under fourteen percent.

Exercise 17: Supplier Risk Priority

Supplier risk scores are:

S=8,\quad O=4,\quad D=5

A containment action improves detection to:

D=3

Compute RPN before and after.

Solution

Before:

RPN_1=8(4)(5)=160

After:

RPN_2=8(4)(3)=96

Engineering Comment

Detection improvement helps, but occurrence remains unchanged. The supplier corrective action should address root cause, not only sorting.

Plausibility Check

Detection score drops from five to three, so RPN should fall by forty percent.

Exercise 18: Supplier Release Gate

A supplier release package has:

Gate	Requirement	Current result
on-time delivery	at least $90\%$	$33.3\%$
validated capacity reserve	positive	$+400$ units/week
document closure	$100\%$	$94.4\%$
quality yield	at least $98\%$	$97.0\%$

Decide whether to release.

Solution

Validated capacity passes:

400>0

Delivery, documentation and quality gates fail:

33.3\%<90\%,\quad 94.4\%<100\%,\quad 97.0\%<98\%

The supplier is not releasable for unrestricted production.

Engineering Comment

Supplier release requires timing, quality and documentation evidence. One positive capacity margin does not compensate for failed delivery and quality gates.

Plausibility Check

Three hard gates fail, so the release decision must be hold, restrict or escalate.

Validation Package Checklist

A strong supplier-performance solution should check:

whether lead-time measurement uses the correct boundary;
whether average, on-time percentage and tail risk are all visible;
whether outage coverage uses usable stock and current demand;
whether alternate-source capacity is approved and ramp timing is included;
whether backlog recovery time is acceptable for the business need;
whether quality performance separates severity and defect class;
whether documentation and deviations are closed before release;
whether expedite dependence is temporary, controlled and visible.

Common Release Mistakes

Common mistakes include planning from quoted lead time instead of measured release lead time, using average lead time while ignoring late-tail risk, assuming safety stock is usable without quality status, claiming dual-source recovery before ramp week is covered, using supplier capacity claims instead of demonstrated output, releasing material with incomplete documents, treating sort containment as root-cause correction, and approving a supplier because one gate passes while delivery or quality gates fail.

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