FE Industrial & Systems Practice Question Solution included after investigation
CASE E-089 · FE

The Part That Lost $45, Not $60

Quality loss did not grow linearly with deviation from target. Under the Taguchi quadratic model, a 3-unit deviation caused a $45 loss.

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Case E-089 engineering failure visual
HOW THIS WORKS

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Follow the investigation process used in the field — in five guided steps.

1

Inspect

Review the problem, diagram, and evidence.

2

Commit

Choose your hypothesis.

3

Prove

Run calculations and test your idea.

4

Fix

Select and validate a safe correction.

5

Sign Off

See the full debrief and key takeaways.

Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A quality characteristic has target T=100 units. A deviation of 4 units from target is associated with an $80 quality loss. Assume the Taguchi loss function L=k(y-T)^2. A produced part measures y=103. A note scales the $80 loss linearly by 3/4 and reports $60. Determine the correct loss.

Quality Industrial Systems Design Verification Root Cause Analysis Safe Correction
E-089
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

Loss was interpolated linearly from the calibration point.

What was missed

The Taguchi function squares the deviation from target.

Corrected model

Use L=k(y-T)^2 after determining k from the given loss condition.

QUICK ANSWER

From $80=k(4²), k=$5 per squared unit. At y=103 with target 100, deviation is 3, so L=5(3²)=$45.

ENGINEERING TAKEAWAY

Determine k from a known loss-deviation pair, then apply the quadratic Taguchi loss function L=k(y-T)^2.

CASE QUESTIONS

Questions this case should settle.

What is the Taguchi loss function?

L=k(y-T)^2 for the quadratic model used here.

What deviation keeps loss at or below $20 when k=5?

A deviation of 2 units or less.

NEXT FE PRACTICE QUESTION

The 5% Defect Lot That Was Accepted 73.6% of the Time, Not 95%

Quality · 5–10 min

Continue Practice →
WHAT YOU’LL LEARN

Real failures. Lasting skills.

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  • Apply core engineering concepts to real-world problems
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  • Strengthen exam-ready thinking through realistic scenarios
COMMON QUESTIONS
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