FE Industrial & Systems Practice Question Solution included after investigation
CASE E-088 Β· FE

The Process With Cp 1.67 That Still Had Cpk 0.67

The process spread fit comfortably inside the specification width, but the mean had shifted toward the USL. Cp looked strong while Cpk exposed the centering problem.

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Case E-088 engineering failure visual
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Follow the investigation process used in the field β€” in five guided steps.

1

Inspect

Review the problem, diagram, and evidence.

2

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3

Prove

Run calculations and test your idea.

4

Fix

Select and validate a safe correction.

5

Sign Off

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Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A process has specifications 9.5 to 10.5 mm, mean ΞΌ=10.3 mm, and standard deviation Οƒ=0.10 mm. A quality report calculates Cp=(10.5-9.5)/(6Γ—0.10)=1.67 and concludes that the process is highly capable. Determine Cp and Cpk and explain why the conclusion is incomplete.

Quality Industrial Systems Design Verification Root Cause Analysis Safe Correction
E-088
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CASE CLOSED Β· ENGINEERING VERDICT

What actually failed β€” and what should change.

What failed

A favorable Cp was treated as proof of actual centered capability.

What was missed

The process mean was shifted close to the upper specification limit.

Corrected model

Use both Cp and Cpk; Cpk is governed by the nearest specification limit.

QUICK ANSWER

Cp=(10.5-9.5)/(6Γ—0.10)=1.67. Cpk=min[(10.5-10.3)/(0.30),(10.3-9.5)/(0.30)]=min(0.67,2.67)=0.67.

ENGINEERING TAKEAWAY

Cp measures potential capability from spread only; Cpk also accounts for process centering by using the smaller distance from the mean to a specification limit.

CASE QUESTIONS

Questions this case should settle.

What is the difference between Cp and Cpk?

Cp measures potential capability from spread; Cpk also accounts for process centering.

When are Cp and Cpk equal?

When the process mean is centered between the upper and lower specification limits.

NEXT FE PRACTICE QUESTION

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

Quality Β· 5–10 min

Continue Practice β†’
WHAT YOU’LL LEARN

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