Enclosure 3: Statistical Process Control: Chapter-wise Previous Year GATE Questions (With Solutions)

Chapter-wise Previous Year GATE Questions (With Solutions)

Statistical Process Control

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🔹 Chapter 1: Introduction to SPC

GATE Question 1 (Conceptual – 1 Mark)

Which of the following is the primary objective of Statistical Process Control?

(A) Detection of defects
(B) Prevention of defects
(C) Sorting of products
(D) Replacement of inspection

✅ Answer: (B)

Solution

SPC focuses on monitoring and controlling processes to prevent defects, not merely detecting them after production.

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🔹 Chapter 2: Statistical Foundations for SPC

GATE Question 2 (Numerical – 1 Mark)

For a normally distributed process, approximately what percentage of observations lie within ±3σ?

(A) 95%
(B) 97%
(C) 99.73%
(D) 100%

✅ Answer: (C)

Solution

By the empirical rule:

• ±1σ → 68%

• ±2σ → 95%

• ±3σ → 99.73%

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GATE Question 3 (Numerical – 2 Marks)

Five observations are: 10, 12, 14, 16, 18.
Find the mean and range.

✅ Solution

[
\bar{X} = \frac{10+12+14+16+18}{5} = 14
]

[
Range = 18 - 10 = 8
]

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🔹 Chapter 3: Process Variation & Rational Subgrouping

GATE Question 4 (Conceptual – 1 Mark)

Variation that is inherent in a stable process is known as:

(A) Special cause variation
(B) Assignable variation
(C) Common cause variation
(D) Measurement variation

✅ Answer: (C)

Solution

Common cause variation is natural, random, and unavoidable in a stable process.

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GATE Question 5 (Conceptual – 1 Mark)

Making frequent adjustments to a stable process leads to:

(A) Process improvement
(B) Reduced variability
(C) Increased variability
(D) Zero defects

✅ Answer: (C)

Solution

This phenomenon is known as tampering, which increases variability.

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🔹 Chapter 4: Control Charts for Variables

GATE Question 6 (Numerical – 2 Marks)

For an X̄–R chart:

• ( \bar{X} = 50 )

• ( \bar{R} = 4 )

• ( A_2 = 0.577 )

Find the UCL for X̄-chart.

✅ Solution

[
UCL = \bar{X} + A_2 \bar{R}
]
[
= 50 + (0.577)(4) = 52.31
]

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GATE Question 7 (Conceptual – 1 Mark)

Which chart must be examined first in an X̄–R control chart?

(A) X̄-chart
(B) R-chart
(C) p-chart
(D) u-chart

✅ Answer: (B)

Solution

Process variability must be in control before interpreting the process mean.

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🔹 Chapter 5: Control Charts for Attributes

GATE Question 8 (Conceptual – 1 Mark)

Which control chart is used to monitor the fraction defective?

(A) np-chart
(B) p-chart
(C) c-chart
(D) u-chart

✅ Answer: (B)

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GATE Question 9 (Numerical – 2 Marks)

For a c-chart, if the average number of defects is 25, find the UCL.

✅ Solution

[
UCL = \bar{c} + 3\sqrt{\bar{c}}
]
[
= 25 + 3(5) = 40
]

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🔹 Chapter 6: Process Capability Analysis

GATE Question 10 (Numerical – 2 Marks)

Given:

• USL = 110

• LSL = 90

• σ = 4

Find the process capability index ( C_p ).

✅ Solution

[
C_p = \frac{USL - LSL}{6\sigma}
]
[
= \frac{20}{24} = 0.83
]

❌ Process is not capable.

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GATE Question 11 (Conceptual – 1 Mark)

If ( C_p = C_{pk} ), the process is:

(A) Off-center
(B) Unstable
(C) Centered
(D) Incapable

✅ Answer: (C)

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🔹 Chapter 7: SPC-Based Improvement

GATE Question 12 (Conceptual – 1 Mark)

Reduction of common cause variation requires action by:

(A) Operator
(B) Inspector
(C) Supervisor
(D) Management

✅ Answer: (D)

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🔹 Chapter 8: Acceptance Sampling

GATE Question 13 (Conceptual – 1 Mark)

Producer’s risk is the probability of:

(A) Accepting a bad lot
(B) Rejecting a good lot
(C) Accepting a good lot
(D) Rejecting a bad lot

✅ Answer: (B)

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GATE Question 14 (Numerical – 1 Mark)

In a single sampling plan, n = 100 and c = 2.
If 3 defectives are found, the lot is:

✅ Solution

Since defectives > c
❌ Lot rejected

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🔹 Chapter 9: Measurement System Analysis

GATE Question 15 (Conceptual – 1 Mark)

Repeatability in a measurement system is associated with:

(A) Operator variation
(B) Equipment variation
(C) Part variation
(D) Process variation

✅ Answer: (B)

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GATE Question 16 (Numerical – 2 Marks)

If total variation = 10 and Gage R&R variation = 3, find %Gage R&R.

✅ Solution

[
%GRR = \frac{3}{10} \times 100 = 30%
]

⚠️ Measurement system is marginally acceptable.

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🔹 Chapter 10: SPC Implementation & Trends

GATE Question 17 (Conceptual – 1 Mark)

SPC charts should NOT be used for:

(A) Process monitoring
(B) Process improvement
(C) Employee performance appraisal
(D) Quality control

✅ Answer: (C)