CUET-PG - Statistics · India · National Testing Agency
Original practice questions written to the published syllabus · not past papersMonitoring and accepting quality: Shewhart charts for variables and attributes, CUSUM and EWMA charts, process capability, acceptance sampling plans with their OC, AOQ and ATI curves, and reliability models, applied to seed testing, food processing and input quality. The Agricultural Engineering track covers control charts briefly; this is the full subject.
In the exams: UPSC ISS Statistics III (heavy, reported); SSC CGL JSO (present); AICE-JRF Dairy Microbiology syllabus names 'statistical quality control' (present); light in AICE-JRF Ag Stat
How our questions for CUET-PG spread across the units of Statistical Quality Control & Reliability. Difficulty: 20 easy, 39 medium, 4 hard.
| Reliability: hazard rate, series and parallel systems, life testing | 9 | |
| Control charts for variables: X-bar, R and s charts | 7 | |
| Control charts for attributes: p, np, c and u charts | 7 | |
| CUSUM and EWMA charts | 7 | |
| Acceptance sampling by attributes: single, double and sequential plans | 7 | |
| Chance and assignable causes of variation | 6 | |
| OC, AOQ, AOQL, ASN and ATI curves | 6 | |
| Acceptance sampling by variables | 5 | |
| Six Sigma and design for quality (introduction) | 5 | |
| Process capability indices | 4 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
For subgroups of 5 with R̄ = 0.40 kg, D₃ = 0 and D₄ = 2.114. What is the R chart upper limit?
A. 0.846 kg
UCL = D₄R̄ = 2.114 × 0.40 = 0.846; LCL = 0.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
With R̄ = 0.40 kg from subgroups of 5 (d₂ = 2.326), what is σ̂?
B. 0.172 kg
σ̂ = R̄/d₂ = 0.40/2.326 = 0.172.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
Only one moisture reading per batch is available. Which chart is used?
A. Individuals and moving-range charts
With n = 1 no within-subgroup range exists; the moving range of successive values estimates σ (MR̄/1.128).
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
With p̄ = 0.04, how large must n be for the p chart to have a positive lower limit?
C. More than 216
LCL > 0 requires p̄ > 3√[p̄(1 − p̄)/n], i.e. n > 9(1 − p̄)/p̄ = 216.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
An EWMA uses λ = 0.2 and L = 3. What are its steady-state limits?
C. μ₀ ± σ
Lσ√[λ/(2 − λ)] = 3σ√(0.2/1.8) = 3σ/3 = σ.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
A dairy laboratory has one fat reading per batch, slightly skewed, and wants to detect slow drifts. Which chart suits it?
C. An EWMA chart
EWMA averaging makes it robust to mild non-normality and sensitive to small drifts with individual data.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
Which international standard provides variables plans matched to ISO 2859?
B. ISO 3951
ISO 3951 covers inspection by variables; ISO 9001 is a management-system standard.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
Three components with reliabilities 0.95, 0.98 and 0.99 are in series. What is the system reliability?
A. 0.922
Series: product = 0.922. 0.999999 is the parallel arrangement.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
A pump with reliability 0.95 is duplicated in parallel. What is the reliability of the pump stage?
B. 0.9975
Parallel: 1 − (0.05)² = 0.9975; 0.9025 is the series value.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
Three identical sensors (reliability 0.9 each) form a 2-out-of-3 system. What is its reliability?
A. 0.972
P(at least 2 work) = 3(0.9)²(0.1) + 0.9³ = 0.243 + 0.729 = 0.972.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
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