Indian Statistical Service Examination (with Indian Economic Service) · India · Union Public Service Commission
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 Indian Statistical Service Examination spread across the units of Statistical Quality Control & Reliability. Difficulty: 22 easy, 44 medium, 18 hard.
| Control charts for variables: X-bar, R and s charts | 11 | |
| OC, AOQ, AOQL, ASN and ATI curves | 10 | |
| Chance and assignable causes of variation | 9 | |
| CUSUM and EWMA charts | 9 | |
| Acceptance sampling by attributes: single, double and sequential plans | 9 | |
| Reliability: hazard rate, series and parallel systems, life testing | 9 | |
| Control charts for attributes: p, np, c and u charts | 8 | |
| Process capability indices | 7 | |
| Acceptance sampling by variables | 7 | |
| Six Sigma and design for quality (introduction) | 5 |
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
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
An EWMA with λ = 0.2 starts at z₀ = 500. The next two observations are 503 and 501. What is z₂?
A. 500.68
z₁ = 0.2 × 503 + 0.8 × 500 = 500.60; z₂ = 0.2 × 501 + 0.8 × 500.60 = 500.68. 502 is the plain average of the two observations.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
A filler has specifications 98-102 g, mean 100.5 g and σ = 0.5 g. What is Cpk?
A. 1.00
Cpk = min(1.5/1.5, 2.5/1.5) = 1.00; 1.67 uses the farther limit; 1.33 is Cp, which ignores centring.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
What two points are commonly used to design a single sampling plan?
A. (AQL, 1 − α) and (LTPD, β)
Choose n and c so that P_a ≥ 1 − α at the AQL and P_a ≤ β at the LTPD.
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
In a Type II censored exponential life test with r failures and total time on test T, what is the distribution of 2T/θ?
A. χ² with 2r degrees of freedom
T is a sum of r exponential spacings scaled by θ, giving gamma(r) and 2T/θ ~ χ²₂ᵣ, the basis of exact limits.
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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