ICAR AIEEA-PG - Group 07 Statistical Sciences (Master's admission and PG scholarship) · India · National Testing Agency for ICAR
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 ICAR AIEEA-PG spread across the units of Statistical Quality Control & Reliability. Difficulty: 14 easy, 14 medium, 0 hard.
| Control charts for attributes: p, np, c and u charts | 5 | |
| Acceptance sampling by attributes: single, double and sequential plans | 5 | |
| OC, AOQ, AOQL, ASN and ATI curves | 5 | |
| Reliability: hazard rate, series and parallel systems, life testing | 4 | |
| Chance and assignable causes of variation | 3 | |
| Control charts for variables: X-bar, R and s charts | 3 | |
| CUSUM and EWMA charts | 1 | |
| Process capability indices | 1 | |
| Six Sigma and design for quality (introduction) | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Subgroups of 5 bags give x̿ = 50.12 kg and R̄ = 0.40 kg; A₂ = 0.577. What are the X̄ chart limits?
C. 49.889 to 50.351 kg
x̿ ± A₂R̄ = 50.12 ± 0.231 = 49.889 to 50.351. A₂ already includes 1/√n, so dividing again is wrong.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
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
What is plotted on an OC curve?
D. P_a against lot quality
The OC curve shows P_a(p) for each incoming fraction non-conforming.
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
Twenty nozzles run 500 hours; four fail at 120, 250, 310 and 430 hours. Assuming exponential lives, what is the MLE of MTTF?
D. 2277.5 hours
Total time on test = 1,110 + 16 × 500 = 9,110 h; θ̂ = 9,110/4 = 2,277.5 h. Using only failed items' times gives 277.5 h.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
Ten here, 28 in the app. The Laisha app has every practice question we have written to ICAR AIEEA-PG in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.
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