ASRB Agricultural Research Service (ARS) - Agricultural Statistics scientist · India · Agricultural Scientists Recruitment Board (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 ASRB Agricultural Research Service spread across the units of Statistical Quality Control & Reliability. Difficulty: 2 easy, 25 medium, 8 hard.
| Process capability indices | 6 | |
| Six Sigma and design for quality (introduction) | 6 | |
| Chance and assignable causes of variation | 4 | |
| Control charts for attributes: p, np, c and u charts | 4 | |
| CUSUM and EWMA charts | 3 | |
| Acceptance sampling by attributes: single, double and sequential plans | 3 | |
| Acceptance sampling by variables | 3 | |
| Control charts for variables: X-bar, R and s charts | 2 | |
| OC, AOQ, AOQL, ASN and ATI curves | 2 | |
| Reliability: hazard rate, series and parallel systems, life testing | 2 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A dairy's fat chart signals constantly after the season changes, though nothing in the plant has changed. What is a sensible response?
B. Adjust for the raw-material input
The input (milk composition) changed; charting output adjusted for known input effects separates plant problems from raw-material variation.
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 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
A filler has specifications 98-102 g and σ = 0.5 g. What is Cp?
B. 1.33
Cp = (102 − 98)/(6 × 0.5) = 1.33.
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
A filler's σ is halved from 8 g to 4 g. Keeping the same protection against under-weight packs, by about how much can the mean fill be lowered with a 3σ margin?
D. 12 g
The margin above the lower limit falls from 3 × 8 = 24 g to 3 × 4 = 12 g, saving 12 g of give-away per pack.
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
A supplier complains that a lot was rejected though no sampled item exceeded the limit. Under which plan type can this happen?
B. A variables plan
Variables plans reject when x̄ is too close to the limit relative to σ, even if every item conforms.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
Germination testing is destructive and slow. Why might a variables approach be attractive if a suitable continuous measure exists?
D. Fewer items are needed
Fewer test units cut destructive testing cost, provided the measure is approximately normal.
Further reading: Montgomery, Introduction to Statistical Quality Control; Duncan, Quality Control and Industrial Statistics; Schilling and Neubauer, Acceptance Sampling in Quality Control
What do the letters of DMAIC stand for?
A. Define, Measure, Analyse, Improve, Control
DMAIC is the Six Sigma improvement cycle.
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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