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23-Ind-B1 Reliability and Maintainability: December 2017

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Oil-Well Drilling — Binomial, Geometric, Normal Probability, and a Sum of Normals
  2. Question 2 Job Time in System — Sample-Size Design, CI, Anomaly Check, Two-Sample Comparison
  3. Question 3 Halifax Ferry — Joint Distribution, Expected Profit, Marginals, Conditional Expectation
  4. Question 4 Piecewise-Linear Density — Normalization, Mean, Variance
  5. Question 5 BMI vs. Age — Simple Linear Regression, ANOVA F -Test, Prediction Interval
  6. Question 6 Deflection Temperature of Plastic Pipe — Variance Test, Two-Sample t -Test, Sample-Size Design
  7. Question 7 Hop-Plant Yields — Bartlett's Test, One-Way ANOVA, Tukey's Test, and a Single-df Contrast
  8. Question 8 Marathon Time — Multiple Regression via $(X'X)^{-1}$
  9. Question 9 Photocopier Gluing Power — Three-Factor ANOVA with Replication
  10. Question 10 $2^2$ Factorial Experiment — Design Matrix, Contrasts, Effects, ANOVA, Regression

Start with Question 1 →

National Exams — December 2017 — 98-Ind-B1 Applied Probability & Statistics. Three-hour, closed-book exam; one of two permitted calculators (Sharp or Casio), one 8.5″×11.0″ aid sheet (both sides), statistical tables supplied. Format: three sections — Section A: do 2 of 4 (30 marks); Section B: do 2 of 3 (30 marks); Section C: do 2 of 3 (40 marks) — a 6-question, 100-mark paper as printed. All ten questions across the three sections are solved below for completeness.

Reference texts: Montgomery & Runger, Applied Statistics and Probability for Engineers (7th ed., Wiley) — discrete/continuous distributions (ch. 3–4), joint distributions (ch. 5), point/interval estimation and sample size (ch. 8), hypothesis testing incl. two-sample tests (ch. 9–10), simple linear regression (ch. 11), design and analysis of single-factor experiments (ch. 13). Montgomery, Peck & Vining, Introduction to Linear Regression Analysis (6th ed., Wiley) — multiple regression by matrices (ch. 2–3). Montgomery, Design and Analysis of Experiments (9th ed., Wiley) — multi-factor and $2^k$ factorial designs (ch. 5–6).