23-Ind-A6 Systems Simulation · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2013 — 98-Ind-A6 Systems Simulation. Three-hour, closed-book exam; one of two permitted calculators (Sharp or Casio), one 8.5″×11.0″ aid sheet (both sides). Format: 14 sub-questions across four parts — Part A (do 1 of 2, 25 marks), Part B (do 3 of 5, 15 marks), Part C (do 1 of 3, 10 marks), Part D (do 2 of 4, 20 marks); 7 questions, 70 marks constitute a complete paper. All fourteen sub-questions are solved below for completeness (the source restarts its own numbering at 1 within each Part). Statistical tables (Normal, t, chi-square, F) were supplied with the exam; the values below are the same table values obtained by direct computation.
Reference texts: Banks, Carson, Nelson & Nicol, Discrete-Event System Simulation (5th ed., Pearson) — simulation study design, random-number generation, input/output data analysis, variance reduction, verification & validation, queueing simulation; Montgomery, Design and Analysis of Experiments (9th ed., Wiley) — factorial designs and ANOVA.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Transit time is a strictly non-negative, physically bounded-below quantity (a shipment cannot arrive in negative time, and there is a practical minimum given fixed distance and maximum vehicle speed) — a Normal distribution places positive probability on negative values and is symmetric, neither of which matches a process whose typical failure mode (weather, customs, mechanical delay) adds an occasional long tail on the SLOW side without a mirrored long tail on the fast side. We should therefore be surprised if transit time were exactly Normal, and Question 6's own test confirms it: the true distribution is right-skewed. Distributions that are naturally bounded at zero and can carry a long right tail — Lognormal, Gamma, or Weibull — are the standard input-modelling choices for a duration/transit-time variable of this kind (Banks et al. list exactly this trio for "time to complete a task" data), and any of the three would be a defensible next hypothesis to fit and re-test.
If the underlying transit-time distributions are non-Normal, a two-sample $t$-test on the raw times is weakened for two related reasons: the $t$-test's exactness relies on Normal populations (with $n=9$–10 per firm here, the Central Limit Theorem has too few observations to rescue a badly skewed population), and a skewed distribution's mean is itself a less representative "typical value" than its median, so a test built around comparing means can be answering a less useful question than the one management actually cares about (typical delivery experience). The appropriate alternative is a distribution-free (nonparametric) test: the Mann–Whitney U / Wilcoxon rank-sum test compares the two firms' transit-time distributions using only the RANKS of the pooled observations, requiring no Normality assumption and remaining valid at small $n$; a permutation test on the mean (or median) difference is an equally defensible alternative if an exact reference distribution is wanted.
