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.
(a) Batch means vs. deletion/replication. The Method of Batch Means runs ONE long simulation, discards an initial transient, and splits the remaining output into consecutive, roughly independent "batches," each batch mean treated as one observation for computing a confidence interval. Benefit: only one long run is needed, so the warm-up cost is paid once; drawback: successive batches are not truly independent (autocorrelation can bias the variance estimate low unless batches are made long enough to decorrelate, which is hard to verify). Deletion/Replication instead runs the model $R$ independent times (different random-number streams), deletes each replication's own warm-up period, and treats each replication's remaining-run average as one independent observation. Benefit: replications are genuinely statistically independent, so standard $t$-based confidence intervals are valid without an autocorrelation caveat; drawback: the warm-up transient is discarded $R$ times over, wasting more total computation than a single long batch-means run for the same number of "clean" observations. Recommendation: given the yard/subcontractor model is being newly built and validated, deletion/replication is preferred here — independence makes the resulting confidence intervals defensible without a batch-length judgment call, which matters more for a first model whose credibility is still being established than the extra CPU cost.
(b) Run length. Because the real system's demand profile spans the full 30-year contract (ramp-up, peak, wind-down are all part of what management needs sized), the run length should not be chosen for statistical convenience alone: each replication should simulate the FULL 30-year horizon so every phase of the demand curve is represented, and the number of replications $R$ (not the length of any one run) should instead be increased until the half-width of the output confidence interval (e.g. on required yard area) is acceptably small relative to the estimate.
(c) Warm-up. Yes — the yard's initial inventory level and the newly-established Halifax–subcontractor relationships are artificial starting conditions unrepresentative of steady operation, so a warm-up allowance is appropriate for any STEADY-STATE performance measure (e.g. average utilization once the system is fully ramped). Its length should be set with Welch's graphical procedure: overlay the moving average of the output statistic across several independent replications and visually identify the point beyond which the curve has flattened; that time index becomes the truncation point applied to every replication. Because this system is deliberately non-stationary over its own 30-year life (demand itself ramps and tapers by design), a single "steady-state" warm-up is only meaningful WITHIN a sub-period assumed roughly constant (e.g. within the years-2–25 plateau); performance during the ramp-up and wind-down years should be reported as its own (non-steady-state) transient result, not warmed-up away.
