Mfg-B3 — Systems Simulation
Computer simulation of systems. Design of simulation models of discrete systems. Statistical foundations and methodology. Generation of random variates. Design of simulation experiments. Simulation programming languages. Applications: the analysis and design of systems for production, and distribution. Model validation, Simulation output analysis. Use of software.
Subject outline
Mfg-B3 Systems Simulation is a Manufacturing Engineering technical exam (PEO National Examination 08-Mfg-B3) on the statistical and modelling method behind a discrete-event simulation study: probability and random variables; input modelling and distribution fitting with chi-square and Kolmogorov–Smirnov tests; random number generation and the Hull–Dobell conditions for a full-period generator; random variate generation by the inverse transform and Box–Muller; queueing theory and Little's law; the mechanics of discrete-event simulation; output analysis for terminating and steady-state runs — warm-up, replications, batch means and the half-width that sizes them; variance reduction by common random numbers and antithetic variates; validating a model against the real system with F, t, Welch and paired tests; comparing scenarios by one-way ANOVA with Tukey's test; and factorial experimental design.
The paper is 3 hours and closed book. Candidates may use one of two permitted calculators (Sharp or Casio models) and may have an aid sheet of one 8.5″ × 11.0″ sheet of paper, with writing permitted on both sides; statistical tables are provided. Each sitting is set in three sections with a choice inside each, and the front page says DO NOT ATTEMPT TO DO ALL QUESTIONS, so choose before you start writing. May 2019 prints ten question sets: Part A, three of five at 10 marks each; Part B, two of three at 15 marks each; Part C, one of two at 20 marks — six questions and 80 marks. Its front page lists Section B as one of two for 20 marks and totals the paper at 70; the instructions inside Part B, and the three questions it prints, are what the solutions follow. December 2018 prints seven: Part A, two of three at 10 marks each; Part B, one of two at 20 marks; Part C, one of two at 20 marks — four questions and 60 marks, as its front page totals them. Where a question is open to interpretation the paper asks for a clear statement of the assumptions made, and on these papers that is worth marks: the December B-Q2 verdict reverses on whether the two samples are paired, an assumption the published solution never states.
Same papers, two codes. PEO lists this subject for Manufacturing Engineering as 08-Mfg-B3 Systems Simulation. The papers solved here are headed 17-Ind-A6, which is how PEO lists the same subject for Industrial Engineering, its syllabus worded slightly differently; the papers are the same under both codes.
What this course gives you
Worked solutions — all seventeen question sets, ten from May 2019 and seven from December 2018, solved in full. Both published solutions answer every set rather than the required subset, and so does this course, so you can work whichever questions you intend to choose. Each question has a final-answers table, and 47 authored diagrams and charts are set into the solutions. Every result has been re-derived independently, and in thirteen of the seventeen question sets a published step or result does not survive the check. Nineteen corrections and cautions are flagged, in fourteen of the question sets, each at the step concerned and quoting the published figure where there is one, so nothing is silently overwritten. Several conclusions reverse. The published May 2019 validation study concludes that the hospital model is valid, but its actual-system mean is 71.37 against a true 71.66 and its variance matches neither mean; corrected, the F test on the variances rejects (F = 5.9333 against 5.8198), and the model is not validated. The published December 2018 replication count of 137 should be 36: a half-width scales as 1/√n, so going from ±4.5 to ±2.0 minutes multiplies n by 2.25² = 5.0625, and 7 × 5.0625 = 35.4. The published December 2² factorial analysis recommends the large bus “to minimize the wait time” when the large bus averages 100.5 minutes of waiting against 50.3 for the small one, and calls the loading policy insignificant when its F is 168. The published December extra-bag answer fits a Poisson that the data's own variance-to-mean ratio of 0.52 refutes; the count is a binomial on the ten members of each patrol. And the published December goodness-of-fit test is run on 9 degrees of freedom where it has 10, on a table with four cells that expect fewer than five; pooled into valid cells, Poisson(6) is rejected clearly, with χ² = 19.72 on 8 degrees of freedom. Study notes — ten condensed topics: how this paper works; probability and random variables; input modelling and distribution fitting; random numbers and random variates; queueing theory; discrete-event simulation mechanics; output analysis for terminating simulations; output analysis for steady state; comparing alternatives and validation; and experimental design for simulation — with 69 authored diagrams and charts and 9 tables between them. Each topic ends by naming the questions on both papers that it answers, and the first includes a table pairing the questions of the two sittings by skill. Practice & case studies — ten multiple-choice questions, each with a worked explanation, and five longer problems with complete worked answers and six figures between them: a density from scratch in exact fractions; two generators, Hull–Dobell and the inverse transform; M/M/1 against M/M/2; an output-analysis sizing problem on half-width, replications and warm-up; and a complete simulation study of a machining cell. All fifteen are written for this course; none is taken from the two papers. Formula sheet — two pages in ten groups: the aid-sheet rule and the supplied tables, expectation and variance, the four distributions these papers use, linear congruential generators, the inverse transform, queueing, output analysis and replication sizing, comparing a model with the system, chi-square goodness of fit, and ANOVA with two-level factorials. The rubric allows one 8.5″ × 11.0″ aid sheet written on both sides but does not say whether a printed sheet is accepted, so treat these pages as the master copy and copy what you need onto your aid sheet by hand. The statistical tables come with the paper, so nothing here duplicates them. Printable resources — ten one-page cards: a “which method do I use?” decision table, probability and distributions, random numbers and variates, queueing, output analysis, comparing two systems, goodness of fit, design of experiments, simulation vocabulary, and an exam-day card of the checks that catch the published errors — plus four blank exam stationery templates. Reference links — nine selected reference websites — PEO's own 08-Mfg-B3 listing with its syllabus, four NIST/SEMATECH handbook pages on the tests and designs these papers set, two Wikipedia articles, a chapter of Rossetti's open Arena textbook and NPTEL's course on discrete-event simulation — and eight YouTube topic searches. Each link carries a note on what it is good for; a search opens YouTube's current results for its topic, so the videos it shows will change. Practice papers — the two question papers on their own, unmarked, for a timed run: May 2019, 8 pages, and December 2018, 22 pages including the thirteen pages of statistical tables the exam supplies — normal, t, chi-square, F at 5% and 1%, Bartlett, Tukey and Wilcoxon.
In all, 122 figures were drawn for this course: 47 in the solutions, 69 in the notes and 6 in the practice problems.