SSA Individual Assignment 2024

Introduction

This repository contains the individual assignment for the S&SA course, due on 22nd November 2024 at 16:00h. The assignment consists of three main tasks that demonstrate various skills in MATLAB programming, data analysis, and discrete event simulation.

Assignment Instructions

General Guidelines

This is an individual assignment worth 25% of your grade. Cooperation and copying are not allowed.
Submit a single ZIP file named assignment.zip on Canvas, containing all necessary .m files without any subdirectories.
Do not include personal information in the .m files.
Perform your tests manually without relying on MATLAB's built-in tests, unless explicitly allowed.
Ensure all required functions are implemented in separate .m files and thoroughly tested.

Task 1: Random Number Generation and Runs Test

Task 1a: Combined LFSRs Generator

Implement the ME-CF generator as described in Table 1 of L'Ecuyer (1999) with the following parameters:

L = 32, J = 4, s1 = 18, s2 = 2, s3 = 7, s4 = 13
Seed values: z1 = 2957, z2 = 646, z3 = 3847, z4 = 947

Create a MATLAB function lEcuyer.m with the signature:

function u = lEcuyer(z1, z2, z3, z4, n)

Generate 10,000 random numbers using this generator.

Task 1b: Runs Test

Implement a runs test in runsTest.m to assess the quality of the generated random numbers. The function signature should be:

function [reject, R] = runsTest(u, a)

Use a significance level of α = 0.05.

Task 2: Data Exploration and Analysis

Task 2a: Data Visualization

Load the dataset dataIndAss2425.mat and analyze the benzene (C6H6) measurements using at least three different visualization techniques. Handle outliers appropriately.

Task 2b: Descriptive Statistics

Compute the seven-number summary, mean, variance, and sample skewness for the cleaned data. Form a hypothesis about the distribution of the processing times.

Task 2c: Comparative Analysis

Perform a comparative analysis of the carbon monoxide (CO) and benzene (C6H6) measurements, identifying any outliers and the times they were recorded.

Task 3: Discrete Event Simulation

Simulate a manufacturing plant modeled as an M|M|1-queue with breakdowns using the provided functions (arrival.m, service.m, breakdown.m, and repair.m). The simulation should stop after the end of the busy period in which product #10,000 is constructed.

Implement the simulation in DES.m with the function signature:

function [avgWaitingTime, avgQueueLength] = DES()

Run 20 iterations and report the distributions of the average waiting time and queue length.

References

L'Ecuyer, P. (1999). Tables of maximally equidistributed combined LFSR generators. Math. Comput., 68(225), 261–269. https://doi.org/10.1090/s0025-5718-99-01039-x

Submission

Ensure all .m files are in the highest-level directory of the ZIP file.
Submit assignment.zip on Canvas before the deadline.

glassmansam/ssa