ISE250-02-HW1
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School
San Jose State University *
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Course
250
Subject
Industrial Engineering
Date
Apr 3, 2024
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2
Uploaded by MinisterNeutronIbis10
ISE 250 Spring 2024
Homework Assignment #1 Due 5 PM of 2/12/2024 (Monday); note that the due time is not 6 PM.
Reading Assignment
Reading 1.1:
Read Chapter 4 (Lean Concepts) and Chapter 5 (Basic Six Sigma Concepts) and Chapter 21 (Hypothesis Testing) of the textbook:
Six Sigma: A Complete Step-by-Step Guide (A Complete Training and Reference Guide to White Belts, Yellow Belts, Green Belts and Black Belts), July 2018 Edition, The Council for Six Sigma Certification; eBook accessible for free at https://www.sixsigmacouncil.org/wp-content/uploads/2018/08/Six-Sigma-A-Complete-Step-by-
Step-Guide.pdf
.
For your convenience, it is posted in the Week-01 folder as
ISE250-01-00-Six-Sigma-A-Complete-Step-by-Step-Guide
Yesterday evening, I showed you a summary Class Schedule and a detailed Class Schedule. They include UNITS and Chapters of the textbook to be discussed in this semester. As you must have realized, I would go far beyond the basic textbook coverage on Six Sigma methods and Statistics. Therefore, reading the chapters of the textbook associated with the topics I covered in a lecture is required for the week following the lecture. This goes without saying, and I may not explicitly state such required reading in future weeks. (If you have not read Chapters 1, 2 and 3, this is a good opportunity to read them. The amount of HW assignment (i.e., exercises) this week is light.)
Reading 1.2:
Read the case “Wind Power Company Gets to the Root of an Icy Issue,” which can be found in ISE250-02-04-DMAIC-Clipper Windpower-wind turbine-2010 .
Homework Assignment: Due 5 PM of 2/12/2024 (Monday); note that the due time is not 6 PM.
HW1.1:
We often see statements like this one, about the quality of a product. Suppose that a randomly selected item of a (mass-produced) product (a) meets the specifications, (b) does not meet the specifications but is otherwise considered acceptable or (c) is not acceptable with probabilities of 0.99, 0.009 and 0.001, respectively (with respect to some well-defined criteria). What this means is that when a large
number such items are selected and evaluated with respect to the criteria, the three corresponding proportions approach (i.e., converge to) the three numbers. But, how large is large enough
? Although some probability theory exists that can help answer this question, as Six Sigma practitioners we need to have some intuition about this question and have some sense about the speed of the convergence. Understanding this probabilistic product quality can be achieved by understanding and working through the following mathematically equivalent but hypothetical problem:
1
Probability is Portion Based on a (Very) Large Sample: A Simulated Case of Tossing an Empty Soft Drink Can (Pepsi, Coke, …):
Consider the random event of tossing an empty soft drink can, which has three sides. Let us make an assumption that the probability of a toss would result in the can lying on its side, its bottom and its top with probabilities 0.99; 0.009; 0.001. Use Excel to simulate tossing such a can 2,000 times (or more times) and then, as the number of tosses increments one by one, update the three proportions, and use the trends of three proportions to approximate the three probabilities. Note that one or more of the proportions may take exactly their corresponding (probability) values. But, this does not mean “convergence.” Convergence requires that the proportions “hover” around their corresponding (probability) values, i.e., returning to them “shortly” after departing from them. (What qualifies as “shortly” can be defined mathematically or in probabilistic expressions. But, let us leave it out for this course.)
Use the Excel template already created for you in ISE250-02-HW1.1-estimating probabilities of a 3-outcome experiment via Excel simulation-
template
and follow the instructions there. Some hints are highlighted in green; some particular cells to pay attention to are highlighted in yellow; some particular cells to pay special attention to at the end of the exercise are highlighted in red.
HW1.2: The purpose of this exercise is for you to
use Minitab to do simple random number generation and make a graph and for you to get familiar with use of Minitab. We will use Minitab in the next class to do some statistical analysis.
Do the same thing as stated in HW1.1 but with the following exception. Since Minitab is not designed as a spreadsheet for user-friendly number crunching, focus on generating 2000 random numbers; do not concern yourself with the progression of convergence of the proportions as the number of random numbers increases.
For this exercise, you need only a small number of functions listed under the category “Calc”, particularly (a) “Set Base” and (b) “Random Data” and then “Discrete”, and the function “Histogram” under the category of “Graph”. (Here Base is the same as Seed in Excel.)
Use the template file entitled
ISE250-02-HW1.2-estimating probabilities of a 3-outcome experiment via Minitab simulation-
template
to do the exercise in the following steps.
Enter the three possible outcomes of 1, 2 and 3 in Column C1. Enter the three corresponding probabilities in Column C2. Then, generate the 2000 random numbers in Column C3. You can use Histogram to visualize the frequencies of the three possible outcomes and find the numbers of their occurrences by clicking on the three vertical frequency bars. After you have created the histogram, state the Base you selected and comment on what you have observed. Add your comments by right clicking the mouse and choose the command “Add Notes”.
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