|
 |
|
|
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ E-Math News Volume 3, Number 3 May 2001 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Contents ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Schedule of Public Classes Math in Industry - The DOE Sandbox Math in Everyday Life - Investing for Retirement How Can You Accumulate What You Need? Family Math - Math activities for ages 7-12 Book Review - Measurement System Analysis 2nd edition Ask Statman - Optimizing Your Preventative Maintenance Plan ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ "The principle of science, the definition, almost, is the following The Test of All Knowledge is Experiment. Experiment is the sole judge of scientific 'truth'." Richard Feynman ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Schedule of Public Classes ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Date Class Location ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ May 16-18, 2001 Performing Objective Experiments Anacortes, WA This class includes a free whale-watching trip! August 8-10, 2001 Performing Objective Experiments Anacortes, WA This class includes a free whale-watching trip! SAVE $300 BY REGISTERING EARLY! Visit http//www.mathoptions.com/class_registration.htm for details. You can learn more about these classes and register to attend at http//www.mathoptions.com/public.htm
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Math in Industry ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The DOE Sandbox Have you ever wanted to try Design Of Experiments (DOE) in your work, but didn't want to invest a lot of time or money just to see if it would help you? If so, you're in luck! Math Options has developed the "DOE Starter Kit" to help you try DOE in your own work so you can judge for yourself if DOE will work well for you. The "DOE Starter Kit" includes a step-by-step worked example for you to use as a guideline. Next to each step in the example is a worksheet for you to use in your own experiment. The "DOE Starter Kit" also includes a simple software tool, the "DOE Sandbox" to help you design your own experiment and analyze the data you collect. While you won't get any contour plots from the Sandbox, you will be able to find your "Sweet Spot" - the combination of factors that will produce responses that meet your goals. And the best news - the "DOE Starter Kit" is free. All you need to do is send an E-Mail message to mailtoBill@MathOptions.com requesting your free "DOE Starter Kit." The "DOE Sandbox" will run on different operating systems, so please be sure to specify the one you are using. Why wait? Request your "DOE Starter Kit" today. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ You can learn DOE in a practical, hands-on workshop in Anacortes, WA, May 16, 17 & 18, 2001. Let Bill Kappele show you how to use DOE in your work - not just talk about it. Learn to apply DOE, instead of how to theorize about it. You can learn more about "Performing Objective Experiments" and register to attend at http//www.mathoptions.com/public.htm
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Math in Everyday Life ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Investing for Retirement Saving What You Will Need Planning for retirement requires that you estimate the amount of money you will need to have available and develop a plan for accumulating that money. The article in the last issue (E-Math News Vol.3 No. 2) provided the math you need to estimate the amount of money to accumulate. This issue will explain the math you will need to develop your plan for accumulating it. The first step is to determine the amount of money you will need to have accumulated by retirement. We did that in the last article. The next step is to decide how often you want to add money to your savings -- annually, monthly, etc. For example, you might add to an IRA once per year at the end of every year. Or you might make monthly contributions to a 401K plan. You then need an estimate of the interest rate you can achieve while saving. This is potentially difficult -- you should consult a financial planner for help here. You will also need to know how many years you have until retirement. When you have this information you are ready to make your calculation. For payments made into your savings at the end of each period (month, year, etc.) the formula is, Payment = (interest rate) x (amount required at retiremnet) / {(1 + interest rate)^(number of payments) - 1} The number of payments depends on the number of years to retirement and how often you make payments each year. For example, suppose you want to have $1,000,000 available when you retire. You estimate that you will be able to collect 10% interest on your money annually and you expect to retire in 20 years. How much should you add to your IRA at the end of each year? The number of payments is 20, since you add only once per year for the 20 years. Here are the steps 1. 1 + interest rate = 1 + 0.10 (10%) = 1.10 2. (1+interest rate)^(number of payments) = 1.10^20 = 6.7275 3. (interest rate) x (amount required at retirement) = 0.10 x $1,000,000 = $100,000 4. Payment = $100,000 / {6.7275 - 1} = $17,460 per year Wow! You can't add that much to an IRA each year. You'll definitely need to consult a good financial planner to help you determine other ways to save your money. Suppose your retirement needs are more modest. You want to have $500,000 at retirement in 20 years and you want to make monthly contributions to your 401K plan. You estimate that you will make 10% interest annually. The number of periods will be 20 x 12, since you will make 12 payments (one per month) for 20 years. So, the number of payments is 240. 1. 1 + interest rate = 1 + 0.10 / 12 = 1.0083 2. (1+interest rate)^(number of payments) = 1.0083^240 = 7.2702 3. (interest rate) x (amount required at retirement) = 0.0083 x $500,000 = $4,150 4. Payment = $4,150 / {7.2702 - 1} = $662 per month ($7,944 per year) Please realize that this article is only intended to show you the math required for savings calculations. For advice on how to save, please consult a good financial planner. Good luck and happy saving!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Family Math ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Math Activities for Ages Seven through Twelve by Beth Heffernan By the time children reach this intermediate age group ("the golden years") they have largely sorted themselves into math lovers and haters. Math lovers need more stimulation than is usually pro- vided at school. They also need to be fortified against the teasing or belittling they receive from their peers for liking and/or excelling at math. The math haters generally need to return to basics. True understanding of the fundamentals of math is necessary to proceed, just as basic letter skills are necessary to become a proficient reader. There are entire stores in larger cities devoted to math materials, with games, puzzles, and so many cool toys the most jaded child would be hard pressed to scoff. "Learning" type catalogues also offer these types of materials. Whenever you play a game like Monopoly, the child should be the banker. Checkers is a game that shows a child the value of evaluating each piece before committing its movement, and the beginning of long term placement strategy. Backgammon build on these skills and chess is the ultimate developer of strategy. If your child likes to cook, now is the time to double and halve recipes. Three dimensional puzzles with five to seven pieces that combine to form various shapes can intrigue a child for hours (and make a great car toy for those long summer trips). The basic concept here is "Follow the child". When he or she expresses an interest, look for logical exten- sions of that interest and support them. Most parents reading E-Math News have a technical eduation and career, and can probably remember being teased for excelling at math and science. "Nerds" and "geeks" are among many charming names that are heaped upon children with these skills. One solution for children facing such cruelty is to remind the tormentors who makes the most money when school is over and real life is all there is. Isn't Bill Gates, "geek", the richest man in the world? Another strategy is to kill them with kindness. Offer to tutor the tormentor since math is so hard for them. Unfortunately a good self defense course is often necessary, and a parental commitment to back up the child if self defense is necessary. It is a sad comment on our society that excellence in technical fields is punished. Math haters are often suffering from a largely school-induced phobia. Too frequently elementary teachers are themselves math haters and transmit this attitude to their pupils. To this day girls are teased as unfeminine if they like math and science. See the above paragraph for strategies, and remind the girls that classes in high school and college in math and science are chock full of guys. As puberty begins to affect their every brain wave, that argument may actually carry them through to a career in a technical field where their true abilities lie. Some people genuinely have little aptitude for math, and learn to hate it. Such children would benefit greatly from the Montessori "hands-on" approach. Montessori methods stress tactile learning. Adding, subtracting, multiplying, dividing, fractions, and three dimensional geometry are taught by feel, using special materials that parents can make themselves at home, inexpensively. I strongly recommend a book called "Teaching Montessori in the Home; The School Years" by Elizabeth G. Hainstock. It explains in simple language, with pictures, how to make and use the mathematical materials that can teach your child math with his/her hands first. It is available through the Math Options bookstore at http//www.amazon.com/exec/obidos/ASIN/0452279100/mathoptionsinc. Finally, continue to teach your child about money. Sales tax is percentages. Interest is merely multiplication and addition. It may not be too early to begin a visual demonstration of interest earned and interest paid on credit debt. Using a calender and two jars, add $1.00 to each on Day 1. Add ten percent compound interest (explain that this is a speeded up demonstration) each day to the savings jar (i.e. add ten cents on Day 2, eleven cents on Day 3, etc.) Add 20% compound interest each day to the debt jar. At the end of 35 days the interest jar contains $28, while the debt jar has $590! Which would you rather do, my child? Save or spend? Credit Andrew Tobias in Parade Magazine for this idea, and for the calculations. Remember, what is important to you will be mirrored most strongly in children this age. What you fear and hate will be similary treated. Bring home examples from your work and share them with your child. Most like to hear about the real world and why all this "stuff" in school might actually have a purpose. Make your impressions now before teenage madness unfolds. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Beth Heffernan is Vice President of Math Options. You can reach her at mailtoBeth@MathOptions.com
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Book Review ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Measurement System Analysis "Measurement System Analysis" is one of the most valuable references you can have for Gage Repeatability and Reproducibility studies. This manual, developed by Chrysler, Ford, and General Motors, details every step of the Gage R&R process, from developing a study through collecting data to various methods for analyzing your data. The presentation is clear and accompanied by worked example. You won't want to miss Section 5, "Gage Performance Curve." This curve is a billiant way to communicate the results of a study in in a visual way that everyone can understand, and this book shows you exactly how to create it. If you make measurements in your work, you can't afford to be without this manual. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ You can purchase a copy of "Measurement System Analysis," from the AIAG (Automotive Industry Action Group) by calling (248) 358-3003. The price is $11.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ask Statman ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Written by Dr. Charles Whitman ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Dear Statman- We would like to optimize the preventive maintenance plan for our pump valves. Right now, we don’t know how to set it up. Can you give us some advice? Signed, Un-pumped
Dear Un-Pumped You are lucky. It turns out that statisticians and reliability engineers have long ago worked out a formula for how to optimize your preventive maintenance (PM) plan. For those of you who aren’t familiar with PM, I’ll explain. Let’s take the above example. A pump has parts (like valves, bearings, wiring, etc.) that wear out with time. As these parts wear out, they have to be replaced. One strategy would be to wait for the part to fail and then replace it. However, what if the failure causes a lot of damage to the pump? Then you don’t want to wait until it fails. You would rather replace it before it fails so that no damage will occur. On the other hand, you don’t want to replace the valve too early because it may have a lot of life left in it. A compromise is necessary. What to do? To find out, please read the rest of this story at http//www.mathoptions.com/preventi.htm Thanks, Statman. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If you have a question for Statman, please send it to mailtoStatman@MathOptions.com. Statman will answer questions about basic statistics that are of general interest to people working in industry. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Copyright 2001 by William D. Kappele, Beth Heffernan and Charles S. Whitman ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If you like E-Math News, please forward it to a friend. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A free newsletter published every other month by Math Options Inc. http//www.MathOptions.com 814 Lakeway Drive #179 FAX (503) 218-6587 Bellingham, WA, 98221 Toll Free (888) 764-3958 William D. Kappele, Editor Bill@MathOptions.com
To subscribe to or unsubscribe from E-Math News please visit http//www.mathoptions.com/e-math.htm. If you don't have access to the World Wide Web, please send E-Mail to mailtoEMathNews-request@listdelivery.com with either "suscribe" or "unsubscribe" in the message body. |
|
www.MathOptions.com (888) 764-3958 |
Vol. 3, No. 3