~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ E-Math News Volume 3, Number 5 September 2001 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Contents ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Schedule of Public Classes Math in Everyday Life – Should I Buy the Tank? Math in Industry – On the Shop Floor – The Inch Rules Family Math – Lifetime Learning Book Review – Teach Yourself Tcl/Tk in 24 Hours Ask Statman – Calculating a and b for a Weibull Distribution Using the Mean and Variance ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ "Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics – and they are mostly clever fools – seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way." Silvanus P. Thompson ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Schedule of Public Classes ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Date Class Location ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ November 5-7, 2001 Performing Objective Experiments Bellingham, WA November 8 & 9, 2001 Objective Experiments for Mixtures and Discrete Factors Bellingham, WA Feb. 19-21, 2001 Performing Objective Experiments Bellingham, WA Visit http://www.mathoptions.com/class_registration.htm for details. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Math in Everyday Life ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Should I Buy the tank? You are standing at a counter renting a car. You always have several decisions to make in this situation – should you buy insurance or wave it, should you take the upgrade or stick with the compact car, etc. Lately you have a new choice – would you like to buy the tank of gas? Many rental car agencies now offer you the option of buying the full tank of gasoline at the outset. They often offer you this tank at a price less than the average local price and you can return the car empty, saving you from finding a gas station in a strange city. Is this offer really as good as it sounds? That depends on how much gas you expect to use. If you will use more than one tank, this is a good deal. If you will burn less than one tank of gas, this may or may not be such a good deal. How can you tell? What you need to know is the "break-even point" – the amount of gas you must burn for your cost to be the same whether or not you buy the tank. Once you know this, if you expect to use more gasoline you should buy the tank. If you expect to use less, you will save money by re-filling the tank yourself. To calculate the break-even point you need to know two things: 1.The local average price per gallon. 2.The total cost to buy the tank. You can get these numbers from the agent at the rental counter. Once you have this information, you can calculate the break-even point as follows: Divide the total cost to buy the tank by the local average price per gallon. This is the number of gallons of gas you could buy at the pump for the price you paid for the tank of gas. If you expect to use more than this, buying the tank will save you money. If you expect to use less, you will save money if you fill the tank yourself. Here's an example: On a recent trip to Chicago I was offered the opportunity to buy the tank of gas. The local average price per gallon was $1.75. The cost to buy the tank was $32.40. The break-even point, then, was break-even = 32.40 / 1.75 = 18.5 gallons. I only expected to use about 10 gallons, so I opted to fill the tank myself. This calculation is nice, but you may not want to pull out your calculator at the rental counter to figure this out! Not to worry. At the price of gasoline in the US today and with costs generally offered to buy the tank, you would need to burn at least 80% of the tank to break even. Usually this is closer to 90% of the tank. So, if you think you will use a full tank of gas, buy it. You may save a little money. If you expect to use less than a full tank, you will probably be better off filling the tank yourself. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Math in Industry ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ On the Shop Floor – The Inch Rules by Richard Clark Ever since elementary school we are taught the idea of the Metric system being the perfect base 10 system that will become the world standard system of measurement. It sounds great in a Math classroom, but on the shopfloor level metric does not “add up” to the inch scale. Quality assurance, is attained by being able to make reliable measurements, in order to confirm a product is within a print specification. In order to make reliable measurements a company needs to make choices of which measurement equipment to purchase for inspection use. Standard (inch scale) instruments give a company more choices at a lower cost and in most cases the best instrument choice will not only be the inch scale instrument but most likely the instrument will be less expensive than it’s metric equivalent. To prove this point think of a micrometer on the shopfloor. A metric micrometer of 0.01mm resolution is of limited final inspection use because unless the part specification is wide open a 0.01mm instrument will not meet the 10:1 or even 5:1 ratio that most customers would expect. No problem, we’ll just purchase a micrometer with a resolution of 0.001mm. With this high of resolution we will have much more measurement variation because a production part is very seldom truly round, flat, or parallel within 0.001mm. In order to make a reliable measurement we will have to measure the part several times & determine the average of the multiple readings. The metric scale has given us two instrument choices. The resolution is inadequate at 0.01mm and too high at 0.001mm. We are missing an in-between resolution and the only way too attain that is to purchase a .0001” Vernier micrometer. Looks like inch wins that one. Gage blocks are effected as well. A common Metric gage block set has a 1.00mm block, a 1.005mm block, & a 1.01mm block. If we needed to find the width of a groove we would wring gage block stacks together and measure the grove using a Go/No Go (Fit/ Won't fit) method. When this is done using Metric blocks the uncertainty of the actual groove width is 0.005mm. If we used Inch gage blocks our set contains blocks measuring .1000", .1001", .1002" etc. The difference between the Go & No go stacks can now be decreased to .0001" (0.00254mm). Our accuracy capability is twice as good with the Inch gage blocks. Imagine that, gage blocks are marvels of measurement science and every measurement you make in your shop traces back to them. You buy them to be able to give you choices when engineering set-ups and comparison measurements. When you use metric blocks you will actually decrease the amount of choices you have (my elementary school teacher never taught me about gage blocks). Yet another example can be found in the gage catalogs of about any metric gage manufacturer. A height gage (digital with LCD display) has a resolution of .0005” or 0.01mm sounds like you have the best of both worlds until you look at the manufacturing specs for the gage (.001”) .We can just convert the spec to 0.0254mm but then we have a problem. Our metric resolution is 0.01mm so if the gage has an error of 0.025mm (just under the .001” limit) the metric display may round up to 0.03mm. It will appear that our gage is out of tolerance. When this happens we cannot know if the gage is within tolerance until we change the display to inch, convert the value to metric, and measure again. Our only other choice is to send the gage to an outside lab for calibration. When they send it back the calibration certificate will most likely be in inches. Inch takes another one ! In the real production world wasted time equals wasted money. So far metric is costing a bundle. Maybe we can make the money back with the products we make. Any prints with inch dimensions will need to be converted to metric. When we do this the dimensions do not convert evenly, for example: +/- .001” converts to +/- 0.0254mm and 0.0254mm can not be measured with a metric caliper, micrometer, or height gage. Our tolerances need to be made smaller (+/- 0.02mm) or larger (+/- 0.03) to “fit” our gage resolution. What do you think our customers are going to say when we want to widen the tolerances on their parts? My guess is they’ll say, “If you widen the tolerance you need to lower the cost”. That won’t work so we’ll tighten all of our tolerances. (instead of +/- 0.0254mm, we’ll use +/- 0.02mm). Has anybody ever heard of scrap/rework/non-conforming products? What will happen when we decrease the total tolerance size by 21%? (the total tolerance went from 0.0508mm to 0.04mm). Can you imagine walking into the boss’s office and saying “Sir I have good news and bad news. The good news is we are switching to the metric system. The bad news is our scrap just increased by over 20% across the board.” (I think the noise I just heard was your briefcase hitting the pavement). Bottom line: Metric is perfect in a Math classroom, but parts are made and measured on the shop floor and on the shop floor metric doesn’t measure up to inch….. you do the math. Richard Clark is a Metrologist on retainer by Qualtech Tool & Engineering in Portland, IN. E-mail feedback to qtmetrology@qualtechtool.com. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ You can learn Gage R&R in a practical, hands-on workshop at your company. Let Bill Kappele show you how to use Gage R&R in your work - not just talk about it. You can learn more about "Practical Measurement System Analysis" at http://www.mathoptions.com ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Family Math ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Lifetime Learning by Beth Heffernan Scientists and engineers are typically individuals who enjoy learning. New or better ways of approaching diverse situations are the spicy part of our employment and leisure. Yet growing in our American society is the attitude that education is a kid-thing you're forced to do at school. "Whew, I'm glad that's over!" is a scary sentiment, personally and for our nation's future and prosperity. We can provide unlimited contributions through our children by teaching and encouraging them to learn, learn, learn as the primary pleasure of their time, and therefore their life. Isaac Asimov has written over four hundred books on widely varying topics. His spur? "I suppose it's sheer hedonism. I just enjoy it so...If you enjoy learning, there's no reason why you should stop at a given age. People don't stop things they enjoy doing just because they reach a certain age. They don't stop tennis just because they've turned forty...They keep it up as long as they can if they enjoy it and learning will be the same thing. The trouble with learning is that most people don't enjoy it because of the circumstances. Make it possible for them to enjoy learning, and they'll keep it up." Surely you can conjure up the classroom scene with all working on the same subject, too slowly for some, too fast for others and of no interest to many. If this is what learning is perceived to be, no wonder our kids run from school with no backward glances. Ideally each child will attend a school that sets an individual pace, like the Montessori system of "follow the child". Home schooling is an option for some, but the parent or teacher and the child must have the temperment for this method. Public education is the reality for most kids. How do you ensure that the public school system doesn't drive the love of learning from your child? Be involved. Stop in on the classroom, or better yet, volunteer to be in the classroom on a regular basis. Don't assume because your child doesn't complain that everything is allright. Working parents can do this too. It must be a priority and presented as such to your employer. Just as you would stop in unannounced on daycare to monitor the level of excellence in tending your child's physical needs, you must similarly visit your child's classroom. After school, on weekends and holidays and on vacations, you listen to your child's questions and interests and provide followup materials. The library is a must. A child's primary ticket to success in the public or private education system is the ability to comprehend and assimilate information via the written word. Every child has interests that can be expanded via the library. Animals, trains, fantasy, sports, clothes, music, cars and nature are only some examples. If you don't know your child's interests, start NOW by looking at their room. It is your responsibility to furnish art supplies, musical instruments, park time, pets and similar tools to the best of your financial ability, and TIME to work with your child and these tools. You know which child likes to learn with others, which with someone in the room, and which alone but with a resource for questions available (you). Like every other worthwhile activity in life, you will get from your child what you put into your child. The payoffs are higher though. Lastly you must model and discuss the learning you invest with your energy. Your frustrations with difficulties and plateaus are invaluable to your child, as they need to know these feelings are normal and not unique to them. All learners struggle at times. Share the joy of victory -- play that sonata proudly, or bring home the code you wrote that saved so much time on the job. Learning with someone is never more special than when that someone is your own son or daughter. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Beth Heffernan is Vice President of Math Options. You can reach her at mailto:Beth@MathOptions.com ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Book Review ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Teach Yourself Tcl/Tk in 24 Hours One big advantage to engineers and scientist in the pre-Windows days was that it was relatively easy to write a little program to make calculations. You could use a language like BASIC to write a program to calculate the boiling points for salt solutions, for instance. The interface was simply a text display asking for the salt concentration and a text display of the boiling point. Windows changed all that. Now a simple program needs a Graphical User Interface – a complication much too great for most of us to deal with. So we quit writing little programs to help us with our work. Fortunately, things have changed. A very simple programming langusge called Tcl, or Tool Command Language, is now available. It is easily as simple as BASIC. The really good news, though, is that it makes it very easy to add a Graphical User Interface to your programs. And it is free! "Teach Yourself Tcl/Tk in 24 Hours," by Sastry and Sastry, is an excellent book for learning Tcl/Tk. Each of its 24 chapters requires about an hour of your time. When you have completed the book you will be fully prepared to write simple programs for your work with Graphical User Interfaces. The book also includes a CD with Tcl/Tk to get you started right away. If you like to write programs to help you in your work, this book will be a great addition to your library. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ You can purchase a copy of "Teach Yourself Tcl/Tk in 24 Hours," from Amazon.com at the link below: http://www.amazon.com/exec/obidos/ASIN/0672317494/mathoptionsinc You can download Tcl/Tk for free from http://www.mathoptions.com/Tcl/tk.htm ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ask Statman ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Written by Dr. Charles Whitman ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This month's ask Statman article contains graphics that cannot be adequately represented in a text version. You can find "Ask Statman" at http://www.Mathoptions.com/ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If you have a question for Statman, please send it to mailto:Statman@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, Richard Clark, 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, 98226 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 mailto:EMathNews-request@listdelivery.com with either "suscribe" or "unsubscribe" in the message body.