Category Archives: Design/Analysis

Boeing’s Fix for its Flaming Lithium Batteries: Is There A Fatal Flaw?

dubaiupsplanecrash“Boeing Co. is confident that proposed changes to the 787 Dreamliner will provide a permanent solution to battery problems that grounded its newest jet, a senior executive said Monday.” –Reuters, 11 March 2013

The reported changes include “adding ceramic insulation between the cells of the battery and a stronger stainless steel box with a venting tube to contain a fire and expel fumes from the aircraft.” –Reuters, Alwyn Scott and Tim Hepher and Peter Henderson, 5 Mar 2013

Why is Boeing confident? This is a mystery because, based on available published data, it does not appear that Boeing has positively determined the root cause of the battery fires. Furthermore, as for all safety-critical applications, the certainty of the cause should be determined beyond a reasonable doubt. This stringent requirement would be certified by a panel of independent experts of unquestioned expertise and integrity, who have no financial interest in the outcome of their review.

Without positive identification of the root cause, Boeing may be indulging in a logical fallacy that I have seen employed before, with very bad results. The fallacy is in trying to fix what is assumed to be the problem (e.g. inadequate thermal insulation between battery cells). But what if the assumption is wrong? If so, the “fix” could be ineffective, or even make things worse. For example, improving cell insulation will trap more heat within the cells, raising the cell temperature. If the true root cause is related to higher cell temperature, the added insulation could make cell failure more likely, not less.

There are many other troubling scenarios that can be hypothesized, and the only way to disprove them is to dig in and find the true root cause, beyond a reasonable doubt (including rigorous validation as discussed here: “Flying the Flaming Skies: Should You Trust the Boeing Dreamliner?“)

-Ed Walker

P.S. A good review of the genesis of the Boeing battery problem can be found here: “NTSB report shows Boeing’s battery analysis fell short,” Dominic Gates, Seattle Times

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Boeing’s Flaming Lithium Batteries: Was This A Risk Worth Taking?

boeing_batteryIn DACI’s 1st Quarter 2012 newsletter I predicted that a catastrophic safety event would eventually occur due to lithium batteries (please see “Li-Ion Battery Pack Hazards and our Psychic Prediction“). The recent fires in the initial flights of the new Boeing Dreamliner have come close to fulfilling that prophecy.

From “Detecting Lithium-Ion Cell Internal Faults In Real Time” (Celina Mikolajczak, John Harmon, Kevin White, Quinn Horn, and Ming Wu, in the Mar 1, 2010 issue of Power Electronics Technology) it is known that internal cell faults in lithium batteries can lead to thermal runaway, subsequently resulting in fires and/or explosions. Therefore the question arises: do the Boeing lithium batteries have an advanced internal construction that prevents cell faults, or mitigates thermal runaway in the event of a fault? If not, the Boeing team or vendor responsible for the battery system design is in big, big, trouble.

Although deficiencies in basic battery chemistry and/or construction appear to offer the best root cause hypothesis for the fires, there are also other possible factors. For example, it has been reported that perhaps the charging system malfunctioned, causing the batteries to overheat. However, a properly designed charger for an aircraft application would have fail-safe protection, preventing an overcharge. Plus, it was also reported that charging sensors did not detect an overvoltage. Although these factors sound reassuring, they are not sufficient to eliminate the charger from consideration. For example, one can hypothesize a charging waveform that contains spurious high frequency oscillations that create high rms charging currents. This would not necessarily result in overvoltage, but could result in overheating.

It is also possible that battery “cell defects” are nothing more than cell imbalances that vary according to production tolerances. In other words, the lithium battery, by its very nature, tends towards thermal runaway unless the internal cells are very tightly matched. This sensitivity would become more pronounced with a higher number of cells and higher mass, which would explain why no explosions have occurred in  small button-style batteries, but do occur in the larger batteries.

There are other scenarios, including the thorny possibility that some combination of conditions conspired to create the failure. And, of course, the root cause may be highly intermittent, making detection extremely difficult. Such hypotheses are undoubtedly being examined by the Boing engineers. I wish them well, and hope that they are allowed to perform their work calmly, methodically, and thoroughly.

Note: Because it may take quite a long time to conclusively establish a root cause, I would suggest that Boeing immediately begin planning to retrofit the lithium system with one containing battery types that have not shown the proclivity to explode; e.g. nickel metal-hydride, or sealed lead acid gel. Heavier, yes, but in this case safety and the economic timeline indicate that it would be wise to be prepared with a retrofit design.

(For some brief guidelines on design failure crisis management, please see Scenario #6: “Coping with Design Panic,” in The Design Analysis Handbook, Appendix A, “How to Survive an Engineering Project.”

-Ed Walker

Is Your Circuit Simulator Just A Pretty Face? Five Reasons Why Simulations Are Not Sufficient For Design Validation

Jerry Twomey recently pointed out some pitfalls with math-based circuit analysis (“Academic Simplifications Produce Meaningless Equations,” 13 June 2012, Electronic Design.com.)

I agree with the general sentiments of Mr. Twomey, but would like to point out that there is a simple solution to avoiding the pitfalls he mentions: develop equations from component data sheets, not from academic simplifications. This is straightforward and will be discussed further in a future post.

Also, it should be noted that simulations are not some miracle cure-all elixir. Indeed, simulators are also math-based creatures: SPICE and its cousins simply grind out numerical solutions to the multitude of hidden equations that are buried beneath their pretty graphical interfaces.

So what’s the problem with simulators? A lot. For example,

1. Because simulator math is hidden behind the user interface, simulators don’t promote engineering analysis (thinking). To the contrary, they promote lazy tweak-and-tune tinkering.

2. Because simulator component models are typically very complex, the interactions between important variables are usually obscure, if not downright unfathomable. Obscurity does not promote engineering understanding.

3. Simulator results typically do not provide insight into important sensitivities. For example, can your simulator tell you how sensitive your power supply’s thermal stability is to the Rds(on) of the switching Mosfet, including the effects of thermal feedback?

4. A simulation “run” is not an analysis, but is instead a virtual prototype test. Yes, it’s better to check out crappy designs with a simulator rather than wasting time and money on building and testing crappy hardware. So simulators have their place, particularly when checking out initial design concepts. Eventually, however, hardware testing is required to verify that the simulator models were correct. And you will still need to do a worst case math analysis to determine performance limits, and to confirm that desired performance will be maintained in the presence of tolerances and aging.

  • Proper Design Validation = Testing/Simulations + Analysis.

5. Simulators don’t really do worst case analysis. Yes, you can use a simulator to implement a bunch of Monte Carlo runs, but valid results requires (a) identification of all of the important parameters (such as Rds(on)), (b) assignment of the appropriate distributions to those parameters (such distributions are typically not available), and (c) the generation of enough runs to catch errors out in the tails of the overall resultant distribution (and how many runs should you do? Hmmm…).

  • Monte Carlo is not a crystal ball. It only shows you the production performance you will get if all of your assumptions were correct, and if you did enough runs.
  • The knowledge required to determine the number of runs requires an exhaustive study of the circuit’s parameters, distributions, and interrelationships (not practical), or a knowledge of the limits of performance.
  • But if you know the limits of performance, then why do you need a Monte Carlo analysis? You don’t. You can skip it altogether and go directly to a math-based Worst Case Analysis.

For further insights into math-based Worst Case Analysis versus simulations, please see “Design MasterTM: A Straightforward No-Nonsense Approach to Design Validation.”

-Ed Walker

Four Costly Myths About Worst Case Analysis

Myth #1: Worst Case Analysis (WCA) is a rigidly defined mathematical method of determining the limits of performance of a design.

There are actually a few different types of WCA, primarily:

Extreme Value Analysis (EVA)

Statistical Analysis (Monte Carlo)

WCA+

WCA+ is safer than Monte Carlo and more practical than EVA. Monte Carlo can miss small but important extreme values, and EVA can result in costly overdesign. WCA+ identifies extreme values that statistical methods can miss, and then estimates the probability that the extreme value will exceed specification limits, thereby providing the designer with a practical risk-assessment metric. WCA+ also generates normalized sensitivities and optimization, which can be used for design centering. (Ref. http://daci-wca.com/products_005.htm)

Myth #2: Worst Case Analysis is optional if you do a lot of testing

To maintain happy customers and minimize liability exposure, the effects of environmental and component variances on performance must be thoroughly understood. Testing alone cannot achieve this understanding, because testing — for economic reasons — is usually performed on a very small number of samples. Also, since testing typically has a short time schedule, the effects of long-term aging will not be detected.

Myth #3: Worst Case Analysis is optional if we vary worst case parameters during testing

Initial tolerances typically play a substantial role in determining worst case performance. Such tolerances, however, are not affected by heating/cooling the samples, varying the supply voltages, varying the loads, etc.

For example, a design might have a dozen functional specs and a dozen stress specs (these numbers are usually much, much higher). To expose worst case performance, some tolerances may need to be at their low values for some of the specs, but at their high or intermediate values for other specs. First, it’s not even likely that a tolerance will be at the worst case value for a single spec. Second, it’s impossible for the tolerance to simultaneously be at the different values required to expose worst case performance for all the specs. Therefore it’s not valid to expect a test sample to serve as a worst case performance predictor, regardless of the amount of temperature cycles, voltage variations, etc. that are applied to the sample.

Myth #4: Worst Case Analysis is best done by statistics experts

No, it is far better to have WCA performed — or at least supervised — by experts in the design being analyzed, using a practical tool like WCA+ that employs minimal statistical mumbo-jumbo. Analyses (particularly cook-book statistical ones), when applied by those without expertise in the design being analyzed, often yield hilariously incorrect results.

-Ed Walker

1st Qtr 2012

(c) 2012 Design/Analysis Consultants, Inc.
Newsletter content may be copied in whole or part if attribution
to DACI and any referenced source is prominently displayed with the copied material

This Issue: NEWS BITE: Creepy Swarming Electronic Insects Are Real! / GOVERNMENT FOOLISHNESS and Incandescent Bulbs / WORST CASE ANALYSIS and the Fukushima Nuclear Plant Meltdown / RISK ASSESSMENT and Lithium Battery Explosions / ANALYSIS QUIZ: Answer To Last Quarter’s Question / DESIGN MASTER 8.2 UPGRADE if you’ve had troubling generating WCA reports on a Win7 PC

NEWS BITE: Creepy Swarming Electronic Insects Are Real!


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GOVERNMENT FOOLISHNESS: Incandescent Bulbs Banned? No Problem, Just Buy A Heat Ball
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From “Upset about Big Brother’s Ban on Incandescent Bulbs? Buy a Heatball!
by Selwyn Duke in the 30 Dec 2011 issue of American Thinker

For earlier Newsletter comments on the absurdity of banning incandescent bulbs, please see “Unintended Consequences: Nanny Engineering” in the 2nd Qtr 2011 issue.

WORST CASE ANALYSIS: What We Learned From Fukushima – Again

“Japan is not a technically backward country  … Its nuclear power plants were designed and built with an acute consciousness of extreme earthquake dangers.

“So how is it, despite that sophistication, awareness, and preparedness, that the Fukushima crisis has nonetheless exceeded worst-case thinking? Here, the story is reminiscent of Three Mile Island and Chernobyl, and the message seems to be the same: Worst-case scenario builders consistently underestimate the statistical probability of separate bad things happening simultaneously, as the result of the same underlying causes. [Emphasis added]
Japan Nuclear Accident Worse Than Worst, Again” by Bill Sweet, 12 Mar 2011, Energywise
Image: http://www.digitalglobe.com

RISK ASSESSMENT: Li-Ion Battery Pack Hazards and our Psychic Prediction

“Internal cell faults continue to lead to thermal runaway failures in Li-Ion battery packs used in the field. Though these events are rare, the proliferation of Li-ion-powered consumer electronics has increased the risk for an event occurring on an aircraft, or at a similarly inauspicious location or time … At present there is no [battery] pack-protection circuitry in commercial use that is designed to continuously monitor the cells for the symptoms of a latent incipient internal cell fault before such a fault causes thermal runaway.”
Detecting Lithium-Ion Cell Internal Faults In Real Time” by Celina Mikolajczak, John Harmon, Kevin White, Quinn Horn, and Ming Wu, in the Mar 1, 2010 issue of Power Electronics Technology

Even though there have been several fires and a few folks have been injured or killed due to exploding lithium batteries, we predict that the risk will be tolerated until a catastrophic explosion occurs. This will be  followed by the usual screaming headlines belatedly warning of the dangers, hind-sight experts suddenly popping up on TV, hand-wringing congressional investigations, and finally, heavy-handed and grossly over-reactive governmental regulatory responses.

ANALYSIS QUIZ (Answer from Last Issue): Adjustable 3-Terminal Regulator Output Tolerance

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An LM317T regulator with 36V input is set for 24V nominal output, using 1/8W 1% 100ppm thick film resistors (10K and 549 ohms). The regulator must deliver 1A and operate from 0 to 50 C for 10,000 hours.


Q: What will be the approximate worst case output tolerance?

-2/+2%        -4/+5%         -7/+6%         -6/+11%         -9/+15%

A: -9/+15%

Surprised? You might be if you only consider initial tolerances, and don’t factor in the effects of temperature and aging. Here are the normalized sensitivities, which gives one a better sense of the significant error contributors:

DESIGN MASTER™ 8.2 UPDATE: WCA Report Generator Bug Corrected

To facilitate the efficient creation of professional worst case analysis reports, Design Master includes an automated Word document report generator, based on Microsoft Office automation technology. We’ve recently had a few Win7 users notify us that the report function is not operable on their systems. Although Design Master has been tested on other Win7 systems with no problems, variations in Win7 system speed appear to prevent the report generator from functioning properly in some cases. Design Master Rev 8.2 allows more tolerance for speed variances, which has corrected the reported issues.

4th Qtr 2011

(c) 2011 Design/Analysis Consultants, Inc.
Newsletter content may be copied in whole or part if attribution
to DACI and any referenced source is prominently displayed with the copied material

This Issue: NEWS BITE: Rising Sun Gets Snagged On Mountain And Breaks Apart! / DESIGN MASTER TIP: Minimizing Calculation Time / ANALYSIS: Why Do A Worst Case Analysis? / TECH TIP: Nice Overview of Considerations for External Components for Switching Regulators / MORE UNINTENDED CONSEQUENCES: Wind Power Kills Endangered Species / ANALYSIS QUIZ: Adjustable 3-Terminal Regulator Output Tolerance

NEWS BITE: Rising Sun Gets Snagged On Mountain And Breaks Apart!
Motorists cautioned to avoid area due to high temperatures.

First planet with two suns reported found
15 Sep 2011, NASA and World Science

DESIGN MASTER™ TIP: Minimizing Calculation Time

Do an initial run and check sensitivities. Thereafter set the variables to their respective worst case values to reduce calc time until the design is finalized. Then set the variables back to their full range for a final calculation to obtain probabilities for risk assessment.

ANALYSIS: Why Do A Worst Case Analysis?

 
TECH TIP: Nice Overview of Considerations for External Components for Switching Regulators
See “Power System Performance Requires The Right Actives And Passives” by Tim Watkins, 8 Sep 2011 Electronic Design

MORE UNINTENDED CONSEQUENCES: Wind Power Kills Endangered Species

In the Bay Area, when activists in the 1980s demanded a cleaner planet, the state responded with the Altamont Pass Wind Resource Area. The state-approved wind farm, built with federal tax credits, kills 4,700 birds annually, including 1,300 raptors, among them 70 golden eagles…

“There’s a big, big hypocrisy here,” Sue Hammer of Tehachapi Wildlife Rehab in Kern County said. “If I shoot an eagle, it’s a $10,000 fine and/or a vacation of one to five years in a federal pen of my choice.”

From “Energy in America: Dead Birds Unintended Consequence of Wind Power Development” by William La Jeunesse, 16 Aug 2011, FoxNews.com

ANALYSIS QUIZ: Adjustable 3-Terminal Regulator Output Tolerance

An LM317T regulator with 36V input is set for 24V nominal output, using 1/8W 1% 100ppm thick film resistors (10K and 549 ohms). The regulator must deliver 1A and operate from 0 to 50 C for 10,000 hours.


Q: What will be the approximate worst case output tolerance? (Answer will be posted in the next newsletter.)

3rd Qtr 2011

(c) 2011 Design/Analysis Consultants, Inc.
Newsletter content may be copied in whole or part if attribution
to DACI and any referenced source is prominently displayed with the copied material

This Issue: NEWS BITE: Mutant Singing Cantaloup Wins Karaoke Contest! / MORE UNINTENDED CONSEQUENCES: Hands-Free Faucets / DESIGN MASTER TIP: AC Rectifier Worst Case Analysis Made Easy / ART MEETS ENGINEERING: The Invisible Man / STATISTICAL DESIGN PITFALLS: Monte Carlo Is Not Worst Case Analysis

NEWS BITE: Mutant Singing Cantaloup Wins Karaoke Contest!

Freaky Robot Mouth Learns to Sing,”
Evan Ackerman, 13 July 2011, IEEE Spectrum

MORE UNINTENDED CONSEQUENCES: Hands-Free Faucets Harbor More Germs Than Standard Faucets

Details here.

DESIGN MASTER TIP: AC Rectifier Circuit Worst Case Analysis Made Easy

In our previous Newsletter we provided a pretty good estimate for the ripple current for the bulk capacitor in an AC rectifier circuit. But what if you have a large volume product and you need a full worst case analysis to ensure high reliability, but one that is not overly pessimistic so that you can minimize cost? Design Master can help you achieve that optimum balance.

As readers are aware, we’ve started to release some DMeXpert “fill in the blank” WCA templates to make the design engineer’s life a bit easier. One of these is our AC Bridge Rectifier Analysis (ACBR1 $19) which allows the designer to determine all of the worst case component stresses within a minute or two. The analysis includes the effects of source impedance Rs (such as transformer secondary winding ohms), which if present can be used to reduce capacitor ripple current requirements, hence reduce capacitor cost.

As those who have studied AC rectifier circuits are aware, this seemingly simple circuit has resisted for decades all of the attempts to generate a single-formula solution, until recently, which we’ve included in ACBR1. Based on Keng Wu’s article, “Analyzing Full-Wave Rectifiers With Capacitor Filters” (1 Jan 2010, Power Electronics Technology), Wu’s formula allows a straightforward circuit solution, greatly reducing computational time. So with ACBR1 you can just fill in the blanks, click Calculate, and let Design Master do the rest.

ART MEETS ENGINEERING: The Invisible Man

Engineers who work for the military are sometimes required to design clothing, equipment, or even entire shelters to be “invisible” to various detection means. Chinese artist Liu Bolin has a gift for applying such camouflage in a non-technological way, as seen below. Hint: If you can’t spot Liu, look for his shoes first.

From “The Invisible Man: Dragon Series,” Vurdlak, 28 June 2011, http://www.moillusions.com

Some more fascinating photos here and here.

STATISTICAL DESIGN PITFALLS: Monte Carlo Is Not Worst Case Analysis

A lot of folks like to let a simulator crank out “worst case” results, using Monte Carlo statistical methods. But as we’ve explained previously (“Design Master vs Extreme Value, RSS, Monte Carlo, & Simulation,” and “Design Master vs Monte Carlo“), this can be not only time consuming, but risky. For example, Monte Carlo can easily miss small but significant errors (see example below). In addition, if the Monte Carlo runs are improperly implemented (such as including temperature or other dynamic variables) you will likely obtain wildly inaccurate results.

The Design Master Advantage

Instead of statistical sampling, Design Master uses a top-down approach to achieve safer and more cost-effective results, by (a) detecting the extreme limits of performance, and then (b) using a proprietary probability algorithm to estimate how often those results will exceed the specification limits.

EXAMPLE

Design Master results at 2 samples/variable versus
Monte Carlo at 10,000 samples/variable, for the gain of an 8-variable filter

As can be seen, the Monte Carlo analysis detected a minimum of 8.42 versus the actual minimum of 7.86, a 7% error, and a maximum of 16.0 versus the actual maximum of 18.8, a 15% error.

Transient Voltage Suppressor (TVS) DMX Analysis File Released

Transient Voltage Suppressor (TVS) with Optional Steering Diode DMX Worst Case Analysis File
TVS1 $12.50
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(DMX files are available free to Design Master™ Professional Edition users who purchased or upgraded DM not more than one year prior to the DMX file release date.)

The Transient Voltage Suppressor analysis determines whether a TVS avalanche diode and optional steering diode will (a) survive a specified surge voltage or current, (b) clamp the surge below a specified voltage limit, and (c) not clamp the normal operating voltage. Good for any TVS diode and steering diode; just fill in the blanks using data sheet values, and get an answer in a few seconds. TVS diodes are typically rated with 10x1000us current waveforms. Steering diodes are typically rated with line frequency half-sine current waveforms. When the applied surge has a different waveform, however, the TVS and steering diode ratings must be adjusted accordingly. In addition, the ratings must also be adjusted for pulse width and temperature. To help make the design engineer’s job a little easier, this analysis contains adjustment formulas for all of these factors. Also provides standard surge waveform requirements and helpful hints.

DMeXpert™ (DMX) files guide the user with pop-up instructions, component selection lists, standard part values, important formulas, and a variety of other tips that are activated when entering a Formula cell. It’s like having a design/analysis expert at your side.

AC Full Wave Bridge Rectifier DMX Analysis File Released

AC Bridge Rectifier DMX Worst Case Analysis File
ACBR1 $19

(DMX files are available free to Design Master™ Professional Edition users who purchased or upgraded DM not more than one year prior to the DMX file release date.)

This updated and easy-to-use analysis provides all of the key waveforms, voltages, and currents for the AC full wave bridge rectifier circuit, including the effects of source ohms. Output includes average input amps, rms input amps, input watts, Rs watts, capacitor rms amps, average load volts, average load amps, and output watts.

Capacitor Current

DMeXpert™ (DMX) files guide the user with pop-up instructions, component selection lists, standard part values, important formulas, and a variety of other tips that are activated when entering a Formula cell. It’s like having a design/analysis expert at your side.

4th Qtr 2010

(C) 2010 Design/Analysis Consultants, Inc.
Newsletter content may be copied in whole or part if attribution
to DACI and any referenced source is prominently displayed with the copied material

This Issue: NEWS BITE: Reporters Scramble To Adapt To Cameramen Layoffs During Economic Downturn! / DM V8 And DMX Released / REVIEW: The Social Network: Entertaining But Not True / NEWS BULLETS: Unintended Consequences (Reusable Grocery Bags) / RECREATION: Having Fun With Fantasy Football

NEWS BITE: Reporters Scramble To Adapt To Cameramen Layoffs During Economic Downturn!


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Teleactor Annamarie Ho. Photo: Bart Nagel
Q&A: Ken Goldberg Discusses Telerobots, Androids, and Heidegger,” by Erico Guizzo, IEEE Spectrum, 1 Oct 2010

DESIGN MASTER: DM V8 with DMeXpert™ (DMX) Released

DMX provides expertly-designed “fill in the blanks” templates for thorough and efficient worst case analysis. Click here for details. If you purchased Design Master on or after October 4 2009, you can obtain an update at no charge; please contact us for download instructions (new install required for V8).

REVIEW: The Social Network: Entertaining But Not True
“Mark Zuckerberg, Facebook’s young and intrepid creator, is portrayed as a geek who starts his path to dot com glory after getting dumped by a girl … If it were true it would be a lot more compelling.  Back in 2005 and 2006, shortly after the film is set, I interviewed Zuckerberg on several occasions, and he wasn’t much like the guy on-screen.  In addition to actually having a girlfriend, a fact left conveniently out of the film, he had a lot of thoughtful things to say about the world he was creating online. ”
The Social Network’s Science Fiction,” by David Kushner, IEEE Spectrum, 7 Oct 2010

The Bozo Award is presented to screenwriter Aaron Sorkin and the movie’s producers for their lack of integrity, as demonstrated by their willingness to damage reputations through false representations of actual events.

NEWS BULLETS: Unintended Consequences Strike Again

“The CALL7 Investigators tested several reusable bags used by 7NEWS colleagues and another from a woman going into a Denver grocery store. Marchetta took the lab results to Dr. Michelle Barron, the infectious disease expert at the University of Colorado Hospital. ‘Wow. Wow. That is pretty impressive,’ said Barron. Barron examines lab results for a living. ‘Oh my goodness! This is definitely the highest count,’ Barron commented while looking at the bacteria count numbers.”
-“Reusable Grocery Bags Breed Bacteria” By Theresa Marchetta, 28 Sep 2010 Denver News

RECREATION: Having Fun with Statistics and Fantasy Football
Design Master™ is used by engineers to help create highly reliable products, but it has been suggested to us that it can be used for some fun, too, such as fantasy football or other games that use statistics. It might even provide a bit of an edge, because its probability models provide more information than simple statistical averages.

For example, you can define a group of players in the Variables Library, enter the raw stats for each player, and let Design Master generate their “player strength” probability models (Tools/Make A Model From Raw Data).

In the worksheet, you create a simple Team formula that defines the strength of the team, using a weighted sum of all the players —

TeamA = 0.2*Player1 + 0.10*Player2 + 0.15*Player3 + …

— where the weights add to 1.0 (100%).

Then press Calculate to generate the team’s probability model.

Repeat this for a competing TeamB and its players, and then compare the team models:

 

 

TeamA strength = 5 to 10                                                TeamB strength = 4 to 16

There are many ways to make a  comparison, but a simple way would be just to subtract the teams. For example, to determine the probability of TeamA losing to TeamB,

TeamAWin = TeamA – TeamB

where the minimum limit is set to zero (i.e. the case where TeamA is less strong than TeamB).

Probability models help guard against counter-intuitive bets. In this example, it may appear that TeamB (max strength of 16) is superior to TeamA (max strength of 10). But if you look at average strengths, TeamA comes out on top (8 to 7). How should these factors be evaluated?

Press calculate, and the resultant probability distribution indicates that the “weakling” Team A only has about a 12% chance of losing to TeamB:


Furthermore, knowing the actual probability of 12% provides an added edge for intelligent odds-making … all in fun, of course.

Q&A: Ken Goldberg Discusses Telerobots, Androids, and Heidegger