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Statistical Thinking

“It ain’t what you don’t know that gets you in trouble. It’s what you know for sure that just ain’t so.” – (Attributed to Mark Twain, but real origin seems unknown)

Statistical thinking generally does not come naturally to most of us. As humans, we are good at deterministic thinking. In other words, we can normally come to a logical conclusion as to why a certain event leads to a specific outcome. When things are black and white, it is relatively simple to conclude that a specific action will lead to a specific outcome.

What we are not so good at, is when we are dealing with the grey areas of life. Unfortunately for us, most areas in life are grey. One action can potentially lead to many different outcomes, many of which may not have occurred to us, or may in fact be undesirable.

In other words, we live in a world where outcomes are more a matter of probabilities rather than certainties. Within this world, we can easily be tripped up when we believe that we know what the outcome of an action will be, when in fact there could be many different outcomes.

Cultivating the ability to apply statistical thinking is therefore an important skill when we are trying to gaze into the future to divine what may lie in store for us. It helps us to understand that the best way to approach uncertainty is to move towards the area of greater probability, rather than making decisions based on our own perceptions of reality and our own biases. Join me in exploring the world through statistical thinking...

This web page is essentially a compendium of articles published in The WelderDestiny Compass that deals with statistics and statistical thinking. It assists those that want to follow our discussion regarding statistical thinking without having to actually read all the back issues of The WelderDestiny Compass. It will be updated every time we discuss statistical thinking or statistics in general.

Games of Chance: When we are involved in games of chance, then we understand that there are many outcomes, and that there are certain probabilities associated with the outcomes. In our everyday lives we struggle to apply the same concepts.

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Compendium of Articles Dealing With Statistical Thinking

As you read the compendium of the articles within this page, please keep in mind that these articles also have reference to other articles within the same e-zine edition in which they were originally published. This may make the different articles below appear a little disjointed. If you would like to see the broader context of any specific article, please click through to the full e-zine to get a more complete picture.

The other advantage of looking at the whole e-zine is that there may be supporting articles posted there by some of our readers, and their insights may just be what you are looking for.

Is The Exacta-Bet Principle Tripping You Up?

Issue #003 - January 18, 2017 - Titled: The Internet of Things and the Exacta-Bet

I like to do a spot of stock market investing. I believe that it is a skill needed to survive into my retirement years, so I have started down this road. As with any of the other fields of interest that I have, I do a lot of reading, and follow a lot of different stock analysts and stock newsletters. Every stock market newsletter analyst has a different approach to how they pick stocks.

The newsletters that I really enjoy reading are those that do high level macro-economic analyses and then give stock tips based on their projections of how the macro-economic picture is going to play out. I do however seldom follow their recommendations for stock purchases, because my experience is that these analysts usually have the poorest records for stock market returns. From my experience, the analysts with the best results tend to be those with a more company specific selection methodology, or those with a more quantitative analysis methodology. Why would this be? Surely the big economic picture should give pretty good investment results?

Now, with investing there are many factors at play, but the one that is important within the discussion today is the “exacta-bet” factor. So, for those of us that are not gamblers, let me quickly explain what an exacta-bet is.

As applied to horse racing, the person placing the exacta-bet must not only predict the winner, but must also predict which horse will come second. To win this bet, the punter must correctly predict both the first and second placed horses in their correct sequence. Instinctively we know that this must be much more difficult than just predicting which horse comes first. To try and get our heads around what is going on, we can take a simple example.

Let us say that there are 10 horses in the horse race, then if we randomly guess the winner, then we have a 10% (1 in 10) probability of being right. If we got the first guess right, then we have a 11% (1 in 9) probability of randomly guessing the second horse. The probability of guessing both the first and second horses in the correct order is then 10% times 11%. Mathematically this is: 0.1 x 0.11 = 0.011 = 1.1%. We can see how quickly the probability of getting this right falls, when one prediction is based on the outcome of another prediction.

So, in the case of the stock tippers, let us look at a topical example. Let’s say that an analyst looks at the American presidential elections and then makes a stock tip based on his/her analysis. This prediction is based on the following train of predictions:

  • Which candidate will win.
  • What the broad market reaction will be to that candidate winning.
  • Which sector within the market will therefore be positioned to experience the best gains.
  • Which stock within that sector will reflect those good gains.

In essence, the analyst needs to get 4 factors right, to give us a positive return on our investment. To get a feeling of how big an effect this has, let us consider a quick hypothetical example. Let us say that our financial analyst is really talented, and would normally be able to be 80% accurate in any of these predictions on their own. This would be a very talented analyst, so we are actually giving the analyst “the benefit of the doubt” regarding their ability level.

In our example, the probability of the analyst picking the right stock, based on his/her prediction of the election outcome is: 0.8 x 0.8 x 0.8 x 0.8 = 0.41 = 41%. Given that this is below 50%, we would have to conclude that a monkey throwing a dart to select stocks would be just as accurate as the really talented analyst. It is not that the analyst does not have ability, it is just that the odds are being stacked against the analyst by the methodology s/he uses.

So, what does this have to do with welding and The WelderDestiny Compass? Well, seeing as we are in the game of predicting and anticipating the future, we need to understand our limitations. The more detailed, and the “further down the line” we try to make the predictions, the less accurate they will be.

We are therefore not in the business of predicting exactly which technologies will become predominant. Rather, we are in the business of predicting which technologies could impact the world of the Welder, and how the Welder could position him/herself to take advantage of these technologies. Some of the technologies we focus on could be superseded by other technologies, or the way in which they are eventually implemented may be totally different from what we anticipate.

Within this context, please understand that this is a journey that we are on, and that there is no clear “finish line.” It is like navigating through a storm. Only once we get really close to any object will it become clear. While we are at a distance, the objects are little more than a blurry shadow.

Furthermore, it shows us that even those people and companies that are at the forefront of the newly emerging technologies, that will eventually form our world, cannot consistently steer their technology to the final finish line over a long timeframe. Even if they have an 80% success rate for each of their planned steps to “conquer the world”, after 4 planned steps they only have a 41% probability of success.

The companies that get their technology widely adopted will therefore be those that can adapt rapidly as conditions change, and that can think in terms of trends rather than specific roads of how to get from point A to point B.

Are you able to align your thinking to give you a statistical edge in anticipating the future, and taking advantage of the changes coming?

In future editions of The WelderDestiny Compass, we will look at further factors that tend to reduce our control of future outcomes and our ability to predict the future. By understanding these factors, we start to see how to position ourselves and the need to be flexible in meeting the challenges heading our way.

To read this article within the context of the original e-zine that it appeared in, please click here...

Uncertainty in Engineering

Issue #008 - February 22, 2017 - Titled: Sensors in Welding

In engineering, there are many uncertainties. These uncertainties need to be compensated for during the design phase of a product, and some need to be controlled within limits during manufacture. Typical uncertainties for a welded structure are: 

  • Variations in the strength of the materials. 
  • Uncertainty in the loading conditions. 
  • Uncertainty in dimensional tolerances. 
  • Uncertainty in fabrication results. (e.g. weld quality and weld properties.) 

To compensate for all these uncertainties and variations during design, design factors (also called “safety factors”) are introduced. By introducing these design factors, the conservatism of the design is increased. It is not untypical for a design to have a cumulative design factor of 3 or 4. This means that if the designer knew all the relevant factors 100%, the structure or component could be one third of the strength and cost than the component with a design factor of 3. 

Under circumstances where the high design factors result in an uneconomic product, the design factors can be reduced by performing higher levels of engineering to confirm design loadings, and testing during fabrication to assure a tighter tolerance on material properties and fabrication quality.

Often the additional engineering requirements and testing can also be extremely expensive and result in great increases in project schedules. 

Communicating the extreme levels of quality assurance and control activities can also introduce risk into the whole manufacturing process. 

Is it possible that there are technologies out there that could result in reduced risk and lowered cost, resulting in significant efficiency improvements for welding?

To read this article within the context of the original e-zine that it appeared in, please click here...

Welding is a High Uncertainty Operation

Issue #008 - February 22, 2017 - Titled: Sensors in Welding

Welding is defined as a “special process” within ISO 9000. What does this mean? It means that it is not possible to fully confirm the results of a weld without rendering the weldment unusable. In short, the only way to fully confirm the properties of a weld is to subject it to destructive testing. 

To overcome this uncertainty, welding is subjected to a qualification process, and the Welders are also subjected to a qualification process. The welding procedure qualification is qualified to be carried out within a narrow range of essential variables. The idea being that as long as the weld is performed within the allowable range of essential variables, then the result should be acceptable. 

A big issue is however that much of what we would really like to know about the weld, cannot be monitored practically during welding. Typically, we would like to know what the maximum temperatures are that the base metal reaches at different distances away from the weld interface. We would also like to know what the cooling rates are. All of this is required to estimate what the weld microstructure is going to look like, and even what the corrosion resistance will be for some materials. To date, these factors could not be measured directly, so we have used “proxy” measurements to estimate these values. 

A typical proxy measurement for deciding what the weld microstructure will be, is the welding heat input. It is a proxy measurement for the maximum temperatures and the cooling rates, when taken in conjunction with the material thickness, thermal conductivity and the pre-heats and inter-pass temperatures. 

Surely it would just be better to measure the actual cooling rates? It will significantly reduce the uncertainty with all these proxy measurements. 

Another big issue is the design allowances that are needed for welding distortion and welding residual stresses. If we could dynamically measure the actual welding distortion and the welding residual stresses, then we could again reduce the uncertainties that need to be addressed with high design factors. 

It starts being clear that we could significantly improve component efficiency while reducing risk associated with failure by knowing more about the results of the welding operation. 

We will spend a lot of time looking at technologies that could aid us with this outcome, which brings us to the reduction of welding uncertainty by using sensors during welding.

To read this article within the context of the original e-zine that it appeared in, please click here...

An Uncertain World

Issue #012 - March 22, 2017 - Titled: The Special Process

I grew up in the age when the media told us that saturated fats like butter was really unhealthy. It was much better to use margarine. Every now and then there would be some "voices in the wilderness" claiming that butter was better, but those voices were dismissed as misinformed.

Then, slowly there was a swing away from this thinking, to claim that in fact margarine, that was based on hydrogenated fats, was much worse for our health than butter.

How could the "facts" around the health benefits of butter versus margarine change?

In the same manner, I was continuously told by the media that fats in general are really bad for me. Eating fats will result in cardio vascular disease and death! Rather, we should eat our grains. A healthy breakfast was a bowl of breakfast cereal.

Now we are told that grains in general, especially those containing gluten, are bad for us. In fact, refined carbohydrates in general can result in many chronic diseases. Best to eat proteins and "good fats". The good fats protect our hearts and minds!

How could the "facts" around the health benefits of carbohydrates, fats and proteins change?

Getting sun exposure has been vilified for decades. We are told to do our best to stay out of the sun, because the sun will result in us getting cancer. We were told that there is no such thing as a healthy tan. Now we are told that the lack of sun exposure is responsible for a myriad of cancers, chronic diseases and even psychological illness such as depression.

I can continue showing "facts" that have changed 180° in direction in my lifetime. Why is it that deeply held, and widely published "facts" can change? Surely if the people that "did the research" were not sure of their facts, they should have told us, right?

One of the obvious answers is that most research and reporting is biased. There is always somebody making a buck from getting a particular answer. That is why the organization sponsored the research in the first place! We have already discussed this shortcoming of human nature in a previous e-zine, so we will not pursue this line of thinking further today.

The ability to "find the answer we like" in data presented to us, is made possible by the fact that the data does not necessarily give obvious yes / no or right / wrong answers. The data collected during research has many different factors that influence the answers. Many of the influencing factors we are not even aware of.

The bottom line is that the less we know about something, the greater the uncertainty associated with the conclusions that we draw. The more we know, the smaller the uncertainty associated with the answers. But, how much do we really know?

The whole subject area of statistical analysis has been borne from this uncertainty in the world around us. Instead of seeing the world as a place where we have certainties, the world really is a place of probabilities. Not black and white, but many shades of grey. (Probably more than 50. - Sorry, I could not resist that!)

Given our current state of knowledge:

  • Butter is probably healthier than margarine. 
  • Eating certain fats is probably healthier than eating refined carbohydrates. 
  • Getting some minimum level of sun exposure is probably better for our health than hiding in the dark.

As our state of knowledge increases, the probabilities associated with the conclusions above either increases or decreases.

Engineering obviously also lives in this uncertain world. In our world of welding, there are uncertainties associated with:

  • The actual chemical compositions of the materials we are joining. 
  • The actual state of heat treatment of the materials we are joining. 
  • The level of defects in the materials we are joining. 
  • The actual chemical compositions of the welding consumables we use. 
  • The actual levels of contamination of the materials and welding consumables. 
  • The actual compositions of shielding gasses or fluxes used during welding. 
  • The level of discontinuities present in welds.
  • The assumed stresses that the welded components will be exposed to. 
  • The thermal conditions present when the welding is being performed. 
  • The amount of dilution of the welding filler metals with the base metals. 
  • The effect of random fluctuations in welding parameters during production welding due to human influence and power source characteristic influence. 
  • The levels of residual stresses induced by the welding process.

To compensate for uncertainties, engineering uses a number of different strategies to enable us to make economical, useable and safe welded components and structures. One of those strategies is to treat some processes as "special". 

To read this article within the context of the original e-zine it appeared in, please click here...

Special Process

Issue #012 - March 22, 2017 - Titled: The Special Process

If the outcome of a manufacturing process cannot be measured without destroying the component manufactured, then the process is termed a "special process". Welding is a special process. Theoretically we cannot perform enough "non-destructive testing" on a completed weld to know with a high degree of certainty that the weld will be suitable for the application.

Machining is not a special process. We can measure all the necessary dimensional tolerances required on our final component, so we know if it meets the requirements or not.

Baking a cake is also a special process. There is no way to know for sure if a cake is 100%, without destroying the cake. Destruction through taste! So, how could we "know" that a cake will be good before we take a bite?

Well, after somebody develops the new recipe for the cake, we bake the cake the first time per a well-defined recipe, following a well-defined "method". Then we taste the cake. If the cake tastes good, then we are certain that future cakes will also be good, if we follow the recipe, use adequate equipment and make sure that the person baking the cake has the skill required to do the baking.

This is the same "qualification" methodology that is followed for all special processes. It is achieved by doing the following:

  • A procedure is "qualified" by producing a representative component by following a standard procedure for our process, and then doing all the necessary destructive testing on this "prototype". 
  • We qualify the equipment to be used when applying the standardised procedure. 
  • We qualify the people that are going to follow the standardised procedure, to make sure that they understand how to follow the procedure, and that they have the necessary skill required to achieve a good outcome.

In the case of welding, we can clearly see how this works: 

  • We qualify the procedure by welding a "coupon" and then performing all our required non-destructive and destructive testing. If the tests all comply, then the procedure is qualified. This is recorded in a document typically called a Procedure Qualification Record. (PQR) 
  • The limits within which the production welding is to be performed is placed on a Welding Procedure Specification. (WPS) The WPS is provided to the Welder to do the production welding. 
  • We ensure that the equipment to be used by the Welder in doing the final production welding is representative of that used during the procedure qualification process.
  • We qualify the welder through "coding tests". 

What we need to appreciate at this point is that there are uncertainties associated with this qualification process. The mechanical tests are made on a limited number of test pieces, so statistically speaking, we do not know 100% that the mechanical properties are adequate. We only know within a certain probability that the mechanical properties are adequate.

The same goes for the corrosion properties, or the propensity of the procedure to induce welding defects.

If the necessary tests are passed, then we have a reasonably high probability that future welds following that procedure will be acceptable, but we never have complete certainty.

To read this article within the context of the original e-zine it appeared in, please click here...

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