Archaeological Quality Control
I used to own an archaeological site in Texas. I found a number of lithic artifacts there, mostly Archaic Culture, but one more recent and a couple older. I found two pieces about 6 cm long and about 1.5 cm thick in cross section. The cross section was roughly a rhombus. They sort of look like heavy wrought iron nails, but are made of flint. I am not sure what their purpose was, but it has been suggested to me that they are pre-forms, pieces to be traded or worked later to a final form. The two pieces are virtually identical, same size, same shape. They are a remarkable example of Quality Control several thousand years old among Stone Age People.
Another piece I have is a small point about 3-4 cm long. It is nominally an "arrow point," but it has no notches or stem. It has a flute on one side. The butt end is blunt. Unlike the other pieces, which are made of a gray flint that corrodes to white, this piece is reddish, I think made of jasper perhaps. Although many of the points and tools I found at the site are still somewhat sharp, this item is pretty dull, almost like it was stream worn a bit. I picked up an old used archaeology text book which had a section on Paleo-Indian culture. It had a two page layout of the collection of the Lehrner Site points found in southern Arizona, mostly within the bone scatter of a mammoth. The drawings it says are actual size. Item D in the display looks just like my jasper fluted point. If I lay it down on the page, it fits right in the outline of the drawing, as though it is the same point. However, from another source, I found that Item D has flutes on both sides, while my point is fluted on only one side. Nevertheless, the Quality Control at two sites several hundred miles apart is pretty good.
Mean
And old definition of "mean" is common, ordinary, perhaps even typical, in a low sort of way. This sounds more like "mode" or "median" but a "mean" is presumed to be typical, an ordinary value as well. All of these are different ways of seeking that typical, ordinary, common value.
Logic
Logic does not live up to its reputation, compared to Science. Logic is thinking about it. Science is observing it.
Which are you going to believe if they contradict? Seeing is believing.
When you use logic, five things can happen and four of them are bad ...
You have incorrect premises and your conclusion is wrong.
Your premises are incomplete and your conclusion is wrong.
You have irrelevant premises that work into your logic and your conclusion is wrong.
Your logic is faulty and incorrect, so your conclusion is wrong.
Or ...
You have a complete set of correct premises uncontaminated by irrelevant ones and you apply perfect logic and arrive at the correct conclusion.
Actually, there is a fifth thing that can happen. You can have incorrect, incomplete, and irrelevant premises with faulty logic and yet still arrive at the correct conclusion. This happens all of the time, because the conclusion was observed in fact and the logic to explain it was constructed afterwards, using whatever premises are conveniently at hand. That is, the conclusion was observed (science) and the logic constructed as an afterthought.
This last sort of thing seems to confirm the logic process as a good method in people's minds, since it so often gives correct conclusions. This is where the reputation of logic as a good method comes from. Then people apply the convenient premises and more faulty logic to arrive at other conclusions, in which they place great faith, since it apparently worked so well before.
Science is based on data, observed facts. It is not based on logic. If it was based on logic, we would have figured everything out already by thinking about it, and there would be no point to collecting data, observing things, and performing experiments. As Einstein said, you only need one observed fact to overthrow a logical theory.
Folk Wisdom, Dogs, and Statistics
I was talking to a chance encountered person at a gathering the other night and this person told me that the worst class they ever took was "Statistics," unaware of my background. I agreed that Statistics is often poorly taught, often at the introductory level by people who do not understand it. It becomes a hodgepodge of seemingly unrelated equations, terminology, and counter-intuitive rules.
I said that actually, the fundamental ideas of Statistics are common sense. Sometimes they are embodied in folk sayings. Some of these are ...
Measure Once, Cut Twice. Measure Twice, Cut Once.
We learn from our mistakes.
Failure teaches Success.
Actions speak louder than words.
An Experiment speaks louder than an Expert.
Don’t put all your eggs in one basket.
Only a fool tests the depth of the water with both feet.
The burnt child dreads the fire.
There is safety in numbers.
There are two sides to every question.
Some years ago I took my dog to Obedience Training. We were given handouts for each week's homework. Now dogs do not know anything about human language or what we want them to do, at least not at first. How do you train a dog? It was immediately obvious to me that the methods presented in the class and in the handouts were just a presentation of controlled data with replications. The dog as a Statistician would need to analyze this data, draw conclusions, and learn what was required. Dogs understand statistical reasoning. So do humans. We are all Statisticians.
Experts, Logic, and Experiment - A Plumbing Story
My wife hired a plumber to install a new kitchen faucet set which she had bought. It was an easy job. However, when she tested the left hot water faucet, holding her hand under the flowing water, it never warmed up but remained cold. When she tested the right cold faucet the water became warm, then hot. The plumber had mismatched the faucets to the water feed lines under the sink.
She recalled the plumber. He was incredulous. He came back and checked, just as my wife had and confirmed the problem. He said he did not see how this could have happened since he installed the lines correctly.
He looked under the sink and the left line went to the left faucet and the right line went to the right faucet. The plumber said that the builder had installed the feed lines backwards, the left feed line should have been hot but it was cold, and the right should have been cold but was hot. He switched the feed lines so they crossed under the sink to the correct faucets on top. Now the left hot faucet gave hot water and the right cold faucet gave cold.
Experts say that the left feed line should be hot and the right feed line should be cold.
Logic says that if you attach the left faucet to the left feed line it will be hot. If you attach the right feed line to the right faucet it will be cold.
Experimental testing showed that the left faucet was cold and the right faucet was hot.
Which of these methods of determining the truth actually determined the truth: Experts, Logic, or Experiment?
A Control Chart (X-Bar-and-S Chart, the basic prototype of all Shewhart Control Charts) is a kind of open ended One-Way Analysis of Variance. Each new Subgroup is a new “Treatment.” If all of these subgroup treatments have the same population or process mean, then the process is “In Control.” If some of the subgroup treatments have different such means, then these are Special Causes and the process is “Out of Control.”
Usually the Special Causes are thought of as specific changes like Fixed Effects in Analysis of Variance. But much of the undercurrent of Special Causes is random. No one plans them or can predict them. If the Random Effects One Way Analysis of Variance is then the model for a Control Chart, then in effect we are dealing with Variance Components.
Variance Components is a good first step in analysis of a process before implementing a Control Chart.
Control Charts that are Not Control Charts
Frequently "Control Charts" display Individual Values. The primary response to "Out of Control" with these Charts is generally not to review the Process for inadvertant changes. If so, then it would be a Control Chart, although it would be an insensitive one, since it is using Individual Values instead of a more precise Sample Mean, to detect changes in the Process Mean.
Sometimes the Response to "Out of Control" is primarily is to make adjustments. If so, the Chart is not a Control Chart but a "Feedback Control Chart." It is a sort of manual Automatic Process Control, better done with PID Condrol methods and others.
Commonly, when the Chart is monitoring a Product Parameter, especially a final Customer Specified Product Parameter, the primary response is "Containment." That is, the specific Lot or Lots or Segment of Product "associated with or "near" the "Out of Control" event is pulled for special handling and inspection. Only after it has been checked and found okay or else purged of potential questionable material is this material allowed to go to the Customer, or else it is "scrapped." The use of the Chart like this is not as a Control Chart. This is Acceptance Sampling put in a format of a Control Chart. The sampling plan is one unit from some Production Segment (like a Lot). This is a pretty lousy Acceptance Sampling Plan, especially if it is one size fits all and not set up this way for good reasons other than administrative simplicity.
Labels: Control Chart, Individual Values
