Is six sigma logical?

photo credit: incurable_hippie

From Wikipedia:

In logic, an argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. The process of demonstration of deductive and inductive reasoning shapes the argument, and presumes some kind of communication, which could be part of a written text, a speech or a conversation.

More simply put logic is the study of the rules of correct thinking. It concentrates on the principles that guide rational thought and discussion. The most fundamental concept in logic is that of an argument: a set of statements, one of which is the conclusion, the others are premises, and the premises support the conclusion. In other words, it is a statement along with the evidence that supports it.

I believe that the use of well constructed arguments in six sigma is often lacking. I’ve seen too many flimsy conclusions based on the pre-conceived ideas of the practitioners involved with the data being “manipulated” to support unclear premises. Are you guilty of this?

Here are some statements; which ones are not based on logical arguments? I’ll reveal the answers in my next post below in red….

Illicit Minor
Every Black Belt is an asset to the company
Every Black Belt is a person
Therefore every person is an asset to the company

FALSE -

This fallacy has the form:

All A are B.

All A are C.

Therefore, all C are B.

Example:

All cats are felines.

All cats are mammals.

Therefore, all mammals are felines.

Undistributed Middle
All defects are bad
All blue products are defects
Therefore all defects are blue products

FALSE -

These fallacies occur if you attempt to argue that things are in some way similar, but you don’t actually specify in what way they are similar. Examples:

“Isn’t history based upon faith? If so, then isn’t the Bible also a form of history?”

“Islam is based on faith, Christianity is based on faith, so isn’t Islam a form of Christianity?”

“Cats are a form of animal based on carbon chemistry, dogs are a form of animal based on carbon chemistry, so aren’t dogs a form of cat?”

Illicit Major
All Black Belts are intelligent
No sales person is a Black Belt
Therefore no sales person is intelligent

FALSE -

Example:

• All dogs are mammals.
• No cats are dogs.
• Therefore, no cats are mammals.

Denying the Antecedent
If six sigma tended to waste money, then it would be stupid to implement it
Six sigma does not waste money
Therefore it is not stupid to implement it

FALSE -

One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example:

If Queen Elizabeth is an American citizen, then she is a human being.

Queen Elizabeth is not an American citizen.

Therefore, Queen Elizabeth is not a human being.

Affirming the Consequent
If this process is really not capable then customers would be complaining
Customers are complaining
Therefore this process is really not capable

FALSE -

One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example:

If Bill Gates owns Fort Knox, then he is rich.

Bill Gates is rich.

Therefore, Bill Gates owns Fort Knox.

That argument is obviously bad, but arguments of the same form can sometimes seem superficially convincing, as in the following example:

If I have the flu, then I have a sore throat.

I have a sore throat.

Therefore, I have the flu.

But of course many illnesses cause sore throat, such as the common cold or strep throat.

Denying a Conjunct
The defective product is blue and round
The defective product isn’t blue
Therefore the defective product is round

FALSE -

Not both p and q. Not p. Therefore, q.

Son: Can I have the cookies and ice cream?
Dad: You can’t have both the ice cream and the cookies.
Son: Can I have the ice cream?
Dad: No.
Son: So I can have the cookies.

The reason that the son can’t have the cookies and the ice cream, may be because he can’t have either one of them.

Some/All Confusion
All Master Black Belts are highly trained people
Some highly trained people are CEOs
Therefore some Master Black belts are CEOs

FALSE -

A kind of ambiguity that arises when the words ’some’ or ‘all’ are omitted and the context does not make it absolutely clear which is intended.

Cats have tails - all cats have tails? False: Manx cats don’t. Most cats have tails - true. Cats typically have tails - true. In most cases the context eliminates the ambiguity. However, beware as this is not always so. All can be easily be refuted by a single example.

Improper Transposition (a)
If I work on project X, I’ll get promoted
Therefore if I don’t work on project X, I won’t get promoted

Improper Transposition (b)
If defects don’t fall to 100PPM, the company will suffer
Therefore, if defects fall to 100PPM, the company won’t suffer

FALSE -

Tavis Smiley (interviewer): How are you going to respond to folks on the campaign trail when they ask what qualifies you to be the commander-in-chief given that you have not served in the country’s military?

Al Sharpton (interviewee): I think that just because one served in the military does not make one a competent commander-in-chief.

Smiley says that some people will raise the objection: “If ['given that'] someone has not served in the military then he is not qualified to be Commander-in-Chief”. This is equivalent, by proper transposition, to: “If someone is qualified to be Commander-in-Chief then he has served in the military.” Since Sharpton had not served in the military, this would imply that he is not qualified for the Presidency, by Modus Tollens.

However, Sharpton says that he will respond to anyone who raises Smiley’s objection by denying: “If ['just because'] someone has served in the military then he is qualified to be Commander-in-Chief”. This is the improper transposition of Smiley’s objection, and is not logically equivalent to it. To see this, notice that Smiley’s objection is at least plausible, for it says that military service is a necessary condition for being Commander-in-Chief. However, Sharpton denies an easily refuted claim, namely, that military service is a sufficient condition for being Commander-in-Chief. It isn’t a sufficient condition because there are other conditions required to fill the office of President.

Note that the negation in Sharpton’s conditional has wide scope, that is, over the entire conditional. Otherwise, the scope would be on the consequent of the conditional, producing the implausible claim: “If someone has served in the military then he is not qualified to be Commander-in-Chief”.

So, Sharpton did not answer the objection raised by Smiley, but pulled a logical “bait and switch” by improperly transposing it into an easily refuted claim. The two claims are similar enough that most people will not realize what Sharpton has done, and it is even possible that Sharpton himself did not realize it.