Random cause

Tom:
 
I would agree that this topic is worthy of further discussion.  I would also agree that these two words, as well as their union, are frequently misunderstood and inappropriately applied (by novices and experienced practitioners alike).
 
Some would say that nothing in nature happens by chance, everything moves in some sort of trend, shift or cycle.  If this is true, then one would also tend to believe that every X plays a role (of some type or form) in the consequential determination of Y, given that Y = f ( X1 , … , XN).  However, not all variables are created equally.  Some have more influence than others.  Thus, we recognize that some of the Xs are more influential than others.  Hence, the “vital few” versus the “trivial many.” 
 
This is not to say the “trivial many” Xs have a random influence on Y.  However, this is to say that the “trivial many” are not as influential in terms of their relative weight (with respect to a point estimate of Y or some parameter thereof).  In other words, the related partial derivatives of the “trivial many” is of such a small magnitude that the related set of variables are of no practical value during an improvement effort.
 
The capability of DOE to discern the “vital few” is well established; however, would you not agree that sample size plays a highly interactive role in this capability?  The practice of DOE may be capable of separating the independent effects, but if the sample size is too low, the DOE will not be able to detect a given amount of change (for a selected level of alpha and beta risk).  As sample size is increased (for a given alpha and beta risk), the probability of being able to detect a fixed amount of change (in the response mean or variance) also increases.
 
From another angle, we can consider the temporal behavior of Y (or any given X).  If the outcome of an autocorrelation study fails to reveal an association (across all possible lags), is it safe to say the observed behavior is not patterned (i.e., random)?
 
Is the idea of randomness a curiosity of the human imagination, or does it have some basis in the real world?  If so, how do we conclusively prove it?  If not, then what are the implications?
 
Reigle Stewart

“But the core idea of Six Sigma is that we should pursue variation to the PPM level, which requires that we take ‘random causes’ seriously.”
I don’t necessarily agree with this approach to a six sigma project.  Usually a SS project deals with either adjusting the process mean or reducing variation (from a stats perspective).  If there’s assignable cause, assign it and eliminate it.  If there’s no assignable cause, reduce the variation.
Are you saying that a project is initiated, a control chart or capability study is completed, and the conclusion is nothing needs to be done?  If that’s the case, there’s probably a fundamental error in selecting the critical Y(s) of the project.  Gotta be an identified performance gap BEFORE you start analyzing!

Tom:
I love your last sentence: “Randomness is just another word for ignorance about the causes.”  Great numerical example. 

Reigle

“Perhaps our kind forum consultants might comment on this particular aspect of the discussion.”Why? So you can jump on as Reigle and give us a Mikel or ASU reference.

How can a process be in control and have too much variations? I can understand that an in-control process can have random variations but “too much variation” rimes better with assignable causes.

Issa, a process can be in a state of statistical control
(random variation only), yet be too wide relative to the
performance specification limits. For example, consider a
given manufacturing technology that is centered on the
target value such that M = T, where M is the process
mean and T is the design target. To further our
discussion, it will also be understood the individual
“deviations” that comprises the variance are fully
unpredictable (i.e., random). In this case, it would not be
practical or economically feasible to track down and
eliminate the source(s) of such deviations. Hence, it can
be said that the given technology is centered and
operating at its maximum capability, say 2 sigma. In this
simple example, we can see that the process is “in
control” but unfit for use. This process would be “in
control,” but producing a high defect rate. To resolve this
problem, one must; a) live with the variation, b) increase
the specifications, c) find a robust solution that minimizes
the variance, d) upgrade the underlying technology, e)
block the effect of causative variables, or some
combination of the above.

Reigle Stewart,
I fully agree with you and I do not see any contradiction with what I said.

SS Tom –
Randomness is just ignorance of cause?  You just said prior to that post that it is a question of what is economically feasible to investigate.  So, which is it?  Is it ignorant to choose not to investigate?  Is it possible to assign cause to every variation?  I don’t think it is… unless someone around here has reached god like status!

One of my favourite quotes.”The generation of random numbers is too important to be left to chance.”Robert R. Coveyou, Oak Ridge National Laboratory