Interview of Bill Hunter on Statistical Variability and Interactions by Peter Scholtes, 1986:
In this interview Bill Hunter describes how results are made up of the impact and interactions of many variables. Many of those variables we don’t know about or account for. What we normally do is try to figure out the most important variables for processes and then experiment with those variables to find the best options given what we are trying to achieve.
Often the description of what is going on in such cases is that there is arbitrary error or random variation that influences the final results. What Bill discusses in this interview is that what is seen as arbitrary or random is often identifiably caused by specific variables. But often we don’t know what those variables are or how they are varying while we are getting different results over time.
He discusses how many research efforts seek to find the most important 2 variables and create a model based on those 2 variables to predict results. Even in PhD level research that is often done. He then discusses how to deal with other important variables.
He discusses the real world problems businesses must face in creating solutions that work.
If they are going to sell the product in Mississippi, and they are going to sell in Arizona and North Dakota, they have to have a robust product that will work in all these different conditions… It is not good enough for them to have a model that works sometimes… they’ve got to probe deeper and learn how relative humidity affects things and build that into the whole system in a different kind of way… they have to try and dig out the effects of these other x’s
So the business has to figure out the impact of many more variables in order to create reliable and robust products and services. This example is about variables that impact the use of the product by a customer, but the same concept applies to processes within your business.
For some processes it is enough to know a couple important variables and have an understanding of how they interact to impact results. Often though problems are created because the organization doesn’t learn enough about variables that can have a substantial impact on results and therefore feels blindsided by poor results. In some of those cases they were blindsided not by unforeseeable random factors but by variables they should have learned about. And then based on that knowledge designed their processes to take into account the potential impact of variations in that variable.
Bill also discusses the issues with how statisticians often approach analysis where the take the model (often based on only two important variables) and then use “experimental error” (“which we endow with all kinds of wonderful mathematical properties”) to explain the variation in results.
Result = f(x1 + x2) + g (x3 + x4 + x5 + x6 + …)
is seen as just:
Result = f(x1 + x2) + error
There is some justification for some of these assumptions [around normal error] because errors when you look at them do tend to be normal. However, they don’t tend to be independent, which is a key assumption.
…
If you really want to understand a system then you keep studying and studying and studying and moving some of the x’s in the g function to the f function. That is when you learn, and that is how you reduce variability, because this is where the variability comes from because some of [the items in g function] jump around.
The g function includes all those variables that are shown in one way of viewing a model as “random error.” So by learning about your system you discover move variables that are important and should be considered and managed and move them into variables that are considered in your model. By taking account of those variables that moved from function g to function f you can design the system to reduce variability. For example, if some measure of the input you receive from the supplier impacts the final result it may be possible to adjust a couple of variables that you have control over to adjust for that variation in order to get the result you wish to achieve.
In a service example, it could be if more than 1 of the senior level engineers are pulled off a project then it is necessary to adjust the team in some way (add a senior level project manager or add an extra person to the team)… in order to maintain the expected result of the team. The concept (learning about the processes and systems in your organization and knowing how variables will impact the results) is applicable to many situations. It is often easier to understand examples in manufacturing production but the concept is not limited to that domain.
Bill ends the interview with some thoughts on the challenges of learning and experiments in the social sciences.
In the video he is proposing this view (the g function with many x variables rather than just a catch all error function) would be a better way to introduce variation to statistics students. It seems to me it is also a better way for those interested in improving processes in their organization to understand variation.
Related links:
- More information on variation and interactions
- Life and Legacy of William G. Hunter web site
- Bill Hunter videos
- More Curious Cat videos
Part two of this interview: Improving Quality and Productivity in Organizations.
Related posts: Root Cause, Interactions, Robustness and Design of Experiments – The Art of Discovery by George Box – 200,000 People Die Every Year in Europe from Adverse Drug Effects, How Can We Improve? – Common Cause Variation
