March 2006

"Quality Focus" - monthly Genesis column

Probabilities and Possibilities

Moving from averages into the world of variation...

Welcome back to “Quality Focus.”  If you have been following the column, I briefly discussed the concept of “quality” in January and that of Arithmetic versus Statistics in February.  Under the assumption that we all are comfortable with the subject of Arithmetic, we now turn our focus to Statistics. 

First, let us lay the foundation by stating that – at least in the mass-production world – quality cannot be defined apart from Statistics.  Period.  Of course one might describe the “quality” of a single can, a container of ink, a section of substrate, etc. without resorting to Statistics.  But when in the canmaking world are we ever interested in the “quality” of a single item?

 So, what about Statistics?  Why is this branch of Mathematics so powerful?  Furthermore, what could it possibly have to do with the production of cans?  Or the supplies and equipment that support that production?

 Let me first declare that if you – the reader – can average a column of numbers, you are “halfway” toward becoming a Statistician, as the first consideration in Statistics is the “mean” or average value of a set of data.  For instance, if we consider, say 10 beverage cans whose diameters measure – in inches - 2.600,2.601, 2.599, 2.599, 2.600, 2.601, 2.600, 2.599, 2.601, 2.600 – the average, or mean, can diameter is 2.600.  Easy enough.

Let us examine another group with measurements of 2.601, 2.598, 2.601, 2.602, 2.600, 2.599, 2.601, 2.598, 2.602, 2.598.  Again, a mean of 2.600, but these are two very different groups of cans.  Why? 

Enter the concept of variation, which is essentially the second half of becoming a Statistician, albeit this part of the science is HUGE. 

Allow me then to introduce the statistical concept of sigma – or standard deviation.  This is a calculated value for any set of data (for a detailed explanation click here). 

For the first group of cans, sigma is .0008” and for the second .0016”.  So what?  Well, let us assume our target diameter lies between 2.595” and 2.605”.  Both groups appear to satisfy this requirement, right?  Well, not quite. 

Statistical calculations will show that the first group is from a total population of cans that will probably not deviate from the specification.  Why probably?  Statistics deals with what is probable from a set of possibilities.  Obviously one could make an argument that almost anything is possible but not that anything is probable. 

The same calculations performed on the second group of cans indicates that several thousand cans will probably fall outside the specification for every million produced.  Even though both groups are “on target,” and apparently “within specification,” the “quality” of the first group is exponentially higher than that of the second. 

As I discussed in the January column, “quality” is defined as the ability to hit the “target” as closely as possible as often as possible.  This brief example provides us a general concept of how “good” might be “good enough.”  I hope I have clearly illustrated the need to be as “good as possible (within practical limits).” 

Next month we will grapple with a subject probably even more difficult to deal with than all the high-level mathematics required to properly control a process, namely “measurement.”  I promise you will be surprised – and hopefully more informed - by my observations.