Stability, Capability or Normality – What comes first?

From the time we used to be kids, a question always used to rage around the town, “Who came first – The hen or the egg?” I guess a similar notion needs to be applied to three really important considerations for a process and the data distribution of the process variables. The three important considerations here are – Stability, Capability and Normality.

The question is – Which one of them comes first? Meaning – Which one of these three would you check first, then second and finally list? Can you just check any of them in random order? Let us first understand what each of these conditions mean.

Stability means the process being stable and in other words that means the process is producing stable output at all times. With the consistency with which the process produces the outputs, it could be very easy to predict how well the process would perform in future.

Walter Shewhart called this a state of statistical control: Normality means a condition or the state of the data distribution which follows a normal distribution. I am not going to talk about the characteristics of a normal distribution but I can definitely tell you that a normal distribution follows symmetry about the mean and can be described in terms of mean and standard deviation.

Capability describes how capable the process is in meeting the customer needs. When the customer describes his needs, he often ends up giving two things – The target and the specification limits. The specification limits also known as spec limits are provided to the business to give them an idea on the acceptable variation to the customer. The customer by providing these limits immediately tell the business that they should endeavor to produce their product within this range.

Mean or specification limits?
With the customer giving both target mean and spec limits, the question is – Should the business strive to meet the target or should it try to be within the spec limits? Let us understand this with an example. You have demanded a shirt size from a store of 40. The target for the store is 40. Additionally, you also specify that the store could give you shirts between 38 and 42.

That means you can now accept shirts given to you in the range of 38 and 42. If the store gives you 39 consistently, you would still accept it because the shirt is in your acceptable range but you would still look out for shirts that are accurately 40. Subjectively though it means you would be satisfied but not pleased. So, given an opportunity the business should always strive to meet the target and not the range. Point besides, any comment on the process conditions should and can be made only if we have ascertained if the process is in control or not. A statistically unstable or out of control process will always produce unpredictable results and thus we cannot even determine if the process is capable or not. Thus always and always, stability check comes first.

A Six Sigma practitioner needs to know if his process is stable or not. If the process is stable, he can go ahead and check if the process data follows normal distribution. Remember at this time the practitioner may sample his data and talk of sampling, Central Limit Theorem kicks in. Besides the point, you have a variety of tests like the Anderson Darling test, the Ryan Joiner test and so on, which will help you ascertain normality status of your process data. And then once Stability and normality is checked and confirmed, we move on to knowing if the process is indeed capable or not.

Process Capability is often centerd on knowing the Cp and Cpk value for the process. You would be able to know these values by applying their standard mathematical formulas and you shall also be able to interpret the readings. But any decision to understand the Cp and Cpk value can only come after you have ascertained stability and normality.

The catch here is --- The process could still be stable, but in terms of meeting customer specifications, it is not capable. That means, the process is stable but it is stable in producing bad outputs. In such a scenario, the process being in statistical control means nothing in terms of deciding how good or how bad the process is. In simple words thus, stability and capability need to be treated hand in hand in terms of interpretations, but at all times, the word stable needs to come before saying the word capable.

Often, Six Sigma practitioners ignore checking these basic goalposts for a process leading them to deduce or make wrong inferences about the process. Hoping that this article is able to guide you to the right set of inferences!