Russell Veitch mentioned boids in response to my post on XmR Process Behavior Charts for count data. Boids are modeled by defining an initial velocity, emission rate, an attractive force between each boid to form a flock, a minimum separation distance, a maximum and minimum velocity and angular velocity to determine how tightly they turn, a target attractor to determine where they go, some randomness, a "Q-Skills3D" (plus some other stuff). I cranked up the randomness to make my boids look more like drunk sea gulls, than starlings.
Real Life
Real life is not controlled by models. However we can try to build models to mimic real life. I could tune my model by reducing randomness etc, and adding some flapping, to make my boids look more like birds.
Processes are not controlled by models. Most processes are changing and may be almost impossible to model. However, traditional statistics depends on models.
Dr Shewhart
Dr Shewhart’s brilliance was to show that he could characterize processes WITHOUT a model. He hypothesized that his Process Behavior Charts could be used for any process without knowing anything about the process. Dr Wheeler proved Dr Shewhart’s assertion, for 1143 different distributions. Knowledge of data distributions is not needed for Process Behavior Charts. Process Behavior Charts work for ANY data distribution. There is no need to test for normality and NEVER corrupt your data by normalizing.
NP, P, C, U charts
By contrast, NP, P, C, U charts, do depend on a data model. NP and P charts are based on the binomial distribution; C and U charts are based on the Poisson distribution. Each has a set of 4 different assumptions. If these assumptions are not met, the chart is inappropriate. Each of these assumptions must be considered before using these charts.
XmR for Count data
XmR charts, like XbarR charts, do NOT depend on a data model. They can be used for either variable or count data. XmR are the perfect, multipurpose chart, suitable for every employee, without needing computers.
Dr Shewhart and NP, P, C, U charts
The obvious question is why did Dr Shewhart use NP, P, C, U charts and not XmR?
Simple. XmR charts didn’t exist until almost 2 decades later, when they were invented by Jennett.
Specialty Charts
The classic example for the use of C and U charts is blemishes. As a guideline, when one can count blemishes but not “non-blemishes”, it suggests Poisson distributed count data. When one can count the number non-conforming, it suggests binomialy distributed data.
Challenge
Suppose a customer says they want to chart complaints. What do you do? What would be the first questions you would ask (hint: think of the “operational definition”)? If for some reason, you wanted to use Specialty charts, which would you use, and what questions would you first ask? How would you know if you had chosen the right chart?
by Dr Tony Burns BE (Hon 1) PhD (Chem Eng)