Service times are important for any industry and we know intuitively that good performance is frequently connected with fast response times. Queensland, Australia has provided data about the customer center wait and service times at various locations, where the times are given in seconds. This gives us the opportunity to compare one aspect of how the quality of service differs at these locations.
Usually, customers are interested in good and fast service, which is why they seek to minimize their total waiting and service times. For each service center, we can take the median of the sums for each day in which measurements were made. This is how we come to the following graphic:
From this figure we see that the minimal median service time was achieved at the Mount Isa customer service center. The centers in Warwick and Toowomba also appear very high on the list, where the Brisbane service center is at the upper middle of the ranking. In general, my expectation was that in bigger cities the waiting times would increase, but in this particular case this wasn't so. In Townsville Garbutt the median service time was above 1000 seconds, which is more than 15 minutes. If every customer had to wait that long every time, we could expect that this would impact everyone's quality of life. In one case a customer waited approximately 20000 seconds (≈6 hours), but since this is an outlier, the median isn't too sensitive to it.
We can also draw the servicing times over time for all centers. This is the graphic we can observe.
It seems that between 2009 and 2010 only few centers participated in the measurement program. But as more data became available, we see that a peak has been reached between 2011 and 2012, where the performance of many service centers has declined and the waiting times increased. Even when we know that lower service times are better, we still see how it takes a minimum of around 500 seconds to serve a customer in most of the centers in Queensland. The individual colors, when they change at the bottom, show which centers have provided the fastest service during that period. And we see that these colors have changed frequently during the examined period—from orange to green to yellow. Unfortunately, indicating the color-service center name correspondence would quickly overwhelm the graphic.
We could also attempt to show which centers were the most improving over time, which is what the next figure is about.
This graphic doesn't show seconds on the x axis, but an index obtained by computing a weighted sum for each service center. We know that shorter times are more important, so we can spread coefficients from the past to the present, starting from a big number and ending in a small one. This is because more recent events can be seen as more important than events that happened a long time ago. If the weighted sum is minimal, this could mean that the service center is decreasing its service times fastest relative to other centers. At the end we "invert" the graphic, by taking the maximal value and subtracting all others from it. This way we see that the Carseldine, Cannon Park and Townsville City service centers appear as most improving. If we return to the first figure to see their positions, we observe that they all appeared few places before Brisbane.