Complaints Response Times


M Greenaway

Hi stats guru's.

I am trying to analyse our response times on complaints statistically, and have created the attached chart to determine if the response times show a normal distribution - which clearly they do not.

Any ideas, or do I simply have a process totally out of control ?


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The main meaning of control (Don Wheeler in Modest Proposal):

So to understand just what Shewhart meant when he used the word "control," we return to his own definition: "A phenomenon will be said to be controlled when, through the use of past experience, we can predict, at least within limits, how the phenomenon will vary in the future." Here we see that predictably is the essence of Shewhart's use of the word control. A phenomenon that is controlled is predictable, and conversely, a phenomenon that is not controlled is unpredictable.

So...., nothing to do with the distribution, in order to know if the process is in control you should chart it in a control chart (ordered by date/time) in a Individual and moving range chart.

Many stats guru's beleive that if the distribution is "non normal" (non gaussian,... I hate the term "normality"), you should transform the data to a normal distribution (with log transformation for example).

I charted your data and looks like out of control, I used X^0.5 transformation and looks fine to me.



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M Greenaway

Darius thanks, that looks very interesting.

Can you tell me how you have constructed this graph ?

I thought we had to show 'normality' before we plotted a run chart else the points are meaningless or unpredictable.

Atul Khandekar

I would agree with Darius here that for run chart / control chart purpose, first you need to get the data in time series. So you have to arrange the data in ascending order of complaint receipt date and then plot a run chart (X^0.5 transform is plotting square root of every value, there are many other transforms available - such as Log(x)). A run chart, if plotted in time series, (as the data comes in) may be useful in showing trends and patterns. You may also plot a histogram. However, as your complaint response time improves (reduces) the histogram would be stacked up more on the lower side of the scale - obviously the data is not going to be normal. ( One minor question about measurement system resolution - when a complaint is resolved on the same day, should the time be zero or one day?).

Another issue is whether the data pertains to the same 'type' of complaint. There are some complaints that can be resolved quickly, say within a day or a week, while some others cannot be resolved even after 90 days. If this is the case, IMO, you should not try to plot all the times on the same chart. This would be like clubbing two characteristics dia 10 and dia 50 on the same chart. You should try to determine a realistic, practical 'target' for completion time. (ideal target = zero). Then you either plot different run/control charts for each 'type' of complaint. If you want to plot all data on the same chart then it must be converted to a unifirm base - say by plotting deviation or % deviation from real target.

Run chart showing abnormal peaks should then prompt you to look for an assignable cause for delay in response. In this case (complaint response time), the improvement goal is not just reduction of variation but also reduction in the mean time taken to service a complaint.

For the amount of data available (less than 400 raw data points), I don't see any reason for obscuring the data by transforming it. The closer you are to the actual raw data the better. In any case, 'normality' is not an issue with a run chart.

As for prediction, I suggest you can either use a trend-line on the run chart or use a three-week moving average charts. (You can easily do moving average forecast if you have MS Excel with Analysis Tool pack). Moving average method is routinely used for forecasting sales, inventory etc.


PS: Not being a statistician, I have presented this in layman's language. A trained statistician can probably blow this to pieces. I would therefore, welcome other peoples' views on Martin's problem - I see it as a great opportunity for some brainstorming on a real life case study.



Atul Khandekar


I think there is an error in the moving avg chart I uploaded - I should have taken average time per complaint every week and not the total. Modified chart attached. Also, I have taken the complaint receipt date as the basis for calculating weeks.



M Greenaway

Thanks Atul

What I was initially trying ot do was to see if the data was 'normal' as I had it in my head that one has to demonstrate normality before one can use calculations such as standard deviation to derive control limits on run charts - am I mistaken ?

Anyways I have averaged each 5 closed complaints (sub groups of five) as they occurred in closed date order, and have plotted a histogram of days to closure based on this average, and in groups of 0-5 days, 6-10 days, etc, etc. This has produced a reasonable looking normalish distribution, slightly skewed as expected to the left.

I was pretty pleased with this, and as such took all data up to the current day, averaged each group of five closed complaints in closed date order, and plotted these averages on a run chart, with mean and UCL calculated from the first 30 groups of readings.

This has given me reasonable looking graphs, but would be interested in the opinions of the Cove regarding its statistical validity - I will post it up here tomorrow when I am back in work.

My reason for doing this is such that we can use the rules of control charts to do some proper decision making regarding our complaints process. At present the QM sends out snotty e-mails every month when he gets the response time figures, asking for improvement, and guessing at why the figures are as they are (perhaps its due to holidays - strueth !). We have no idea of the current process capability, or the variation we can expect from the process. Also we have no real log of significant process changes that might affect the capability of reaching response time targets - I hope a little science can give us clearer direction.
I guess I'm a little dense this AM. What have you determined to be your average response time in days? Also now knowing your average response, what is the nwxt move?

M Greenaway


There is a mean value plotted on the charts.

The next step is to demonstrate that this process, like any other, is subject to variation - hence knee jerk reactions based on last months figure is not a good idea. Also the charts will be annotated with process changes, such that we can see what effect the changes might have on process performance.
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