Upper & Lower Control Limits

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    How do you decide when to use the +\- 3 standard deviation of the mean or an X bar chart to calculate the UCL & LCL?

    I am working at a call center and trying to put limits for customer wait time, and tech support call time. What would be the best chart to use for this type of data?


    Robert Butler

    One control chart for an entire call center isn’t reasonable. You are making no allowances for differences in call type, call difficulty, operator experience, staffing differences (time of day, weekends, skill sets, etc.) and so on.

    If you want to lump everything together and ignore all of the above you could do this just to see what you see. However, since both wait time and support time have a natural lower bound (0 time) a standard +/-3 std calculation will give you a lower bound in negative time territory. What you will have to do is log the times (and if there are actually 0 wait/support times you will have to add a small increment of time to all of your data before you take the log), run the analysis on the logs and then back transform. What you will get will be a run chart with asymmetric “control limits” which will not go below 0. It won’t be of much value but it will give you some idea of what things look like.

    A much better approach would be time series box plots (you will want to be able to see the individual data points not just the overall box plot shape) for the various operators (one boxplot covering an entire week for a single operator would be a good place to start). Plots like these will allow you to see how things have changed across time and across operators. If you see some odd or interesting patterns you can take the data for that period of time and break it down further – again using box plots. Since you will know things like time of day, you can parse the time sequence box plots in various ways.

    The information gleaned from an examination of plots of this type will most likely be far more informative than any control chart you might chose to construct.



    You use calculated +3/-3 for control limits and don’t change them without good reason. But I can surmise this isn’t your real problem. As all of us have experienced, customers don’t give a damn about statistical control limits. We want to get help as fast as possible and the longer it takes the less happy we are. We don’t give a damn if the call response time is statistically controlled, no matter how you measure that. If you don’t get that you don’t understand the difference between control limits and specification limits. I used to get grief when I added lines for USL and LSL to control charts. Sure, that’s different from SPC but if the process is statistically under control but out of spec don’t you want to know about that?

    If I were you I’d use X bar R because it tells you a lot but I’d add a USL line. How do you know the USL? It’s easy if you have a service level agreement. If you don’t have that, you’ll have to collect data and do research and customer surveys to determine reasonable tolerance. If your SPC median is not well below USL you know you have a problem. Also, you need to track call response and resolution times separately.

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