Calculating the likelihood of an event

Six Sigma – iSixSigma Forums Old Forums General Calculating the likelihood of an event

Viewing 7 posts - 1 through 7 (of 7 total)
  • Author
  • #44678


    I am working in a Contact Center environment. Have recently implemented a Helpdesk. Estimated the number of Agents required by 15-minute segment based on previous data collected believing it would flow similar to overall call volumes by 15 minute segment.
    Based on the above a schedule was designed for the agents.
    Collected call termination data (caller hangs up before answered by agent) for the past 34 working days by 15-minute segment. Some have 0 values others have values above that.
    What I am trying to determine is what the likelihood is that a specific time segment will experience a call termination due to more calls coming in than there are agents to answer on an average day.
    This would allow us to determine if we need to change schedules.
    I am not sure what tool to use to analyze this count data
    Data currently resides in Excel with rows being the 15 minute segment and the top row being the date
    I use Mini-tab 13
    Thanks, John


    Eric Maass

    I’m guessing that your data includes the amount of calls that are being handled or coming in during every time slot – but that, if there are more calls than agents, the data is “censored”: if there are 10 calls coming in and only 5 agents, then the number of calls would be recorded as 5.
    It’s not entirely clear whether you want to determine the probability overall that the number of calls will exceed the number of agents, or whether you want to analyze this by time slot. 
    If the former, you could do censored data analysis (under Reliability/Survival –> Distribution Analysis (Right Censored) ) – then, given the distribution, determine the probability that it exceeds the number of agents.
    If the latter, you may need to group time periods together (perhaps analyze for each hour or each 2 hour period) and do a similar analysis by time slot.
    Perhaps other experts will suggest some other ways that might be quicker or more effective.
    Best regards,Eric



    Hello Eric,
    Thank you for responding. I am not sure what you mean by censored.
    We do know the number of calls initiated within the 15 minute segment and the number of agents logged into the queue. What we can not see is how many, if any calls “bleed” (cross-over) from one segment to the other. There is a procedure to terminate an attempt on the queue if wait time exceeds a specified time period.
    What we are trying to determine if we have enought agents on the queue for each time segment to answer the number of probable calls coming in based on previous experience.
    Assuming that all agents are logged in as per schedule and that calls follow a predictable pattern (we know that they don’t entirely) are there time periods when right now we don’t have enough agents to possibly succeed and do we have periods when the likelihood is we have too many.
    Thanks for you assistance, John



    Consider the following questions:
    Concerning the estimated number of Agents required:

    Are you carrying a full-time, permanent staff every day of the month? Or is variable staffing already in place?)
    In order to reveal a repetitive cycle, was the previously collected data an accumulation of at least three-month (by day of week, by week of month, or by month of quarter)?
    Are standards in place? (How long a telephone call lasts?)
    Are you keeping track of those calls that are exceptions, understanding what is happening? What should be happening? And what’s the difference?
     It sounds like you’re dealing with large volume swings, for which you need some form of variable staffing to be cost effective!
    On another note, think of it this way: if you were the customer calling in to your specific help desk unit, how long would you like to be placed on hold before hanging-up? If the call is not picked-up according to a pre-set expectation (customer perception is reality!). The goal here is, as a customer, what options do you have before hanging-up? Are you listening to lousy music? Is a recorded message telling you how valued your are, but continues to tell you that the wait time is ten more minutes? You as a customer, you’re calling because your situation is out of control and you’d like someone to help you put it back in control, ASAP! You want options, so what options is the recorded message giving you? Can the customer e-mail the problem? No, because the internet service is down and that’s why they’re calling you. Okay, can they text their problem? …. Think of other solutions! Most important of all is, will someone be there to acknowledge that the customer exists? Hi, remember me? I am the customer!Good Luck!


    Eric Maass

    Here is the section of the Minitab Help menu on Censored data:
    “If your data include exact failures or if test units do not fail before your study is over, your data are right-censored…..Data are often censored or incomplete in some way. Suppose you are monitoring air conditioner fans to find out the percentage of fans that fail within a three-year warranty period. This table describes the types of observations you can have.

    Type of observation



    Exact failure time

    You know exactly when the failure occurred.

    The fan failed at exactly 500 days.

    Right censored

    You only know that the failure occurred after a particular time.

    The fan had not yet failed at 500 days.

    Left censored

    You only know that the failure occurred before a particular time.

    The fan failed sometime before 500 days.

    Interval censored

    You only know that the failure occurred between two particular times.

    The fan failed sometime between 475 and 500 days.
    It sounds like you may have to start first with analyzing right-censored data for various sets of times, then also use some approach to determine which time periods have significantly heavier traffic. This analysis may involve time series forecasting.
    I will be tied up for the next 3 days. If you need my help after that, you can email me at [email protected]
    Best regards,



    A couple of thoughts:
    have you tried control charting your data (I would use a p-chart I think percent lost calls)  You could do this for all the data on one chart and then stratify it (split it into individual days and plot all the Mondays on one chart etc) to see if there is a difference between days.
    You could also try some sort of regression to see if the number of lost calls is related to the total number of calls in a 15 minute period.  Both are discrete variables so Chi squared analysis is probably most approriate, although it may not cope well if you have lots of zeros so you might have to group the data into 1 or 2 hour slots for example.
    Finally you might be able to try a multi-vari study with the inputs day and time slot and the output number of lost calls or total calls in queue, I would do both and then compare the reults.



    Most call centers will use an Erlang computation to determine the potential service level, likelihood of blocked calls (if your number of trunk lines is limited), answer time, etc given an inbound call pattern, service level target and staffing level.  All the major workforce management tools use this computation model.  If you go out to google and search on Erlang Calculator you will also find some great spreadsheet based tools (couple hundred bucks) and some limited free calculators.

Viewing 7 posts - 1 through 7 (of 7 total)

The forum ‘General’ is closed to new topics and replies.