Dee,
I think you are going about this the wrong way.
First question you must answe ris: what does that 360 sec actually mean?
Option A:
This number is something the client (of the boss for that matter) stated as the maximum time he/she is willing to spend on the phone, then that there is your and and only Upper Specification Limit (USL) (and not the ‘mean’). Using this and assuming the distribution of time spent is lognormal (which is often the case for such process) you can then calculate the target mean and st dev using the appropriate formulas.
Of course, you should take some samples of the actual time spent and assess whether you’re assumption on distribution is correct. Using this same sample you can also assess how big the gap between the actual process average (and st dev) and your calculated ‘average’ (and st dev) is. This will give you an indication of how much work you have ahead of you and how to best go about it.
Option B:
This number is the average calltime as measured by you (or your system). Now, if you are able to calculate the average of a sample, then you are also able to calculate the standard deviation. Of course, first check what the distribution of the sample is (normal, lognormal, ….) and use the appropriate formulas.
Now compare these numbers to what the client (or boss for that matter) finds acceptable (in other words assess thegap as in option A). Depending on the outcome take the required corrective actions.
Option C:
This number is something your client (or boss) stated as being the maximum average or average maximum or similar type of nonsens. Such ‘concepts’ are simply not workable and mean nothing.
So what to do: get your client or boss to state something more useful => ‘What is the maxium time you are willing to accept?’ or formulated differently ‘When will you ask for penalties to be awarded’, ‘When will you hang up’, ….
Note: have a look at the call center data, there might be some clues in there on what clients find acceptable or not. E.g. all clients hang up after 20 sec in waiting queue => USL for call pick-up 20 sec
BTW this does not mean your operators can wait 20 seconds before picking up, it just means they must pick up somewhere between 0 and 20 secs. As explained in option A, looking at the pick-up data, you should be able to identify the distribution, based on that you can use the appropriate formulas to calculate the ideal average pick-up time from the given USL, and based on the data you can of course also calculate the actual process average…..
Of course, you should also evaluate whether the stated USL is a ‘realistic expectation’ (especially when the boss has stated it ;^). By this I mean: given your environment, the type of activities, the actual data colelcted etc… is 360 sec reasonable or can/should it be lower or higher. Discuss with your client of course….
Hope this helps
.
