What should be the Std. Dev.
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 This topic has 17 replies, 12 voices, and was last updated 16 years, 8 months ago by Kumpar.

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September 27, 2005 at 1:38 pm #40825
Hi,
Need a small input, if i have a target to meet which is 360 sec. but there is no target on the std. dev.
What value of std. dev. should be considered as a good value for std. dev. I read some where 10% of the target value should be good target for std. dev.
The process which i’m reffering to is a process involving people, a call centre basically.
– Thanks in advance for the inputs.0September 27, 2005 at 1:56 pm #127494Do you have a lower or upper spec?
0September 27, 2005 at 2:04 pm #127497
GooseneckParticipant@Gooseneck Include @Gooseneck in your post and this person will
be notified via email.In the abscence of any meaningful data , try using the Poisson distribution initially. Poisson fits queuing situations that are likely to be found in call center applications.
Std. Dev is then sq rt (360) = 19.
As you gather data over time , review the need to reassess dist , mean and std. dev.
0September 27, 2005 at 10:00 pm #127529
mark PfannenstielParticipant@markPfannenstiel Include @markPfannenstiel in your post and this person will
be notified via email.Range/4 is also a common, although very rough, estimate for standard dev as well.
0September 28, 2005 at 1:17 am #127530
robin moseleyMember@robinmoseley Include @robinmoseley in your post and this person will
be notified via email.I BELIEVE THAT THE STANDARD DEVIATION SHOULD BE 1.5 SIGMA FROM THE MEAN
0September 28, 2005 at 2:15 am #127533What in the world does that mean?
0September 28, 2005 at 3:45 am #127539
jimmie65Participant@jimmie65 Include @jimmie65 in your post and this person will
be notified via email.Sigma = standard deviation
So 1 Sigma should equal 1.5 Sigma?
I’d be very interested in how you reached this conclusion.0September 28, 2005 at 9:36 am #127551I think some thing useful which came up was std. dev. = sqrt(mean).
I could not understand how std. dev. = 1.5 sigma, i got confused reading this one.
Any more … rule of thumb ….0September 28, 2005 at 9:58 am #127554Dee,
Do you have any specification limits? let say, you have USL as “U” ( if the metric is TAT, then you will have USL only). then in that case, you should keep your SD = 1/6(U) – 60( as mean is 360).
How? For a six sigma process, process capability (Cp) should be 2. then use Cp formula as (USLMean)/3*Sigma. Use Cp as 2 and get the standard deviation.
If you are looking for 4 sigma process, use Cp as 1.33 and so on…0September 28, 2005 at 10:16 am #127555Hi,
I don’t have SL’s if i have limit’s then it is easy to find out what should be the std. dev. in case i don’t have the SL’s then what as a benchmark figure i should consider for a good std. dev.
10% of target value / sqrt (target value)0September 28, 2005 at 10:25 am #127556Instead of taking 10% or sqrt(mean), best thing is set an internal specification limit. what do you want? how much is acceptable from your point of view? based on that find out what should be the standard deviation.
0September 28, 2005 at 10:43 am #127557
jimmie65Participant@jimmie65 Include @jimmie65 in your post and this person will
be notified via email.Dee –
You’re going about this backwards. Decide on customer spec limits before deciding what standard deviation is acceptable. Step back from your process and look at it from the customer’s perspective. Or better yet, get your customer’s input.
You say your target is 360 seconds (time to place an order, time before talking with a tech, ???). What variation is acceptable to the customer? Is any? Perhaps you have an upper spec limit only – of 360 seconds.
Then calculate your mean and standard deviation. Calculate sigma level, and decide if it is acceptable.
0September 28, 2005 at 11:56 am #127559
Mike WalmsleyParticipant@MikeWalmsley Include @MikeWalmsley in your post and this person will
be notified via email.Original posting was :
“Need a small input, if i have a target to meet which is 360 sec. but there is no target on the std. dev. What value of std. dev. should be considered as a good value for std. dev”.
All that exists is a target. It is unknown what the capability is at this point. It is unknown what is realistic at this point. It is unknown as to what would be realistic spec limits at this point.She is essentially asking,what would be a reasonable estimate of sigma to start with. From here she can set up preliminary bounds for the distribution estimate with +/ k sigma.
She will then start tracking the process and will eventually obtain better estimates and sigma from which to drive improvement. She will eventually obtain the real picture and from here scrap the original guesstimates.She will then have a better understanding as to what would be realistic specification limits,limits that would be challenging enough AND realistic.
Again,try poisson (sigma = sq rt mean). For her example , at +/ 3 sigma, she would initially have 6 minutes +/ 1 minute.
From Operations Management Theory (queueing theory) , Poisson would be a reasonable estimate to start with.
Ref Chase & Aquilano “Operations Management”.0September 28, 2005 at 12:22 pm #127562Dee,
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 pickup 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 pickup data, you should be able to identify the distribution, based on that you can use the appropriate formulas to calculate the ideal average pickup 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 helps0September 28, 2005 at 1:57 pm #127565If you don’t know anything but the mean… there is no rule of thumb for the standard deviation based on the mean.
Under normality (and many other distributions) mean and variance are independent of one another. Knowing nothing about your data you can’t assume one distribution or another. Gooseneck and Mike are right about poisson and the threory behind what they are saying is valid, but without data you could end up way off.
You need a spec to determine what your standard deviation should be, and a sample to determine what it could be.
Use what Goose and Mike are saying for the could be…. but you asked the should question.0September 28, 2005 at 2:06 pm #127566
jimmie65Participant@jimmie65 Include @jimmie65 in your post and this person will
be notified via email.The only acceptable standard deviation is that which allows the process to meet customer specs. Process capability is irrelevant unless compared to customer specs.
0September 28, 2005 at 8:11 pm #127587Dee,
How about you try this: Start plotting your time now, find out what the process capability is and calculate the Standard Deviation from that. Is 360 sec truely the mean? or is it 361 or 356? Just food for thought.
Another thing I think you may find is the Hawthorne Effect will help improve your process in this case.
CT0September 29, 2005 at 6:39 am #127606Hi Tipper,
Thanks for your time & advice i think this is the correct way to go abt it.0 
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