What should be the Std. Dev.

Six Sigma – iSixSigma Forums Old Forums General What should be the Std. Dev.

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• #40825

Kumpar
Participant

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.

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#127494

NickA
Participant

Do you have a lower or upper spec?

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#127497

Gooseneck
Participant

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 re-assess  dist , mean and std. dev.

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#127529

mark Pfannenstiel
Participant

Range/4 is also a common, although very rough,  estimate for standard dev as well.

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#127530

robin moseley
Member

I BELIEVE THAT THE STANDARD DEVIATION SHOULD BE 1.5 SIGMA FROM THE MEAN

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#127533

Mikel
Member

What in the world does that mean?

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#127539

jimmie65
Participant

Sigma = standard deviation
So 1 Sigma should equal 1.5 Sigma?
I’d be very interested in how you reached this conclusion.

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#127551

Kumpar
Participant

I 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 ….

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#127554

sumant
Member

Dee,
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 (USL-Mean)/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…

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#127555

Kumpar
Participant

Hi,
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)

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#127556

sumant
Member

Instead 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.

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#127557

jimmie65
Participant

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.

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#127559

Mike Walmsley
Participant

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”.

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#127562

TipperG
Member

Dee,
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

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#127565

Nick a
Participant

If 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.

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#127566

jimmie65
Participant

The only acceptable standard deviation is that which allows the process to meet customer specs. Process capability is irrelevant unless compared to customer specs.

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#127587

CT
Participant

Dee,
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.
CT

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#127606

Kumpar
Participant

Hi Tipper,
Thanks for your time & advice i think this is the correct way to go abt it.

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