# Can we calculate LSL/USL?

Six Sigma – iSixSigma Forums Old Forums General Can we calculate LSL/USL?

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• #37014

Reva
Participant

Our customer wants us to achieve a Target (Avg score on a metric). Thats the specification that they have set. So in any six sigma project that we persue we have problems identifying the LSL/USL in order to calculate the process capability. If we take the customer required mean as LSL/USL we are being extra harsh on ourselves and in this process get a bad sigma multiple for the process being measured.
Kindly guide in case their exists a statistically valid method of calculating LSL/USL basis the targeted mean.
Would appreciate ur help.

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#108040

Schuette
Participant

While you can calculate an USL/LSL by using expected/historical process variation, you would be asking for trouble.
The customer is asking only for average out of ignorance – as soon as they experience the process variation, they will come back to you protesting.  You responsibility is to educate them – ask them how much variation can they tolerate in the process.  Give them example senarios if necessary, but do not accept average only as a specification, when you know that is not enough.
The customer is always right, but they aren’t always complete.

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#108043

Reva
Participant

Thanks for your response Jim !
We are still in the process of convincing our customers about the benefits of looking at process variation ;but till the time they buy our suggestion we’ll have to stick to the target model given by them.
Would appreciate if you can transpire the statistical formula (ref to ur last response) to drill down to the USL/LSL for my process.

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#108057

Schuette
Participant

I don’t see how you can supply an output to a customer without a definition of what is “good”, and what is “defective”.  It might help if you give a bit more detail on what output average you are talking about.
Whatever you are supplying to the specified “average” – what will be your contractual obligation at the shipping dock, or the service counter?
Even if the customer doesn’t think they care, you need an understanding of how your process varies, how that variation affects the end product, and documented evidence that the variation in the product is understood and accepted by the customer.

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#108059

RubberDude
Member

“Our customer wants us to achieve a Target (Avg score on a metric). Thats the specification that they have set.”
The use of the term “average score” in and of itself suggests variation is expected.  You also state that this is a “metric” which leads me to ask if this is a physical characteristic or some other measure they are looking for?  Is the customer asking for a “black box” design with target dimensions/characteristics?
I think to take you through this case study, we would need a little more specific information.

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#108072

Heebeegeebee BB
Participant

This is a classic case outlining the need for a QFD (Quality Function Deployment).
-Heebee

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#108118

Reva
Participant

Lemme explain to you the process which is being discussed here.
We are running a contact center and have to sign a Service Level Agreement(SLA) with the customer. The SLA mentions the list of parameters which we need to meet as specified. The specification asks for an average value of the entire floor on the mentioned parameter say, Call time. Now client does not specify any tolerance on the upper side to help us calculate the USL for call time.
And since we do not have the USL we cannot go ahead and calculate the process capability or z-value.
Pls suggest a relation using which I can calculate the USL for my internal projects/process and the same should also be statistically valid.
Unless we have the USL/LSL we are finding it very difficult to control our projects output in the control stage with just the process mean as a measure.
Pls help. Also its near to impossible for us to immediately get it actioned at customer’s end and get the tolerance quantified. Any solution apart fm this would be appreciated.

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#108121

John SSMBB
Participant

It is really added value,thank you.

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#108130

RubberDude
Member

It sounds as if you have a unilateral tolerance instead of a bilateral.  If I understand correctly, the customer wants an average call time to be a minimum (?) of X seconds?  Or is it maximum?  If this is the case, you can still calculate the capability based on the unilateral tolerance.  However, the first step would be to calculate the normality of the call times over a period of time.

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#108131

KBailey
Participant

Reva,
Your customer doesn’t recognize the importance of that upper spec limit, which should be related to customer satisfaction.

Collect data on your distribution and on caller satisfaction
Set a reasonable USL for yourselves
In reporting to your customer include info about your USL and performance relative to it. Keep it short and simple – like a histogram with some satisfaction numbers for each point, and with a concise explanation of what it means and why you did it.
If they’re smart, they’ll come around. If not, you still have to give them some credit – they were at least smart enough to contract you to help them out.

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#108132

Reva
Participant

My response to the clarifications demanded by you:
Yes we do have a one-sided spec which is the USL and our process avg is expected to be below that to meet the SLA.(Lower the better)
Pls advice how can we calculate the capability/sigma multiple of the process when the only thing we know is the target mean.
How can I come with a USL that is statistically valid.

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#108133

Reva
Participant

Thanks kbailey but…….
The only issue at this point is “How to ‘Set a reasonable USL'” ?
What should be my rationale behind setting the USL/LSL for my process. Is there any formula/relation that can calculate the same.

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#108134

GDS
Participant

Where is your process at currently? (Mean / stdev)
Identify variation with your process to insure that your control limits are within the customer spec limits.

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#108135

RubberDude
Member

You do not seem to understand the difference in a unilateral and bilateral tolerance.  It appears you do not have a “target” as defined in the SS world, but rather a specification limit on only one side.  A maximum limit, with no minimum limit.
In using the “call time” example, it sounds like your customer expects you to have an “average” call time of under a certain number of seconds or minutes.  I’ll assume it is 120 seconds.  This means the customer expects the call time average to be between zero and 120 seconds.  With a unilateral tolerance, the first thing you must do is determine what type of distribution your process characteristic output (call time) has – normal, exponential, etc.
My suggestion would be to gather call times over a period of time and use this data to determine distribution.  Juran’s Quality Control Handbook or other statistical references will give you the formulas for determining distribution types.  Once you’ve done this, then you can work on the capability calculations for the process.
If it turns out that the call time distribution is normal, then you will use a z factor relative to the “right side” of the distribution curve (between mean and the spec limit) to calculate Cpk.
More to the point, I would recommend you read up on unilateral tolerances.
(By the way…. “demand” is a somewhat strong term.  I did not “demand” but merely “requested” clarification.)

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#108136

RubberDude
Member

“Yes we do have a one-sided spec which is the USL and our process avg is expected to be below that to meet the SLA.(Lower the better)”
Please note that Reva has a UNILATERAL tolerance.  The “USL” is already set by the customer.  There is no LSL.

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#108137

Atul Bhatt
Participant

Reva,
The use of “Average value” for a target is confusing our friends here. I have dealt with this contact center call time SLA question in another project.
The customer’s expected average value is in fact their USL. It is not your statistical process average. The customer is demanding that the process average should not exceed “x” minutes. Therefore, your unit of measurement is a daily/weekly/monthly average. You would have to plot this average and measure the process capability with a USL of “x” minutes. For your specific case, you probably don’t need an LSL.
Hope this helps
Atul Bhatt

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#108139

RubberDude
Member

Correct Atul!!
Thanks for backing me up on the unilateral tolerance.  Seems like many of the replies just assumed there is always bilateral tolerance.  And I’m sure using the term “target” and the measurement being the “average” threw them a curve as well.
In your project, did you test for distribution type?  And what did it come out as?  Normal?  Exponential?

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#108142

Atul Bhatt
Participant

The process was bimodal. We further segmented the call data by subject matter (for example password resets were usually less than a minute, but requesting a file restore from an earlier backup was much longer).
Within respective segments, the data was normally distributed.

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#108147

RubberDude
Member

Next question:
Did the customer accept the idea of segmentation of the data due to the bimodal outcome and give you a separate spec for the restoration calls?

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#108149

Reva
Participant

Thanks for all those responses guys!
Things are getting complex….lemme straighten them a bit.
See the customer wants me to meet the avg score for the entire process say on a monthly basis. So the way we take it is the average score taking all associates in process should be less than the specified target. Thus in a situation it can happen that although we are meeting the target(the mean of the process is less than the target) but the moment i consider that target as USL half of my population would be defective.
And since we cannot expect all my agents to be meeting targets thats teh reason why i want to introduce some tolerance.
Also we can have the Target as USL only if we are considering the datapoints as weekly scores or monthly scores of the process which are not a comfortable metric to carry on as we wont be able to control the process unless i drill it down to agent level.
What do u have to add?

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#108150

Atul Bhatt
Participant

Segmentation was aligned with how the call center was staffed. (Pools of resources by skills). The idea was easily acceptable to the process owners. Since the output measure was still the same, the customer was quite ok with segmenting the data to better understand process capability.

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#108152

KBailey
Participant

Reva, there’s no magic formula but there are some factors to consider, mostly related to caller satisfaction.

Is there a time at which the rate of dropped calls increases?
Is there a time at which satisfaction begins to drop off more quickly?
Is there a call at which callers begin to become unhappy?
What kind of satisfaction level does your competition achieve?
Atul is partly correct. You have a USL of sorts, in that it’s a maximum for the average. However, it’s not a USL that lets you identify a particular call as defective – which is what you need to be able to do.
The other approach goes back to the QFD approach someone mentioned. Your customer probably doesn’t really care about time – they care about dropped calls, unhappy callers, and success of calls (closure rate, revenue, etc. if sales). Determine what those true CTQs are and use that to measure your performance. Again, report your performance measures to the customer with a concise explanation of why youdo it in order to deliver more value.

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#108153

Atul Bhatt
Participant

Reva,
You are not clear about your process Y. Your process Y ought to be the average of all agents/month (as seen by the customer).

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#108154

Reva
Participant

Yeah thatz what i mentioned. But that does not make the target an USL as my customer is ok if i come out with an avg of these agent/month datapoints less than the target. He never specifies that each of my data point has to be less than the target. He just wants a healthy avg.

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#108156

RubberDude
Member

You have a somewhat unique situation.  However, the customer criteria still is being met (average less than the “target” or USL).  The fact that individual readings will be “out of spec” is irrelavant in the report to the customer.
If you are looking for a USL for an individual call, then you will have to do more data analysis to determine what individual call USL will still result in the “overall average” to be below the “target” outlined by the customer.
I do recommend using QFD strategy to review what the customer requirements are in segmented form.
The overall goal you are trying to reach is (1) a successful call (2) in a minimum time, correct?  Look at those factors that hinder those two.  Analyze your process for the call results and why the same type of call takes longer/shorter than others.
If you review kbailey’s last post, there is some valuabe information there.

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#108157

Atul Bhatt
Participant

Kbailey,
In outsourced contact center situations, customers (managers who manage the outsourced services0 tend to take a strongly efficiency centric view, since the primary motivation behind outsourcing is improved cost efficiency. Therefore, in addition to effectiveness and wait times, it is crucial that call times are within an acceptable limit.

Reva,
You said “He never specifies that each of my data point has to be less than the target.”
I think you are confused about what you mean by each data point. A data point would be a monthly average for all agents in your case. (Not time spent on each call). If you go with the average as your process Y, you can use the customer specified average as the USL.

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#108162

KBailey
Participant

Atul, I understand what you’re saying. However, from a cost perspective, the “acceptable limit” is itself a function of the return on a call. In most such outsourcing arrangements I’m aware of, the direct cost is born by the contact center operator and not directly by the client. It becomes less of a true customer need-driven CTQ and more of a cost control issue for the call center management.
Because the acceptable limit is a function of expected return, we again get back to the success/failure of an individual call as a CTQ. Your cost to produce it is important to you, but it’s not a customer CTQ. To meet the customer requirement, the monthly average is a data point. To a call center manager who wants competitive advantage, it’s crucial to track performance to CTQs on a per-call basis.
That doesn’t mean you ignore time. You just need to understand the bigger picture in order to set the right performance objectives with regard to time.

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#108164

RubberDude
Member

I agree with most of what you said; however, I would not discount call time as a CTQ issue.  Yes, it is a cost factor if the contractor is being paid on a “per call” basis.  But it is also a quality factor in caller perception, down time to the caller, etc.

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#108165

KBailey
Participant

RubberDude,
You’re right about time as a quality factor. What we’re really saying is that caller perception and down time (or “customer satisfaction”) are CTQ’s we didn’t identify before.

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#177908

Ganesan
Participant

How can calculate the control limit for the unilateral tolerance in Xbar chart. cases of lower the best and higher the best

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