Let's say you are working on a project to reduce Turn Around Time (TAT). The current TAT has an average of 5 minutes with a standard deviation of 2 minutes. The process does not have a lower specification limit but it does have an upper specification limit of 4 minutes.

 

Would you set the goal for your project to reduce the average TAT from 5 minutes to 4 minutes?

What is wrong with this picture? How would you establish a target/goal for this project?

Dear All,

This is an important question. Let us see if someone can come up with the right answer.

VK

if the USL is 4 min the S.D cannot be 2 min

The USL may be close to 3 sigma higher than the mean of any process.

 

Targeting the goal to reduce mean to 4min means  ..Mean=USL(means SIGMA IS ZERO).

 

Therfore reducing mean to exactly 4 min is not possible(100% efficiency is not possible).

 

The LSL and USL are based on individual values and not on averages. Hence, when we set targets for our projects we should not be looking at averages but both the average and the standard deviations.

For example, if the USL = 10, then any measurement that falls greater than 10 is  a defect. If we have 4 series of measurements 8, 11, 8.5, 11.5, the average would be 9.75 (less than USL) but we have two out of the four measurements that are out of spec (50% defective).

When setting up a target, we need to set the mean such that individual values don't cause too many defectives.

 

For our example, where xbar = 5, s = 2, USL = 4

If we desire a performance with Cpk = 1.33 (Sigma Level = 4), then just by reducing the average alone we will not be able to achieve our goal (as mentioned by a few members).

We would have to reduce both the mean and standard deviation in this problem. For example, if we are able to reduce the standard deviation to 0.5 and adjust the mean to 2 minutes, we would achieve our objectives (assuming normal data).

 

Hence, one solution to this problem is reduce the mean to 2.0 and standard deviation to 0.5. Of course, we can have several combinations of the above to meet our requirements.

Any other thoughts on this problem?

USL itself is only 4 minutes. If you're going to reduce your AVERAGE to 4 minutes, you'd still be allowing the project to have a TAT of more than 4 minutes, as long as the average is maintained at 4 minutes. Statistically, you'd still be generating a lot of defectives, except for the fact that the sigma value would have reduced from a -ve value to zero.

One of the sensible approaches might be to reduce the average to 2 and SD to .33...one of the many possible combinations....

 

I should thank Mr.Suresh for posing such an interesting situation and  Mr Khatri for highlighting the importance of this situational question to evoke responses from members. It has brought to me a lots of thoughts and I submit them below for your kind consideration and comments.

 

Firstly,

   Given the problem situation and proposed solution(s), one may often be wondering as to which one one should improve FIRST due to time and budget constraints.

 I  recommend, for most of the situations, FIRST to reduce the std.deviation (s) rather than attempt to shift the mean or average.

 

Secondly,

   Some have used the word "defective" to mean "defect". However, both are different and to be used carefully.

Defect, statiscally speaking, is any performance data point not conforming to the specification limits. Whereas, "defective" is the product or service becoming useless or unfit for the intended use.

 

Not all defects make or render a product defective. The classic example is a TV with scratches ( a defect) but still works fine ( not defective).

 

Hence, a data point or an observation of a CTQ value, by exceeding the USL, becomes only a defect and not a defective. All data points BEYOND the specification limits are just defects only and may or may not make the product or service defective.

 

Thirdly,

Some one has linked the  Std.Deviation to USL. These two have NO interdependencies, and are independent vlaues set or derived by two differnt stakeholders of the process namely the manufacturer ( for Std.dev) and USL ( the customer or consumer or the buyer). While Std. deviation ( in turn UCL/LCL) is the "Voice of Process" , USL/LSL are "Voice of Customer".  Hence, statement "if the USL is 4 min the S.D cannot be 2 min" needs attention.

 

Lastly,

   Even when attempting to reduce the std. deviation, such a drastic reduction of current value of 2 minutes to 0.33 minutes is a big dream, because it is almost 600% reduction in the deviation. This indicates that the process may first be re-looked thoroughly to obtain more information like are there many operators or only one operator to know possibilities of R&R issues. My observation is that, since the std.deviation is high, there may more than 1 operator performing this pseudo process.

Ari

Ari, that was a pretty good attempt at analyzing the responses posted in so far. There are couple of points I'd like to clarify.

=> Speaking of defectives and defects, in this particular situation each project is considered a product. And if a product has one or more areas that do not conform to the specs,i.e. defects, that product is said to be defective. In this situation, if a project exceeds the 4 min period, that particular project is considered defective. Whether such a defective piece of project will have any practical significance is beyond the scope of discussion (given the very limited overall picture we have been given). But the fact remains that those individual projects which have the DEFECT of not meeting the TAT in 4 mins are DEFECTIVES!

=> With regards to reducing the SD from 2 min to 0.33, yes, it is common knowledge that it is one of the many possible solutions. We would've been able to pin-point a solution, if we're entrusted with the liberty of taking this as a case-study and been given all the data required. Right now, in this situation, the solution strategy is beyond the scope of discussion and therefore, it may not be apt to indicate whether one's point of view holds water or not.

=> Again, a great job in putting together your view points of the different responses. But do you have a first cut response to the situation posted by Suresh?

Best Regards,

Ram

Ari, Ram, SJ, Radhika, 

We have had some good discussion here.

I agree with Ram that specification limits can relate to defectives when we consider critical dimentions or criteria. Also, Ari is right in highlighting that each defect does not lead to a defective.

Let us take example of external audits. Minor non-conformities are defects but may not consider the management system as defective. However, Major non-conformities are also defects but even a single one is capable of making the management system unacceptable. There are similar product examples in garment industry and automotive industry where we work with minor and major defects. Similarly one critical defect in a call centers is sufficient for the entire call to be rendered defective.  

 

In the example discussed so far, it has been highlighted that if the requirement is Sigma Level = 4 or Cpk = 1.33, several combinations of mean and standard deviation are possible and there is no option of ignoring standard deviation reduction here.

 

To invite more discussion, let us assume this is a process where we want a significant improvement in average TAT (significant reduction in mean) and have already found that the standard deviation can not be reduced. (variation shall continue to play spoilsport). Let us also assume that reaching sigma level of 4 is not a predetermined target.

 

If I repeat the same question - Would you set the goal for your project to reduce the average TAT from 5 minutes to 4 minutes?

 

In case somebody does set that goal and the average TAT actually reduces from 5 to 4 with standard deviation being same as before, can we say that there has been an improvement in the average TAT?

 

Well, if Std Dev cannot be reduced, USL continues to be 4 mins and we're not predetermined about reaching a sigma value of 4 (even if we do, we wont be able to reach it unless you have a -ve TAT), reducing the mean from 5 to 4 mins seems to be the only way around to bring about some improvements.

Dear Shri Khatri,

In case somebody sets that goal and the average TAT actually reduces from 5min to 4min with standard deviation being same as before, we can say that there has been an improvement in the average TAT.

My views are.....

1. Assuming the USL remains the same (i.e. 4 min), by reducing the average TAT from 5 to 4, the mean of the process has been shifted towards the USL; which means moving closer to the VoC, which implies there has been improvement in the average TAT.

2. By reducing the average TAT of the process from the current 5 min to 4 min, we make the mean coincide with the USL. Let us see the two situations "before" and "after" to draw any conclusion.

BEFORE TAT reduction:

Z- value = ( 4-5)/2 = -1/2 = -0.5

From a standard normal distribution curve, for z = -0.5,

OK Region = 30.85%

Defect Region = 69.15%

AFTER TAT reduction:

Z- value = ( 4-4)/2 = 0/2 = 0.0

From a standard normal distribution curve, for z = 0.0,

OK Region = 50.00%

Defect Region = 50.00%

Since, the OK region has almost IMPROVED by 20%, we can resonably conclude that the average TAT has improved after this process improvement initiative.

(Note:I have not addressed specifically the "actual capability" ( Cpk) related points as the question was just about improvement in the "potential capability" of the process per se when shifting the mean without reducing the variation (std.dev)

Please let us know your thoughts / comments.

Regards,

Ari

Dear Ari and Ram,

 

You are right in saying that given the constraints (Std Dev cannot be reduced and will stay at 2, USL is 4min), if the TAT is reduced from 5 min to 4 min, it is going to bring about an improvement. Ari, it was a good idea to look at the sigma level and the defect probability.

 

Hence, you can conclude that setting the goal at 4 min, with nothing else changing will get you an improvement but you still have significant defects. The goal should be lower than 4 min,as Dr Jayaram has already pointed out one of the solutions with this SD could be a mean of 2min.

 

Another thought, you should be watching out for a secondary metric like quality or CSAT if you are setting too low a mean, without changing the SD.

On 06/03/2009 at 8:46 AM, Vishwadeep Khatri said:

Dear All,

 

This is an important question. Let us see if someone can come up with the right answer.

 

VK

 

Is there a solution that you are going to share for this question?

1 hour ago, Venkata Sudhir Kumar Guddati said:

Is there a solution that you are going to share for this question?

Hi Venkata, 

 

The goal originally suggested in the question is not a valid goal because it falls in the common cause variation range. This means that the goal if achieved will not represent a significant difference from the current state of affairs (and can also happen by chance) This can be verified by either the use of control charts or by use of hypothesis testing.  Hope this helps.