# Working out the TO BE Zst value

Six Sigma – iSixSigma Forums Old Forums General Working out the TO BE Zst value

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• #28764

Uma MB
Member

I am workign on a project aimed at increasing productivity of 18 junior team members in a software project. I have collected data of the past 6 months and come out with the current Z value. Following are the values I have worked out:
Total Opportunities = 220 tasks (completed by these 18 members)
Defective tasks = 47 (any task that has taken more than one hour of the original estimated time is considered a defect; e.g. estimated hours to complete task = 10 and it has been actually completed in 14 hours, then this task is a defective task but say if the task was completed in 11 hours, then it is not a defect)
Defect Percentage = 21.36 and Yield is 78.64. Zst = 2.29
Now, when I start working out my target Zst, I have planned on a 75% reduction in defects, say 47-12 = 35.
But how can I at this time (MEASURE-ANALYZE) be sure that when I collect data again after implementing the solution(s), that the opportunities would be 220. I cannot guarantee this. Or I have to wait until 220 tasks are completed. I am lost at this point. Please help.
One more area of concern is : there are two main reasons I have identified for low productivity. The project team lacks functional knowledge of the application and technical experience (the members fall in experience bands of 0-3 months, >3-6, >6-9 and >9-12 months). How can I make control charts to show existing levels of functional knowledge and technical experience of the project. By what will I measure these ? Has somebody done this kind of a project ?
Thank you.
Best Regards,
Uma MB.

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#72108

Sridhar
Member

Hi,
I dont think you have to wait for 220 tasks, because any way you are converting them into defects per million opportunities. If it is 220 or less it doesn’t matters, the final metric you are going to say is defects per million opportunities.
sridhar

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#72113

Erik L
Participant

Uma,
I would probably want to map out the process.  Surely there are phase gate reviews, peer reviews, etc. that need to be completed prior to the completion time of the task.  What’s the yield at these sub-process steps?  Does a miss at a particular stage create a leading indicator that the overall project will be off track?  Are all tasks created equal?  You might want to add a complexity scale based on lines of code etc.
I would probably want to make a pareto plot of tasks missed and then a pareto of tasks missed per your experience brackets.  If you’re looking to substantiate experience, one of the first things that I would do is to make a scatter plot of time to complete a task to years of experience.  This should provide a first glimpse into the relationship between these variables (linear, quadratic, etc.).  Additionally, you could collect data broken down per your experience brackets and collect the time to complete the task.  With these completed, you could perform an ANOVA analysis to compare whether or not there is equivalency amongst all experience brackets (I’d keep the data as continuous as possible and not put it into the ranked categories that you have right now).  After completing that, perform a Tukey analysis to ping in on which experience brackets broke the null hypothesis.
To your question about control charting.  You could use a Target control chart.  The baseline would be the projected end date and then take the actual complete time and subtract this from the base.  This way you can chart all 18 individuals on one chart.  A caution for the chart, it functions under the assumption of equal variance amongst the metrics that you’re plotting, so you’ll have to check that assumption to see if this chart could work for you.  Unfortunately, with this chart you’d only be gaining information after the tasks are completed and you want to identify the leading x’s that influence a success or failure.  As you progress with your analysis you might want to look into logistic regression since your metric of interest is binary in nature.  Good luck with the project.
Regards,
Erik

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#72114

TCJ
Member

You do not need 220 opportunities/task to demonstrate a change in the process.  To determine if you made an improvement to the process you should use a hypothesis test (probably Chi-Squared for your application).  But before you get to that step, is your process capable of a 75% reduction?  Though you listed your current Z value as short-term ST it sound like it may be the long-term value, because your “Total Opportunity” includes several members with various levels of experience (I assume).  Zst is the value given to your process at it’s best.  Under what conditions were the defect rates the lowest? i.e. 1st shift, 2nd shift, > 3 mon experience, etc.  These should be the subgroups that you use for your short-term process capability.
For example, if you perform capabilities studies based on experience subgroups you can discern a reasonable Zst that demonstrates the process at it’s best.  This should become your target long-term process sigma.  The improvements that you develop should focus on reducing the learning curve (additional training, mentoring, and the like).  Once the improvements are realized then use the hypothesis test to determine if an improvement was made and create a final long-term capability study.
Back to the original question, you can determine the sample size required based on the power of test and the proportions of your target and your current process.  I estimate you need at least 70 task to establish a 90 percent power of test on your hypothesis test.  With 70 new opportunities task you can determine with 90% confidence there is 95% percent (Based on 0.05 alpha) chance that the process has changed.

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#72120

Mike Carnell
Participant

Uma,
You do not have to stop at 220 tasks. We can work through it using Z values. Do you know the number of tasks you will have? You can email me the data at [email protected] if you like.
If you want a real good IT guy and a good SS guy (he really hates talking about SS though) try Mark Wood at [email protected].
The training part I am not sure I get. How are you measuring whatever it is that you are measuring (what is the GR&R)? Why do you want to put a control chart on it?
If I were doing training I would pre and post test. You should be able to do hypothesis testing to see if you have a significant shift. You would want to make sure to test means and variance. If other areas are doing it as well you can build enough data that you can test a class before training and have a decent idea if you have a class that is going to need a little extra help or not. I can see an application like this but I need some help understanding the control chart idea.

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#72149

RR Kunes
Member

a yield of 78.4 converts to around 212,000 PPM or a sigma value of ~2.3.
You cannot use a Z value as the human model is not a normal distribution.
I would keep your calculation simple. Calculate the DPMO before you implement your change. Monitor and calculate your DPMO after the change. Utilze a paired T if you solution included retraining. The T test will verify the statistical validation of your change. The DPMO will quantify that change.

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#72154

TCJ
Member

RR Kunes,
As you mentioned the data is not normal, so why use a Paired T-test to determine statistical significance?  The data is attribute and you are looking at proportions; therefore, a chi-squared is necessary for this application.  FYI…Paited T-test, test differences between means and assumes the data is normal.

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#72177

Mike Carnell
Participant

RR & TCJ,
I might have missed something when I read Uma’s question but I did not see her state her data was not normal. Even if it it is not normal that does not preclude the use of test such as a paired t test etc. Transforming data is an everyday occurance. Minitab will even do it for you.
If you do not want to transform data there are non parametric tests which do not require normal data (Minitab again).
Now if you will read my response on pre and post test. First it is typically normally distributed. The normal distribution is not new to testing. As far as attribute data – I am not sure why anyone would take a test score and make attribute – which is what my suggestion was.

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#72190

TCJ
Member

Mike,
I might be off base, but isn’t it obvious that the data is attribute (binomial).  Uma is counting the number of defective task versus the number of opportunities to establish a defect percentage, which was turned into a Z-value.  To determine if the defect percentage/proportion has changed (post improvements), Uma can use a contigency table a.k.a chi-squared test.
I do understand that we can look at the hours as variable data and set a unilateral limit at the designated “defect time” i.e. 10 hours.  But that will not account for varying “defect times” if that were the case.  I know the Six Sigma Gods are frowning…I am making all of these assumptions without looking at the data.

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#72235

Mike Carnell
Participant

You hit on my point. I have not made the assumption it is attribute because it is counting. Uma has sent me har data so I will find out. If it is, you are correct, Chi Square is a definite choice.
If you look at a lot of data ther is frequently variable data behind attribute data. Electronic testing is a good example. You get a red or green light. Somewhere there is variable data the test set uses to decide which light it should light.
Just my opinion.

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#72239

Mike Carnell
Participant

Just another thought. I really appreciate the insight you both have provided me on analysis of data.
If you will notice when I was speaking about hypothesis testing it was in regards to my suggestion to doing pre and post testing which:
1. will generally ne normally distributed
2. does not have to be attribute.
I also mentioned hypothesis testing as a tool. Chi square does seem to come under that catagory.
Thanks for all your help.

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