# Determining If There Really is a Shift in Mean

Six Sigma – iSixSigma Forums Old Forums General Determining If There Really is a Shift in Mean

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• #31627

dizzydom
Participant

Hello all,I am trying to determine if the mean cycle time on a
product line has truly shifted for the worst when an
improvment methodology was abandoned. During the
improvement process, 37 daily avg. cycle times were
collected (x-bar equals 5.34 days). After the methodology
was abandoned 33 daily avg. cycle times were collected
(x-bar equals 6.37days). What statistic can I apply to
show that there truly was a change in the process mean?

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#83516

jediblackbelt
Participant

Take your data sets and check them for normality and then equal variances.  If they pass then use ANOVA.  Otherwise you could just do a simple one-tailed t-test to see if they pass or even ANOM.  There are a lot of different tests you can use.  The bigger question is why did the system get abandoned?  You shouldn’t even be checking for a change for the worse you should be asking those in charge of the process why they allowed it to drift back.  Look at the controls that were put on the better process and see what needs improved to make the input controls better and then monitor the output.  Just an opinion but I would look to ask why the process changed versus proving statistically if the changes are valix.

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#83796

MBBHON
Participant

I agree with jediblackbelt about what should be the focus of your investigation.  If you want to validate that the observed difference is statistically different before “stirring up” things.  You can use the Two Sample t-test, “before” and “after” and not have to assume unequal variances.

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#83799

Robert Butler
Participant

If it is really a matter of comparing the averages of two sample populations then a two sample t-test with unequal variances and unequal sample sizes would be the statistical tool of choice (Minitab gives you these options.  If you don’t have Minitab then pp.299-304 of Statistical Theory and Methodology 2nd Edition by Brownlee has the details for manual computation).  It’s worth checking for data normality but you should remember that the t-test, like ANOVA, is very robust to non-normality.
What concerns me is that the wording of the original post suggests that the situation is not that of comparing populations but comparing populations of averages.  The sentence “33 daily avg. cycle times were collected (x-bar equals 6.37days)” suggests that 33 averages were gathered and the average of these averages was then computed.  If this is the case then the way to check for process changes would be to go back to the averages, note their associated ranges and plot Xbar R charts for before and after and compare these to see if there has been a change in process.

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