Zlt
Six Sigma – iSixSigma › Forums › Old Forums › General › Zlt
 This topic has 3 replies, 3 voices, and was last updated 16 years, 6 months ago by Anonymous.

AuthorPosts

May 14, 2005 at 3:20 pm #39352
I’m confusing about the equation of Zlt = Zst 1.5. How can we get this equation ?
For example, we all know that Zst = (SL – Xst)/ást
And in the long term, Mean (X) shift 1.5ást
So, Zlt = SL/ást – (Xst + 1.5ást)/ást
Zlt = (SL/ást – Xst/ást) – 1.5ást/ást
So, Zlt = (SL – Xlt)/ált
0May 16, 2005 at 11:17 pm #119591Reigle, where are you when there is a sucker for the taking?
0May 16, 2005 at 11:33 pm #119594
Reigle StewartParticipant@ReigleStewart Include @ReigleStewart in your post and this person will
be notified via email.To Wuth:
The following exert is quoted from the “Ask Dr. Harry” section of this website:
The capability of a process has two distinct but interrelated dimensions. First, there is shortterm capability, or simply Z.st. Second, we have the dimension longterm capability, or just Z.lt. Finally, we note the contrast Z.shift = Z.st Z.lt. By rearrangement, we assuredly recognize that Z.st = Z.lt + Z.shift and Z.lt = Z.st Z.shift. So as to better understand the quantity Z.shift, we must consider some of the underlying mathematics.The shortterm (instantaneous) form of Z is given as Z.st = SL T / S.st, where SL is the specification limit, T is the nominal specification and S.st is the shortterm standard deviation. The shortterm standard deviation would be computed as S.st = sqrt[SS.w / g(n 1)], where SS.w is the sumsofsquares due to variation occurring within subgroups, g is the number of subgroups, and n is the number of observations within a subgroup.
It should be fairly apparent that Z.st assesses the ability of a process to repeat (or otherwise replicate) any given performance condition, at any arbitrary moment in time. Owing to the merits of a rational sampling strategy and given that SS.w captures only momentary influences of a transient and random nature, we are compelled to recognize that Z.st is a measure of instantaneous reproducibility. In other words, the sampling strategy must be designed such that Z.st does not capture or otherwise reflect temporal influences (time related sources of error). The metric Z.st must echo only pure error (random influences).
Now considering Z.lt, we understand that this metric is intended to expose how well the process can replicate a given performance condition over many cycles of the process. In its purest form, Z.lt is intended to capture and pool all of the observed instantaneous effects as well as the longitudinal influences. Thus, we compute Z.lt = SL M / S.lt, where SL is the specification limit, M is the mean (average) and S.lt is the longterm standard deviation. The longterm standard deviation is given as S.lt = sqrt[SS.t / (ng 1)], where SS.t is the total sumsofsquares. In this context, SS.t captures two sources of variation errors that occur within subgroups (SS.w) as well as those that are created between subgroups (SS.b). Given the absence of covariance, we are able to compute the quantity SS.t = SS.b + SS.w.
In this context, we see that Z.lt provides a global sense of capability, not just a slice in time snapshot. Consequently, we recognize that Z.lt is timesensitive, whereas Z.st is relatively independent of time. Based on this discussion, we can now better appreciate the contrast Z.st – Z.lt. This type of contrast poignantly underscores the extent to which timerelated influences are able to unfavorably bias the instantaneous reproducibility of the process. Thus, we compute Z.shift = Z.st Z.lt as a variable quantity that corrects, adjusts, or otherwise compensates the process capability for the influence of longitudinal effects.
If the contrast is related only to a comparison of short and longterm random effects, the value of Z.shift can be theoretically established. For the common case ng = 30 and a type I decision error probability of .005, the equivalent mean shift will be approximately 1.5S.st. If the contrast also accounts for the occurrence of nonrandom effects, the equivalent mean shift cannot be theoretically established it can only be empirically estimated or judgmentally asserted.
I hope this helps you.
Regards,
Reigle Stewart0May 17, 2005 at 7:07 am #119609Reigle,
Any shift would be detectable long before 1.5s on a Shewhart Chart, and even more quickly on a Cusum chart?
Most process engineers know ‘process performance’ is calculated on the basis of 30 subgroups of size (3 to 5) – not 30 individual measurements!
Cheers,
Andy0 
AuthorPosts
The forum ‘General’ is closed to new topics and replies.