# Process Yield

Six Sigma – iSixSigma Forums Old Forums General Process Yield

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• #45953

Whitehurst
Participant

How to calculate Process Yield from CP and CPK if mean , sigma , UpperLimit  and LowerLimit are known.

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#151132

Steven Bonacorsi
Member

Steve,
Your response is pretty excessive. I’ll respond to Joe separately and provide him some guidance. Your response does not make Joe look stupid while it surely reflects how intelligent you think you are. I suppose youre a super smart master black belt/consultant? Where did you get your communications skills from a Cracker Jack box?
Lighten up
Steven Bonacorsi

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#151134

Steven Bonacorsi
Member

Hi Joe,
Lets say you had some continuous (variable) response data – for example a set of numbers say (1 thru 10). Lets also say your LSL (Lower Spec Limit) was set to 2 and USL (Upper Spec Limit) was set to 2). You can use the Normal Distribution Process Capability to get a CP of 1.13 and Cpk of .94. Now a CP of 2 = 6-sigma process and a CP of 1 is a 3-sigma process. thus, using a sigma quality conversion table could be used to get a general approximation of yield and range of Defects Per Million Opportunites (DPMO). Now if you were able to additional extract the Mean (Xbar) and Standard Deviation (s) from the data. You could calculate (Zusl = (usl – Xbar)/s)) and Xlsl =(Xbar-lsl)/s)), then you could look up the Z statistic from a Z table (see the back of most statistics books), you can also calculate the actual shift of the process and if unknown you can assume a 1.5 (a standard we have set in Six Sigma), then you can equate the Z-bench  to the yield.
Here is an example below:

ZUSL = Look up Z = 2.0 => 0.0228
ZSL = Look up Z = 3 => 0.00135
Area Total = 0.0228 + 0.00135 = .02415
Yield = 1-.02415 = 0.97585 = 97.6%

Lastly, this is many sources of reading materials, and software tools, and methods that can be used with various levels of discrimination. It would be best to check your work with an experienced Master Black Belt, to check your data assumptions (MSA, Distribution, Shape, Stability, etc…) and help you with the method your using to calculate yield, especially if the process your measuring is critical to the customer.

Hope this overs some guidence,

Steven Bonacorsi

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#151171

Steven Bonacorsi
Member

Well, I do have excessive statistics training, and Mr. Harry did not use Z-Bench. Regardless, the SS table is good enough in getting to an ~ SQL, While Z-bench and the actual shift calculation is a well known and more accurate way of calculating process sigma, statistically. If you have an alternative approach – speak up – else let up. All your doing is effectively letting all know what an ignoramous and bag of wind you are.
Steven Bonacorsi

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#151172

Hogg
Participant

I’ve once again copied a bit of history:Bill Smith, a Motorola engineer claims that for uncontrolled processes “batch to batch variation can be as much as +/-1.5 sigma off target.” He gives no references or justification for this. In reality there is no limit to how much that uncontrolled processes may vary. At that time Motorola used Cp=1. Bill Smith suggested “Another way to improve yield is to increase the design specification width.” He broadens specification limits to Cp=2. Mikel Harry derives +/-1.5 as a theoretical “shift” in the process mean, based on tolerances in stacks of disks. Stacks of disks obviously bear no relation to process. Harry names his Z shift. The Z shift makes a number of additional errors: his derivation dispenses with time yet he refers to time periods; he claims a “short term” and “long term” yet data for both are taken over the same time period. Harry seems to realise his error in the 1.5 and says it “is not needed”. Harry in about 2003 makes a new derivation of 1.5 based on errors in the estimation of sigma from sample standard deviations. For a special case of 30 points, p=.95 he multiplies Chi square factor by 3, subtracts 3 and gets “1.5”. The actual value ranges from 0 to 50+. He calls this a “correction”, not a shift. Harry’s partner Reigle Stewart adds a new calculation he calls a “dynamic mean off-set.”: 3 / sqrt( n ) where 3 is the value for control limits and n is the subgroup size. For n=4 he gets “1.5”. Reigle says “This means that the classic Xbar chart can only detect a 1.5 sigma shift (or larger) in the process mean when subgroup size is 4″Reigle is quite incorrect. Such data is readily available from ARL (Average Run Length) plots.In summary, six sigma tables and the 1.5 used to construct them are nonsense.  Don’t use them or numbers derived from them, such as “yield”.

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#151173

Obsession
Participant

Steven,
Geoff is obsessed with educating this site about the six sigma shift. He’ll show up, re-post the “bit of history” then disappear … It’s kind of an obsession they have in Britain with showing the remainder of the world how superior they are intellectually. It’ll pass … like the splendor of that once so glorious empire.

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