Don’t forget to add the history of six sigma. A brief summary follows:
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 processes.
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 of 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, the 1.5 does not exist, despite the many attempts to prop it up. Calculations involving 1.5 are hence meaningless. That is, 3.4 dpmo is meaningless. Six sigma tables are meaningless. Sigma levels are meaningless.
.
