Six Sigma SPC - Statistical Process Control

Design Margin - Statistical Tolerance
Part of DFSS - Design for Six Sigma

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These articles are from the Six Sigma SPC Newsletter and other publications. All articles written by Jim Winings
From various 2003 Newsletters Go to Part 1

Design Margin - Statistical Tolerance Part 2
for use with DFSS - Design for Six Sigma

Piece part design margins, using statistical tolerancing along with a six sigma agenda can indeed reduce the number of failures in a manufacturing process. However, legacy  parts and processes may make this impossible. Retooling and/or redesigning can be cost prohibitive. But it may be possible to start with new processes, to include updated processes. This should be a big part of any designing for six sigma methodologies. Of course, new designs and processes lend themselves to be shaped into six sigma or more designs margins.

One way to do this is by the addition of statistical tolerances. If you have 3 parts that fit together, for example, and you can get a six sigma design margin on two of them but only a 4.5 sigma design margin on the third, you may still get so close to six sigma that in the end it will not really matter.

Whenever more than one assembly is put together, new dimensions are created as well as new distributions. Because of this, we need to look at the addition of distributions. The distributions that exist on the first distribution are added to the second piece and so on till the building of the component is finished. Because the addition of distribution is statistical in nature, we need to know some rudimentary statistical laws so that we may use this information to predict the best and most reasonable resolution for production.

Formulas and Calculations

There are four laws that govern the addition of distribution.

1. Law Of Additions Averages. If parts are assembled in such a way that one dimension is added to another, the average dimension of the entire assembly will be equal to the sum of the average dimensions of the parts.

Let A = The Mean of Part A
B = The Mean of Part B
C = The Mean of Part C
Average dimension of assembly = A + B + C ,etc. See Fig. 1

2. Law Of Differences. If parts are assembled in such a way that one dimension is subtracted from another, the average dimension of the entire assembly will be the difference between the average dimensions of the parts.

Let D = The Mean of Part D
E = The Mean of Part E
Average dimension of assembly =( D - E )or( E - D )as the case may be. See Fig. 2

3. Law Of Sums and Differences. If parts are assembled in such a way that some dimensions are added to each other and some dimensions are subtracted from another, the average dimension of the entire assembly will be the algebraic sum of the average dimensions of the parts.

Average dimension of assembly = A + B + C - D + E ,etc

4. Law Of The Addition and Standard Deviations or Variances. If the parts are assembled at random, Standard Deviation, (Sigma), of the assembly WILL NOT BE the simple sum standard deviations of the parts, but rather, it will be the value obtained by squaring each of the component standard deviations, totaling the squares, and then taking the square root of the total.*

Let A = The Standard Deviation of Part A
B = The Standard Deviation of Part B
Standard Deviation of the assembly =
(A)2 + (B)2

The forth law should be carefully examined because the statistical addition gives a different result from the one which he/she would be likely to get naturally.

One should note that the squares of the standard deviations are always added regardless of whether the average dimension is gotten by sums of differences. DO NOT attempt to subtract one standard deviation from another as may be done in the case of averages.

The forth law can also be expressed using variances instead of sigma, (standard deviations). Standard deviation is the square root of variance (2). If (A)2 is the variance of Part A and  (B)2 is the variance of Part B, the variance of the assembly will be  (A)2 + (B)2 .

ZeroRejects may be able to help you in determining these values. If you find yourself stuck with a problem and your current statistical tools cannot seem to help ,well try using ZeroRejects on it as well. Sometimes just as you need more than one chart to find the problem, you mat also need a new tool to  use and compare with your existing evaluation.

And at just $150.00 (US), it could save you many hours of time. Purchase it here now 

 

* In special cases where the dimensions do not combine linearly, or are not independent, more complicated calculations may be needed to get the final dimension and the standard deviation.

1 Reference AT&T Statistical Quality Control Handbook Copyright 1956 Western Electric Co., Inc.

 

 


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Last Updated: Sunday, 11-Jun-06 07:19:11 PDT