Tools
Intervals & Tests
Hypothesis Test Of Sample Mean Example
Hypothesis Test Of Two Sample Variances Example
Hypothesis Test Of A Standard Deviation Compared To A Standard Value Example
Distributions
Area Under the Standard Normal Curve
Non-Normal Distributions in the Real World
Rayleigh Distribution for True Position
True-position
Used in ANSI Y14.5 measurements, this selection will use the Rayleigh distribution to model measured characteristics resulting from two Normal variables. To fit a Rayleigh distribution, only the specified sigma (process, sample, or population) is needed. Note that the curve generated will be used for K-S values and process capability, but that process sigma is always used to define the distribution limits on the Individual-X chart.
Pyzdek (1992) recommends assuming a Rayleigh distribution for true-position data:
The Rayleigh distribution results when x and y measurements are converted to radial measurements. The Rayleigh (distribution) assumes that both x and y are normally distributed with zero mean and equal variances. An approximation to this situation occurs frequently with true position measurements. True position is calculated using Equation 13.11:
True Position = 2*SQRT(X2+Y2)In Equation 13.11 X is the deviation from nominal in the x direction and Y is the deviation from nominal in the y direction. With true position, obviously, no negative values are possible. thus, there is no lower specification. Table 13.5 shows the percentage above the upper specification based on the value of Zt where:Zt=True Position Specification / Sigma
(Editor's note: Sigma is the process standard deviation of the calculated true-position values (as defined in a control chart) Also note that Pyzdek subsequently advised using SPC-PC software to predict the percent defective based on a fitted distribution for the calculated true position values. (Quality Engineering 4(2), 235-241 (1991-1992)).
Table 13.5 (abridged)
|
Zt |
% Out of Spec |
|
2.0 |
60.65 |
|
2.5 |
45.78 |
|
3.0 |
32.47 |
|
4.0 |
13.53 |
|
4.5 |
7.96 |
|
5.0 |
4.39 |
|
5.5 |
2.28 |
|
6.0 |
1.11 |
|
6.5 |
0.51 |
|
7.0 |
0.22 |
|
7.5 |
0.09 |
|
8.0 |
0.03 |
|
8.5 |
0.01 |
|
9.0 |
0.00 |
Learn more about the Statistical Inference tools for understanding statistics in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Intro. to Statistics short course (only $89) or his online Black Belt certification training course ($875).
