# True-position

Table 13.5 (abridged)

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

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(XIn 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 Z^{2}+Y^{2})_{t}where:Z_{t}=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)

Z |
% 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 |

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