Browse Prior Art Database

Statistical Treatment of Parallel Elements Including Tracking Distributions and Nesting

IP.com Disclosure Number: IPCOM000085042D
Original Publication Date: 1976-Feb-01
Included in the Prior Art Database: 2005-Mar-02
Document File: 3 page(s) / 36K

Publishing Venue

IBM

Related People

Robbins, GJ: AUTHOR

Abstract

A related publication in the IBM Technical Disclosure Bulletin, Vol. 18, No. 9, February 1976, pages 2894 to 2896 and entitled "Statistical Treatment of Parallel Elements" by G. J. Robbins and J. Saia derives the statistics for the best-worst case distributions of parallel, statistically independent and equivalent elements. Herein the results set forth in the afore-identified publication are modified to account for tracking between groups of paralleled elements.

This text was extracted from a PDF file.
At least one non-text object (such as an image or picture) has been suppressed.
This is the abbreviated version, containing approximately 66% of the total text.

Page 1 of 3

Statistical Treatment of Parallel Elements Including Tracking Distributions and Nesting

A related publication in the IBM Technical Disclosure Bulletin, Vol. 18, No. 9, February 1976, pages 2894 to 2896 and entitled "Statistical Treatment of Parallel Elements" by G. J. Robbins and J. Saia derives the statistics for the best- worst case distributions of parallel, statistically independent and equivalent elements. Herein the results set forth in the afore-identified publication are modified to account for tracking between groups of paralleled elements.

I. Statistics for Eta parallel elements within the totality.

(refer to the figure).

Given: Eta parallel elements each having:

Distribution of mean: e.g., N (T, Sigma(A)/2/ - Sigma/2/(B)

Tracking variation distribution: e.g., N (O, Sigma/2/(B) where; = T = Mean of a single element over the entire population.

Sigma(A)/2/ = Variance of a single element over the entire population.

Sigma(R)/2/ = Variance of a single element over a group to be considered (tracking variation).

Utilizing the results set forth in the afore-identified publication:

T(Eta) (mean of earliest or latest element(s) in the group) = T +/- Alpha(Eta) Sigma(R) and Sigma(Eta)/2/ (variance of earliest or latest element(s) in the group) = Sigma(A)/2/ - Sigma(R)/2/ + (Beta(Eta))/2/ Sigma(R)/2/ Sigma(Eta) = (Sigma/2/(A) + (Beta/2/(Eta)- 1) Sigma(R)2/«/)

II. Statistics for Mu groups of Eta parallel elements within the totality.

Since Mu groups may be considere...