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# Random Failure Graphical Analysis

IP.com Disclosure Number: IPCOM000034246D
Original Publication Date: 1989-Jan-01
Included in the Prior Art Database: 2005-Jan-27
Document File: 2 page(s) / 70K

IBM

## Related People

Breyfogle, FW: AUTHOR [+2]

## Abstract

Random failure tests are often described using the Poisson process; however, tables are not generally available that describe test alternatives. A process to generate a normalized graph which is useful to describe the various test alternatives is described. It is widely known that the Chi-square distribution describes the Poisson time terminated test confidence interval when in the form Lower Confidence = 2 N O Upper Confidence = 2 N O [[[[[ [[[[[ Limit 2 1-b Limit 2 1+a 2r+2' [[[ 2r' [[[ 2 2 where 2 = chi-square value found from the Chi-square tables with 2r+2 or 2r degrees of freedom.

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Random Failure Graphical Analysis

Random failure tests are often described using the Poisson process; however, tables are not generally available that describe test alternatives. A process to generate a normalized graph which is useful to describe the various test alternatives is described. It is widely known that the Chi-square distribution describes the Poisson time terminated test confidence interval when in the form Lower Confidence = 2 N O Upper Confidence = 2 N O

[[[[[ [[[[[

Limit 2 1-b Limit 2 1+a

2r+2' [[[ 2r' [[[

2 2

where 2 = chi-square value found from the Chi-square tables with

2r+2 or 2r degrees of freedom.

a = reject (non-support) risk level

b = accept (support) risk level

N = total usage

O = operating ratio*

r = number of failures

Note: "Confidence limits" are in units of time between

failures

* "Operating ratio" can be assigned values slightly greater than

one to reflect a test "delta". For example, if we

wish to

design a test for 90% confidence that the criteria

will not be

exceeded by 20%, b would equal .1, while the

operating ratio

would be 1.2. Figs. 1 and 2 are generated by substituting "Criteria" for the inverse of "Lower Confidence Limit" and "Upper Confidence Limits". These unique figures can: give the test designer insight to various test alternatives and give the data analyzer quick solution to confidence interval questions. It allows one to graphically (quickly) determine the number of failures allowable for pass and fail at a given con...