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# Graphic Slide Rule for Reliability Computation

IP.com Disclosure Number: IPCOM000096680D
Original Publication Date: 1963-Sep-01
Included in the Prior Art Database: 2005-Mar-07
Document File: 2 page(s) / 69K

IBM

## Abstract

This slide rule minimizes time and effort in planning and evaluating life tests of components or reliability of repairable systems when exponential distributions for time to failure are assumed.

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Graphic Slide Rule for Reliability Computation

This slide rule minimizes time and effort in planning and evaluating life tests of components or reliability of repairable systems when exponential distributions for time to failure are assumed.

The rule has frame 10, slide 11 and cursor 12. Frame 10 has numerals 14 printed on the upper portion indicating the Failure Rate in % per 1000 Hours on a logarithmic scale. The lower portion has three windows 19 through which numerals indicating the number of units are read. Numerals 16 printed alongside each window indicate an exponent by which the numeral read in the windows is multiplied in order to obtain the required Test Time.

Slide 11 has a number of curves 17 printed on it. These represent cumulative sums of Poisson distributions. The Poisson distribution is one of the best known and most widely used distributions of probability theory. Its use is justified thusly: If X = time to failure is an exponential variable with

parameter lambda then the sample sum

T(n) = /n/ Sigma (i=1) X(i)

(Image Omitted)

is a gamma variate with parameters lambda and n. If n is now

regarded as random, then the gamma distribution gives

rise to the Poisson distribution, with parameter lambda t.

The curves are plotted on a grid whose vertical scale is that of the cursor and whose horizontal scale is the Failure Rate scale of the frame. Numerals 18 below the scales identify, except for order of magnitude, the Poisson parameter.

Cursor 12 is tran...