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# Calculating Survival Coefficients in the Reliability Equations for a Storage Device

IP.com Disclosure Number: IPCOM000078886D
Original Publication Date: 1973-Mar-01
Included in the Prior Art Database: 2005-Feb-26
Document File: 3 page(s) / 55K

IBM

## Related People

Bouricius, WG: AUTHOR [+2]

## Abstract

An algorithm can be employed to calculate the survival coefficients in reliability equations for storage devices. For example, such an equation may take the following form: (Image Omitted) being exactly failures in the storage device and wherein the Hf's are the corresponding survival coefficients, i.e., Hf is the probability that the store is effectively error-free in the presence of f failures. The algorithm essentially comprises four steps, viz.

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Calculating Survival Coefficients in the Reliability Equations for a Storage Device

An algorithm can be employed to calculate the survival coefficients in reliability equations for storage devices. For example, such an equation may take the following form:

(Image Omitted)

being exactly failures in the storage device and wherein the Hf's are the corresponding survival coefficients, i.e., Hf is the probability that the store is effectively error-free in the presence of f failures. The algorithm essentially comprises four steps, viz., (a) the generation of generic survival patterns appropriate to a c-tuple error-correcting code, (b) the calculation of the number of permutations associated with each pattern, (c) the calculation of the probability of occurrence for each pattern and the multiplication of this probability by the number of permutations, and (d) the summation of these products over all generic survival Patterns'

The drawing shows a flow chart of an algorithm for determining the term Hf. Step 10 initializes an array to represent all that is needed of a model of a real physical entity. This ARRAY has integers as items in rows and columns. A column represents the bit positions in a store word and the integers in the first column represent failures in the first word. In this connection, many failures can occur in the same bit position as indicated by an integer which is greater than 1. The sum of the integers placed in the ARRAY is equal to F, the total number of failures in the storage device.

The store comprises L words of n-bit length. Each row is indexed by I and each column is indexed by K. An area bounded by F by F, constitutes ARRAY. The area bounded by II.KK constitutes ARRA...