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Guaranteed estimates of the gamma percent residual life of data storage equipment

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The active development of digital technologies, Internet of Things technologies, and virtual tests requires an increase in the volume of information collected and used, which is placed in data storage systems. The rapid growth of data volume leads to stricter requirements for storage. One of the main requirements for storage is to increase the reliability of storing large amounts of information. This implies the need to assess the reliability of storage equipment. For these purposes, it is necessary to evaluate such reliability indicators as the probability of failure-free operation, the probability of failures, the average residual resource, and the gamma percent resource. Traditionally, reliability indicators are evaluated with an exponential distribution of failure time. In a real situation, the samples of failure times of storage equipment are small, for which it is impossible to uniquely identify the initial distribution. In this article, a model is proposed for evaluating reliability indicators as a gamma percent residual resource in conditions of incomplete data presented by small samples of random variables of equipment uptime. The scientific novelty of the presented work consists in obtaining a general solution to the problem of determining the guaranteed gamma percent residual life of equipment in conditions of incomplete data presented by small samples of developments before equipment failure. The mathematical formalization of the problem of estimating the gamma percent residual life of storage equipment in conditions of incomplete data presented by small samples is performed in the form of a stochastic equation model, the solution of which is a guaranteed (lower, upper) estimate of the gamma percent residual life of equipment. A model for estimating the gamma percent residual life of storage equipment in conditions of incomplete data is presented. In the general case, the problem of finding guaranteed (lower and upper) estimates of the gamma percent residual life of equipment on a set of functions for the distribution of uptime of equipment with specified moments equal to sample moments determined from small samples is solved. At two points in the uptime of the equipment, analytical ratios were obtained to determine the gamma percent residual life. The performance of the model is demonstrated by the example of determining the lower guaranteed estimate of the gamma percent residual resource of the HP EVA P6500 disk array model. The results obtained can be used by specialists in evaluating and optimizing the gamma percent residual life of storage equipment. 

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