We introduce a new closed-form equation for estimating the number of data-loss events for a redundant array of inexpensive disks in a RAID-6 configuration. The equation expresses operational failures, their restorations, latent (sector) defects, and disk media scrubbing by time-based distributions that can represent non-homogeneous Poisson processes. It uses two-parameter Weibull distributions that allows the distributions to take on many different shapes, modeling increasing, decreasing, or constant occurrence rates. This article focuses on the statistical basis of the equation. It also presents time-based distributions of the four processes based on an extensive analysis of field data collected over several years from 10,000s of commercially available systems with 100,000s of disk drives. Our results for RAID-6 groups of size 16 indicate that the closed-form expression yields much more accurate results compared to the MTTDL reliability equation and matching computationally-intensive Monte Carlo simulations.

There is no standard method for creating a hardware reliability prediction. Therefore, predictions vary widely in terms of methodological rigor, data quality, extent of analysis, and uncertainty. Documentation of the prediction process employed is often not presented. These inconsistencies can leave the user of the prediction confused, uncertain of the prediction's true value, and unable to compare the results of two reliability predictions of the same hardware. IEEE has created a standard [1], IEEE 1413, that, when followed, results in consistent, complete documentation of a prediction. The prediction users can then understand the strengths and weaknesses of a prediction, and compare the value and usefulness of multiple predictions. The standard creates consistency by requiring documentation for specific processes, activities, and levels of knowledge.

This paper develops an equation that provides a good approximation of the expected number of double-disk failures (data losses) in an (N+1) redundant array of inexpensive disks (RAID) as a function of time. This paper includes the statistical bases for the equation, sources of error and inaccuracies due to approximations, and limitations of its use. The equation is simple and can be evaluated using a hand held calculator or basic spreadsheet. Accuracy depends on four input distributions, which include operational failures, operational failure restorations, latent defects, and data scrubbing. Failure and restoration distributions may represent non-homogeneous Poisson processes and, therefore, not have constant rates. Results of the equations are compared to two other hand calculation methods, to a highly accurate Monte Carlo simulation, and to actual field data for more than 10,000 RAID groups composed of 14 drives.

The statistical bases for current models of RAID reliability are reviewed and a highly accurate alternative is provided and justified. This new model corrects statistical errors associated with the pervasive assumption that system (RAID group) times to failure follow a homogeneous Poisson process, and corrects errors associated with assuming the time-to-failure and time-to-restore distributions are exponentially distributed. Statistical justification for the new model uses theory for reliability of repairable systems. Four critical component distributions are developed from field data. These distributions are for times to catastrophic failure, reconstruction and restoration, read errors, and disk data scrubs. Model results have been verified and predict between 2 to 1,500 times as many double disk failures as estimates made using the mean time to data loss method. Model results are compared to system level field data for RAID group of 14 drives and show excellent correlation and greater accuracy than either MTTDL.

A flexible model for estimating reliability of RAID storage systems is presented. This model corrects errors associated with the common assumption that system times to failure follow a homogeneous Poisson process. Separate generalized failure distributions are used to model catastrophic failures and usage dependent data corruptions for each hard drive. Catastrophic failure restoration is represented by a three-parameter Weibull, so the model can include a minimum time to restore as a function of data transfer rate and hard drive storage capacity. Data can be scrubbed as a background operation to eliminate corrupted data that, in the event of a simultaneous catastrophic failure, results in double disk failures. Field-based times to failure data and mathematic justification for a new model are presented. Model results have been verified and predict between 2 to 1,500 times as many double disk failures as that estimated using the current mean time to data loss method.