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Applied Statistics and Probability for Engineers, 5th Edition by Douglas C. Montgomery, George C. Runger

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A redundant array of independent disks (RAID) uses multiple physical disk drives as one logical unit in a computer system. The array can increase performance and robustness to a disk failure. Data copies can be written simultaneously to multiple drives (known as mirroring) to provide immediate backup and the ability to recover from failures, but with less storage capacity than would otherwise be available. Alternatively, to increase performance, the data can be distributed among multiple disks with only a fraction of the data on each one (known as striping). But a failure to even a single disk can lead to loss of data. An intermediate design is to distribute the source data along with additional data (known as parity data) across multiple disks. With the parity data the source data can be recovered even with disk failures. In particular, a RAID 5 design uses striping and parity to be able to recover the source data if one disk in the array fails, while a RAID 6 design allows for data recovery even if two disks fail. Disk failures due to hardware malfunction are often assumed to be independent with constant probability. With a large number of disks in an array the risk of data loss and the appropriate array design to meet the system performance, availability, and cost criteria are important. The number of failed drives can be modeled as a discrete random variable and the risk of ...

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