Fuzzy Performability Analysis of Disk Arrays

The performability of disk arrays systems has been studied before. However, in the case of imprecise data, a fuzzy model can be the base for the performability analysis. In this paper a performability analysis of a disk array using a Markov reward model (MRM) is presented. The model considers the repair as the reconstruction (rebuild) of the redundancy, not as a hard drive replacement. With traditional, crisp arithmetic, for each change in a single model parameter the model would need to be run again, resulting in a family of curves difficult to interpret. In the approach presented in this paper, the rewards for each of the states of the MRM, as well as other disk array parameters are expressed through fuzzy numbers. The use of fuzzy arithmetic for the performability estimation of a disk array proved significant advantages. First, the model was able to capture the uncertainty variance of each of the model parameters. Secondly, as opposed to traditional, crisp arithmetic approach, the presented model provides the estimation of the lower and upper boundary of the system performability with a single run of the model