International Journal of Reliability, Quality and Safety Engineering

Availability is an important measure of performance of repairable system. The steady state system availability has special importance since it demonstrates the performance of a system after it has been operated for long. The statistical inference about the steady state availability are particularly useful for practitioners. Much work has been done in this regard. Most of these researches proposed certain pivotal quantities for constructing confidence intervals of the steady state availability. Assuming both the lifetime and repair time follow gamma distribution with known shape parameters and unknown scale parameters, we propose a pivotal quantity for making inferences, and further derive the likelihood ratio tests. Tables of critical values are given for the convenience of applying the two-sided likelihood ratio test. Confidence intervals are also obtained by converting the acceptance regions.

A Redundant Array of Independent Disks (RAID) system with n disks or hard drives can be modeled as a k-out-of-n repairable system for which at least k operational disks are required. This paper proposes a hierarchical Markov model to estimate the reliability of RAID systems. The method encompasses Markov models for evaluating the reliability of individual disks at the lower level and the redundant model for evaluating the reliability of entire RAID at the system level. Both hardware and media failures are considered, and the media failures can be potentially recovered via the disk self-restoration mechanism. The system mean-time-to-data-loss is also derived and results are compared to those estimated from system-based Markov models. The major contribution of this work is that the reliability for RAID systems is approached by combining the redundant modeling technique with the single disk-based Markov model, thus simplifying the computational efforts. The proposed method is applied on RAID-5 and RAID-6 systems to demonstrate the applicability and performance of the new model.

A parallel system with n identical units is considered, and its mean time to system failure (MTTF) is obtained when the failure time is exponential. A simple asymptotic method of computing MTTF is proposed and its approximal values are compared with the exact MTTFs when the failure time has a Weibull distribution. It is of great interest that such asymptotic methods give good approximations to exact MTTFs. Furthermore, when the number of units is random, the MTTF and an optimal number of units to minimize the expected cost rate are derived.

A 3-dimensional consecutive k-out-of-n : F system consists of n³ components disposed on a cubic grid of size n; it fails if and only if all the components of at least one cube of size k (1 < k < n) fail (k³ components). Although introduced as early as in 1992 by Salvia and Lasher⁷ as a better model for problems in medical imaging, few results are known about it.¹ In this paper, we propose, in the the independent and not-necessarily-identical case, a new lower bound which has the advantage of being calculated directly from the reliability of a one dimensional consecutive-k-out-of-n:F system. To do this, we derive an intermediate system² which behaves like a one dimensional consecutive k-out-of-n and is less reliable than the initial 3-dimensional system, hence its suitability as the lower bound. The proposed approach converts a three-dimensional system into a one-dimensional system directly. It can be extended to the three-dimensional versions of the k-within-connected-(r,s,t)-out-of-(m,n,p):F system and the m-consecutive-k-out-of-n : F system.

The redundancy is a widely spread technology of building computing systems that continue to operate satisfactorily in the presence of faults occurring in hardware and software components. The principle objective of applying redundancy is achieve reliability goals subject to techno-economic constraints. Due to a plenty of applications arising virtually in both industrial and military organizations especially in embedded fault tolerance systems including telecommunication, distributed computer systems, automated manufacturing systems, etc., the reliability and its dependability measures of redundant computer-based systems have become attractive features for the systems designers and production engineers. However, even with the best design of redundant computer-based systems, software and hardware failures may still occur due to many failure mechanisms leading to serious consequences such as huge economic losses, risk to human life, etc. The objective of present survey article is to discuss various key aspects, failure consequences, methodologies of redundant systems along with software and hardware redundancy techniques which have been developed at the reliability engineering level. The methodological aspects which depict the required steps to build a block diagram composed of components in different configurations as well as Markov and non-Markov state transition diagram representing the structural system has been elaborated. Furthermore, we describe the reliability of a specific redundant system and its comparison with a non redundant system to demonstrate the tractability of proposed models and its performance analysis.