Fault-tolerant redundant repairable system with different failures and delays

Abstract

Purpose The internet of things and just-in-time are the embryonic model of innovation for the state-of-the-art design of the service system. This paper aims to develop a fault-tolerant machining system with active and standby redundancy. The availability of the fault-tolerant redundant repairable system is a key concern in the successful deployment of the service system. Design/methodology/approach In this paper, the authors cogitate a fault-tolerant redundant repairable system of finite working units along with warm standby unit provisioning. Working unit and standby unit are susceptible to random failures, which interrupt the quality-of-service. The system is also prone to common cause failure, which tends its catastrophe. The instantaneous repair of failed unit guarantees the increase in the availability of the unit/system. The time-to-repair by the single service facility for the failed unit follows the arbitrary distribution. For increasing the practicability of the studied model, the authors have also incorporated real-time machining practices such as imperfect coverage of the failure of units, switching failure of standby unit, common cause failure, reboot delay, switch over delay, etc. Findings For deriving the explicit expression for steady-state probabilities of the system, the authors use a supplementary variable technique for which the only required input is the Laplace–Stieltjes transform (LST) of the repair time distribution. Research limitations/implications For complex and multi-parameters distribution of repair time, derivation of performance measures is not possible. The authors prefer numerical simulation because of its importance in the application for real-time uses. Practical implications The stepwise recursive procedure, illustrative examples, and numerical results have been presented for the diverse category of repair time distribution: exponential (M), n-stage Erlang (Ern), deterministic (D), uniform (U(a,b)), n-stage generalized Erlang (GE[n]) and hyperexponential (HE[n]). Social implications Concluding remarks and future scopes have also been included. The studied fault-tolerant redundant repairable system is suitable for reliability analysis of a computer system, communication system, manufacturing system, software reliability, service system, etc. Originality/value As per the survey in literature, no previous published paper is presented with so wide range of repair time distribution in the machine repair problem. This paper is valuable for system design for reliability analysis of the fault-tolerant redundant repairable.

C0–Semigroups Approach to the Reliability Model Based on Robot-Safety System

“…In 1955, Cox [1] first proposed the "supplementary variable technique (SVT)" and established the M/G/1 queuing system. Gaver [2] was the first to apply this technique for reliability models, and subsequently, other authors followed this line of research, such as Linton [3], Gupta and Gupta [4], Shi and Li [5], Chung [6], Oliveira et al [7], Zhang and Wu [8], Shakuntla et al [9], Singh et al [10], Ke et al [11], Shekhar et al [12], Gao and Wang [13].…”