TS-126
Failure Frequency and Availability of 3-Out-of-4:G
Warm Standby System with Nonidentical Components
Tieling ZHANG*, Kenji HIRANUMA*, Yoshinobu SATO* and Michio HORIGOME**
ABSTRACT
Standby techniques are useful to improve system availability. In most cases, components in standby systems can be taken as statistically identical. However, there are some real systems where the statistically identical assumption could not hold. The present paper deals with 3-Out-of-4:G warm standby system with two types of components. They are classified into type 1 and 2. Namely, the two out of four components are of type 1 that have lower failure and higher repair rates. Other two belong to type 2 which have higher failure and lower repair rates. As the result, there exist two system operation modes of Mode I and Mode II. Type 1 components have priority both in operation and repair in Mode I. On the other hand, components of type I have only priority of being repaired in Mode II, namely, components of type 2 do not have priority in standby. By using Markov model, the system availability, reliability and failure frequency are obtained. Examples are given in order to illustrate the results of transient availability and failure frequency of such systems. It is concluded that a higher availability is obtained if the system works under Mode I.
Key Words: Availability, Failure Frequency, k-out-of-n:G Warm Standby System, MTBF
Nomenclature & Notation
A stationary availability of the system
MTTFF mean time to the first failure
m(t) failure frequency of the system
P(i,j), P(i,j) (t) probability that the system is in state (i,j) at time t
P'(i,j), P'(i,j) (t) derivative of[P(i,j)] or P(i,j) (t)]
R(t), A(t) [reliability, availability] of the system at time t
λ1, λ2 failure rate of [type 1 or 2] components in operation
λ'1, λ'2 failure rate of [type 1 or 2] components in dormant
μ1, μ2repair rate of [type 1 or 2] components
1.INTRODUCTION
Standby techniques are widely applied to improve system availability. Usually, a k-out-of-n:G standby system is assumed that when an operating component fails, a standby component becomes active and the system is working if at least k components are in operation. In general, the component standby is classified into three types of cold, hot and warm. Here, a cold standby implies that inactive components have a zero failure rate whereas a hot standby implies that an inactive component has the same failure rate as that in operation. Warm standby stands for that an inactive component has a failure rate between cold and hot. Sometimes, this is also called dormant failure. K-out-of-n:G warm standby systems have been used in several research fields covering medical diagnosis, redundant-system testing, power plant system and so on. It is also suitable to be applied in marine engineering.
In the past thirty years, many articles concerning analysis on availability of k-out-of-n:G warm standby systems were published, which were based on system configuration, components connection and the way of redundancy [1-10]. Schneeweiss [6] reviewed a general (non Markov) 1-out-of-2:G system with statistically-identical components, repair and cold standby, he studied the MTTFF of repairable systems with one cold standby. Akhtar [7] investigated reliability of k-out-of-n:G systems with imperfect fault-coverage where recursive expressions for mean time between failures and mean time to failure were obtained for repairable systems, considering perfect & imperfect fault-coverage with the assumption that the standby units are cold. Gnedenko et al. [8] analyzed the 1-out-of-n warm-standby case. She and Pecht [9] made a brief review on standby redundancy techniques and concluded that the modeling of standby redundancy, especially warm standby has not been emphasized. In their research, a general closed-form equation was developed for system reliability of a k-out-of-n warm standby system where components, however, were assumed to be statistically identical. Furhthermore, as a general case, the analytical procedure for system availability of m-out-of-n:G warm standby system with identical components was presented in [10]. In all of the above papers, the study are only limited to systems of 1-out-of-n:G warm standby systems or a general m-out-of-n:G warm standby one with identical components. However, there are several real systems where the statistically identical assumption for components can not hold. Some power plant systems where the different types of equipment with different failure and repair rates may be operating together.
