Lirong Cui

Optimal allocation of minimal & perfect repairs under resource constraints

The effect of a repair of a complex system can usually be approximated by the following two types: minimal repair for which the system is restored to its functioning state with minimum effort, or perfect repair for which the system is replaced or repaired to a good-as-new state. When both types of repair are possible, an important problem is to determine the repair policy; that is, the type of repair which should be carried out after a failure. In this paper, an optimal allocation problem is studied for a monotonic failure rate repairable system under some resource constraints. In the first model, the numbers of minimal & perfect repairs are fixed, and the optimal repair policy maximizing the expected system lifetime is studied. In the second model, the total amount of repair resource is fixed, and the costs of each minimal & perfect repair are assumed to be known. The optimal allocation algorithm is derived in this case. Two numerical examples are shown to illustrate the procedures.

A study on a single-unit Markov repairable system with repair time omission

This paper introduces a new model for a single-unit Markov repairable system in which repair times that are sufficiently short (less than some critical value) do not result in system failure. We can say that such a repair interval is omitted from the downtime record. First we suppose that the critical repair time is a constant. The model is then generalized to allow the critical repair time to be a non-negative random variable. We calculate system availability for these new models as a measure of reliability. Some numerical examples are given to illustrate the results in the paper.

Analysis for joint importance of components in a coherent system

JRI (Joint Reliability Importance) of two components is a measure of interaction of two components in a system for their contribution to the system reliability. It is defined as the rate at which the system reliability improves as the reliabilities of the two components improve. But, sometimes we may improve system reliability through improving reliabilities of three or more components. This article extends the concepts of JRI & JFI (Joint Failure Importance) of two components to multi-components, and establishes some relationships between JRI & JRI, JFI & JFI, and JFI & JRI. The paper also investigates the concept of Conditional Reliability Importance while the working states of certain components are known. Finally, the JRI of multi-components and Conditional Reliability Importance are analyzed in detail for a k-out-of-n:G system.

Reliabilities for (n,f,k) systems

The (n,f,k) system consists of n components ordered in a line or a cycle, while the system fails if, and only if, there exist at least f failed components or at least k consecutive failed components. For the linear (n,f,k) system with equal component reliabilities, the system reliability formula was given by Sun and Liao (1990). In this paper, we obtain the system reliability formulas for the linear and the circular systems with different component reliabilities by means of a Markov chain method.

Markov repairable systems with history-dependent up and down states

This paper introduces a Markov model for a multi-state repairable system in which some states are changeable in the sense that whether those physical states are up or down depends on the immediately preceding state of the system evolution process. Several reliability indexes, such as availability, mean up time, and steady-state reliability are calculated using the matrix method. A sufficient condition under which the availabilities of the stochastically monotone repairable systems with history-dependent states can be compared is also obtained. Some examples are presented to illustrate the results in the paper.

Modeling the evolution of system reliability performance under alternative environments

The dynamics of a system represented by a finite-state Markov process operating under two alternating regimes, for example, day/night, machine working/machine idling, etc., are modeled in this article. The transition rate matrices under the two regimes will usually be different. Also, the set of states of the system that are regarded as satisfactory may depend on the regime in operation: for example, a particular state of the system that may be regarded as satisfactory by day might not be tolerated at night (e.g., the headlights on a car not working). It is assumed that the regime durations are random variables and results are obtained for the availability of such a system and probability distributions for uptimes. Results and numerical examples are also given for two special cases: (i) when the regimes are of fixed duration; and (ii) when the regime durations have negative exponential distributions.

Reliability evaluation of generalised multi-state k-out-of-n systems based on FMCI approach

Most studies on k-out-of-n systems are in the binary context. The k-out-of-n system has failed if and only if at least k components have failed. The generalised multi-state k-out-of-n: G and F system models are defined by Huang et al. [Huang, J., Zuo, M.J., and Wu, Y.H. (2000), ‘Generalized Multi-state k-out-of-n: G Systems’, IEEE Transactions on reliability, 49, 105–111] and Zuo and Tian [Zuo, M.J., and Tian, Z.G. (2006), ‘Performance Evaluation of Generalized Multi-state k-out-of-n Systems’, IEEE Transactions on Reliability, 55, 319–327], respectively. In this article, by using the finite Markov chain imbedding (FMCI) approach, we present a unified formula with the product of matrices for evaluating the system state distribution for generalised multi-state k-out-of-n: F systems which include the decreasing multi-state F system, the increasing multi-state F system and the non-monotonic multi-state F system. Our results can be extended to the generalised multi-state k-out-of-n: G system. Three numerical examples are presented to illustrate the results.

An Analysis of Availability for Series Markov Repairable System With Neglected or Delayed Failures

A new system is defined based on a series Markov repairable system. In this new system, if a repair time of the system failure is too short (less than a given critical value) to cause the system to fail, then the repair interval may be omitted from the downtime record, i.e., the failure effect could be neglected. Otherwise, if a repair time is longer than the given critical value, then the system remains operating from the beginning of this repair until this repair time exceeding the critical value, i.e., the failure effect could be delayed. In Ion-Channel modeling, we call this situation the time interval omission problem. Incorporating this situation, the availability indices are presented as a measure of reliability. Some numerical examples are shown to illustrate the results obtained in the paper.

Sequential inspection strategy for multiple systems under availability requirement

System failures are usually observed during regular maintenance or inspection and this is especially the case for systems in standby or storage, which is common for safety critical systems. A periodic inspection policy is usually adopted. However, during the inspection, a lot of information is gained about the status of the system. Such information should be used in deciding upon the time for the next inspection. Hence sequential inspection is more appropriate, especially when the aging property of the system is unknown, and has to be estimated with the information from inspection. In this paper, a model is developed and sequential inspection strategies are studied in this situation. The focus is on the case when there are multiple systems inspected at the same, but discrete times. We also do not assume a known distribution of the system life time, and the estimation of that is incorporated into the analysis and decision making. Different availability criteria are considered and numerical examples are provided to illustrate the procedure.

Aggregated semi-Markov repairable systems with history-dependent up and down states

Some states in the aggregated semi-Markov repairable system with history-dependent up and down states are changeable in the sense that whether those physical states are up and down depends on the immediately preceding state of the system evolution process. Two reliability indices of the system, the frequency of failures and the time to the first system failure are given. The Laplace-Stieltjes transforms of several time distributions in a cycle, such as the up and down time, the total time the system is in the up, down and changeable states, the length of a single sojourn in the up, down and changeable states are derived. The means of them are also presented. Markov renewal theory, transform and matrix methods are employed for getting these performance measures. A numerical example is given to illustrate the results in the paper.