Extended Phase-type models for multistate competing risk systems

Stochastic Models in Reliability Engineering

Distribution and availability for aggregated second-order semi-Markov ternary system with working time omission

Reliability variation of multi-state components with inertial effect of deteriorating output performances

In practice many components and systems exhibit more than two output performances, these systems are called multi-state systems (MSSs) [6, 9, 10, 22]. Since the mid-1970s, numerous researches have been conducted which focus on MSS reliability [2]. Four commonly used approaches about MSS reliability have been formed gradually: the extension of Boolean model [26], stochastic process theory [18], universal generating function (UGF) technology [13,14] and MonteCarlo simulation [23]. As to the stochastic process theory used in reliability analysis of MSSs, when the numbers of failures between arbitrary time intervals can be described as a Poisson process, Markov processes are often introduced to solve these questions [16, 20, 21]. When the operating time and repair time are non-exponentially distributed, a SemiMarkov process is often considered [7]. Besides Markov processes and Semi-Markov processes, the Wiener process [15, 19], the Gamma process [27] and the cumulative exposure process [10] are also considered in MSS reliability modelling. Research about MSS reliability has been a highlight topic in recent years and many new achievements are constantly emerging [17]. Studying on Markov repairable systems has always been an active branch in reliability theory. Jinhua Cao [11] studied the general model of Markov repairable systems, concluded the reliability analysis steps and deduced reliability indexes of voting systems, cold standby systems and warm standard systems. Cui et al. [5] proposed the definition of aggregated stochastic processes and applied into reliability analysis of repairable systems. Lisnianski [17] constructed a Markov reward model for reliability assessment of a multi-state system with variable demand. In his study, the process was assumed to be a homogenous Continuous Time Markov Chain (CTMC) with different possible states and corresponding transition possibility intensities. Other studies of reliability of multi-state systems using stochastic processes can be found in [25] and [29]. For a Markov repairable component containing N different output states, i.e., whose output performance is

/pdf/balancing-reliability-and-maintenance-cost-rate-of-multi-i1z1wcas1t.pdf

Balancing reliability and maintenance cost rate of multi-state components with fault interval omission

In this article, we study a single-unit repairable model with working and repair time omission under an alternative renewal process. As the working time is shorter than threshold τ1, we regard some...

A study on a single-unit repairable system with working and repair time omission under an alternative renewal process:

The system’s performance is one of most important issues in both theory and practice The task of evaluation of system performance first needs a series of indexes which can describe the system’s performance properly and correctly Different indexes provide different descriptions and result in different conclusions on system’s performance On the other hand, although it has a lot of indexes for evaluation of system performance such as reliability, availability and safety and so forth, they still cannot meet the variety requirements on the evaluation of system performance Thus it is an important work to introduce and develop some new indexes to measure the system’s performance In this paper, two types of related probability measures, point-wise and interval-wise probabilities, including their concepts and computation formulae, are developed under an alternative renewal process and its derivative aggregated stochastic process with state classifications based on sojourn times All limits of introduced new measures are discussed too, and the relationship among these new measures is studied Finally, two special cases: constant and exponential, are discussed too, and some numerical examples are presented to illustrate the concepts intuitively in this work The work for introduction of new concepts is motivated by some practical problems, specially in repairable systems The research results can be used not only in reliability, but also may be used in finance, engineering, economy and other fields

Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times

The indexes for measuring the performances of systems, availability, reliability and others are important issues in the system design and analysis. Although there are many indices being used, they still cannot meet the various requirements in both theory and practice, so the study on these indices is a significant task. In this paper, we develop some new useful indexes classified into two categories, by introducing a stochastic process in terms of two threshold values on sojourn time. The two-category indices are named as point state and interval state probability measures, respectively. The corresponding computation formulae including some special cases are presented. These introduced indices can be used to describe the degrees of stable, semi-stable and unstable for the operation system. We also believe that the indices can be used in reliability engineering, survival analysis, actuarial study, financial analysis, economy and others, and this work definitely enriches the contents of theory of st...

Quan Zhang

Papers

A study on a single-unit repairable system with working and repair time omission under an alternative renewal process:

Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times

A study on a stochastic process with state classifications based on sojourn times