Average Unavailability Research Articles

Optimal inspection and maintenance for a repairable k-out-of-n: G warm standby system

In many cases, the safety and the reliability of a warm standby system heavily rely on the successful activation and the subsequent operation of its standby components. Optimal inspection and maintenance schedule is one of the most common but essential activities in the real world applications to manage standbys effectively and efficiently. In this paper, we propose a novel state-based method by incorporating inspection activities into multiphase Markov process to model the dynamic behaviors of a general repairable k-out-of-n: G warm standby system with common-cause failures. Here the effects of inspection errors are taken into consideration. Then the expected total cost and the average unavailability of the system are expressed as exact closed formulas regarding the inspection interval (or inspection frequency) in a cycle. Finally, the inspection and maintenance optimization problem is formulated as a nonlinear optimization program which aims to find the optimal periodic inspection interval on a finite time horizon by minimizing the expected total cost while taking into account the limitation of the average unavailability. The proposed modeling approach can be used in various industrial systems, where inspections and standbys are especially necessary, e.g., a feedwater subsystem of a nuclear power plant. A simplified numerical example illustrates the models and the calculations with sensitivity analysis and Monte Carlo simulation.

Simultaneous evaluation of safety integrity’s performance indicators with a generalized implementation of common cause failures

Abstract The average unavailability and the average unconditional failure intensity of safety-instrumented systems represent the main performance indicators of safety integrity. This paper employs an approach based on the exploitation of the availability expression to obtain both performance measures in a simultaneous and straightforward way for any KooN configuration. The implementation of such an approach is generalized to take into account the contribution of common cause failures using any parametric model. The validation of the obtained results is verified through their application using several architectures and using Beta Factor and Binomial Failure Rate models to handle such type of dependent events. Therefore, the contribution of this paper lies in proposing one single formula that can be used to estimate the two main safety integrity’s performance indicators for any KooN architecture using any kind of common cause failures parametric model.

Performance analysis for subsea blind shear ram preventers subject to testing strategies

In a subsea blowout preventer system, a subsea blind shear ram preventer (BSRP) plays as a crucial safety barrier by cutting off the drill pipe and sealing the wellhead to prevent serious accidents. Testing and repairs of BSRPs are the main issues in operation and maintenance activities. It is important to assess BSRPs unavailability during proof and partial testing phases in order to ensure their safety functions. This paper presents a newly state-based approach for unavailability analysis by incorporating testing activities of BSRPs into multiphase Markov process. In the approach, states waiting for repair are taken into consideration. Analytical formulas for evaluation of time-dependent unavailability and average unavailability for BSRPs are developed. In addition, the non-periodic characteristics and effects of degradation are also taken into account in proof testing. The effects of testing errors and postponed repairs on the tendency of unavailability in partial testing phases are checked in the proposed models. Performance analyses for BSRPs configurations, scenarios and cases considered in the paper are carried out to demonstrate the application of the proposed models. Monte Carlo models for both proof and partial testing are developed and simulated. Different comparisons are performed for validation of the set of the derived formulations.

A stochastic alternating renewal process model for unavailability analysis of standby safety equipment

The paper presents a stochastic approach to analyze instantaneous unavailability of standby safety equipment caused by latent failures. The problem of unavailability analysis is formulated as a stochastic alternating renewal process without any restrictions on the form of the probability distribution assigned to time to failure and repair duration. An integral equation for point unavailability is derived and numerically solved for a given maintenance policy. The paper also incorporates an age-based preventive maintenance policy with random repair time. In case of aging equipment, the asymptotic limit or average unavailability should be used with a caution, because it cannot model an increasing trend in unavailability as a result of increasing hazard rate (i.e. aging) of the time to failure distribution.

Unification of Common Cause Failures’ Parametric Models Using a Generic Markovian Model

The main objective of this paper is to provide a unified Markov model which could implement any parametric models devoted to the treatment of common cause failures (CCFs), namely: beta factor, multiple greek letter, alpha factor, multiple beta factor, and binomial failure rate. The choice of the Markovian representation is motivated by the fact that classical reliability approaches (e.g., Fault trees) are not able to catch the dynamic aspect induced by CCF events. The proposed Markovian model is also capable of dealing with any M-out-of-N configuration. It is illustrated on the basis of a system made up of four identical components (N = 4) in order to quantitatively examine the differences between the first four mentioned parametric models. For that purpose, the considered performance indicators are the average unavailability (Uavg) and the average unconditional failure intensity (i.e., failure frequency) (wavg).

Simplification of State Transition Diagrams in Average Unavailability Analysis by Using Generalized Perturbation Theory

Safety analysis studies in nuclear engineering, more specifically system reliability, usually handle a great number of components, so that computational difficulties may arise. To face the problem of many component systems a method for simplifying the state transition diagram in Markovian reliability analyses has been proposed, using the edges which can be cut, since these latter have a smaller influence on system failure probability. In order to extend the application of GPT (Generalized Perturbation Theory), this work uses GPT formalism to reduce the number of states in a transition diagram, not considering the state probability as the integral quantity of interest, but the mean system unavailability instead. Therefore, after simplifying the original diagram, the mean unavailability for the new system was calculated and the results were very close to those of the original diagram integral quantity (giving a relative error of about 2%), showing that the proposed simplification is quite reasonable and simple to apply.

Analytical models of flow availability in two-layer networks with dedicated path protection

Even with protection, user traffic flows can be disrupted due to network failures that are beyond the protection capability. One of the quantitative metrics to measure the service quality in such a context is “availability”. We study analytical models that compute availability of upper-layer flows in two-layer networks with dedicated path protection at either the upper or the lower layer. Our investigations reveal that existing analytical models significantly overestimate availability requirements on lower-layer links, and exaggerate upper-layer flow unavailability by treating correlated upper-layer failures as being independent. In contrast, our proposed model takes into account such correlations by tracing upper-layer failures to lower-layer root causes, thus greatly relaxing unnecessary high-availability requirements on lower-layer links without compromising the availability of upper-layer flows. In our simulation examples, using the existing models, up to 66.6% and 89.2% of the total flows are overestimated on their unavailability under dedicated path protection at the upper and the lower layer, respectively. Moreover, the average unavailability redundancy built into these flows is about 30% and 15% for protection at the upper and the lower layer, respectively. Furthermore, we compare flow availability under the two protection schemes, and show that given the same initial unprotected network states, protection at the lower layer enjoys lower average flow unavailability than protection at the upper layer.

Short-term reliability equivalence algorithm for flexible transmission equipment

Flexible power transmission are based on power electronic elements with series/parallel configuration and redundancy design. Because of the limited time span, fast replacement, and not fully reliable redundant elements due to unexposed failure, it is better to describe their reliability level with short-term evaluation instead of long-term evaluation. In short-term evaluation, the reliability of flexible transmission equipments is time-dependent, and decided by the initial state and the evaluation period, which is different from its steady-state value.In this paper, instantaneous state probability and unavailability for multi-state system within limited evaluation period are described analytically, and equivalenced with the average values. The algorithm is based on state transition matrix, and suitable for systems with different configurations. For systems with series or parallel elements, the steady–state and average unavailability are quantified, and compared with the existing method of multiplying the (un) availabilities each element directly. It is found that due to simultaneous failure and state transition, the existing method may yield error to the fixed and time-variant terms of the average unavailability.

Probability of failure on demand of safety systems: impact of partial test distribution

In accordance with the IEC 61508 functional safety standard, safety-related systems operating in a low demand mode need to be proof tested to reveal any ‘dangerous undetected failures’. Proof tests may be full (i.e. complete) or partial (i.e. incomplete), depending on their ability to detect all the system failures or only a part of them. Following a partial test, some failures may then be left latent until the full test, whereas after a full test (and overhaul), the system is restored to an as-good-as-new condition. A partial-test policy is defined by the efficiency of the partial tests, and the number and distribution (periodic or non-periodic) of the partial tests in the full test time interval. Non-approximate equations are introduced for probability of failure on demand (PFD) assessment of a Moo N architecture (i.e. k-out-of- n: G) systems subject to partial and full tests. Partial tests may occur at different time instants (periodic or not) until the full test. The time-dependent, average, and maximum system unavailability (PFD(t), PFDavg, and PFDmax) are investigated, and the impact of the partial test distribution on average and maximum system unavailability are analysed, according to system architecture, component failure rates, and partial test efficiency.

Availability Analytical Model for Permanent Dedicated Path Protection in WDM Networks

This paper analyses the connection availability of a protection paradigm, termed permanent dedicated path protection (P-DPP), in WDM mesh networks. An analytical model for calculating the unavailability of P-DPP is introduced. Numerical results on COST239 European network show that the average unavailability of the network is proportional to blocking probability of the network, and fits well with the simulation results.

A reliability analysis of a natural-gas pressure-regulating installation

A case study involving analyses of the operability, reliability and availability was made for a selected, typical, high-pressure, natural-gas, pressure-regulating installation (PRI). The study was commissioned by the national operator of the natural-gas, transmission-pipeline network for the purpose of validating the existing operability and maintenance practices and policies. The study involved a failure-risk analysis (HAZOP) of the selected typical installation, retrieval and analysis of the available corrective maintenance data for the PRI’s equipment at the network level in order to obtain the failure rates followed by an elaboration of the quantitative fault trees. Thus, both operator-specific and generic literature data on equipment failure rates were used. The results obtained show that two failure scenarios need to be considered: the first is related to the PRI’s failure to provide gas to the consumer(s) due to a low-pressure state and the second is related to a failure of the gas pre-heating at the high-pressure reduction stage, leading to a low temperature (a non-critical, but unfavorable, PRI state). Related to the first scenario, the most important cause of failure was found to be a transient pressure disturbance back from the consumer side. The network’s average PRI failure frequency was assessed to be about once per 32 years, and the average unavailability to be about 4 minutes per year (the confidence intervals were also assessed). Based on the results obtained, some improvements to the monitoring of the PRI are proposed.

Dynamic management of human error to reduce total risk

Abstract Safety management in companies at the limit of risk criteria must be implemented in order to survive in the very aggressive and competitive environment of modern society. It implies that the risk in process industries is crossing the limit of safe practices. Most major accidents consist of human errors and mechanical component failures, and cannot be explained by a stochastic coincidence of independent events. This work focuses on the coincidence of human error and mechanical failure to introduce a concept of dynamic management of human error. By the dynamic management of human error during a short period, when a mechanical component is temporarily unavailable during periodic testing or maintenance, the probability of a major accident may be reduced significantly without additional investment on improving safety. For the periodically-tested standby component, the majority of total average unavailability of the component may be recognized by operators or workers as well as maintenance mechanics. During this short period, an appropriate dynamic management of human error for improving human performance temporarily may be very effective in reducing total risk in industries. The dynamic management of human error may be a useful method to prevent loss effectively in the process industries

End-to-end WAN service availability

This paper seeks to understand how network failures affect the availability of service delivery across wide-area networks (WANs) and to evaluate classes of techniques for improving end-to-end service availability. Using several large-scale connectivity traces, we develop a model of network unavailability that includes key parameters such as failure location and failure duration. We then use trace-based simulation to evaluate several classes of techniques for coping with network unavailability. We find that caching alone is seldom effective at insulating services from failures but that the combination of mobile extension code and prefetching can improve average unavailability by as much as an order of magnitude for classes of service whose semantics support disconnected operation. We find that routing-based techniques may provide significant improvements but that the improvements of many individual techniques are limited because they do not address all significant categories of network failures. By combining the techniques we examine, some systems may be able to reduce average unavailability by as much as one or two orders of magnitude.

On the availability of atmospheric optical communication lines

Dependence of the probability of “blocking” (unavailability) of an atmospheric optical communication line (AOCL), caused by light scattering by fogs and precipitation, on the length of this line was studied based on an analysis of the statistical data on the meteorological visibility range (MVR). Averaged over several years, this dependence is approximately linear for many geographical locations. It is assumed that the linearity takes place in a wide interval (from kilometers to tens of meters) of the AOCL length. This assumption is confirmed by an analysis of statistical data on the MVR for one of the Moscow airports. The dependence was found to become significantly nonlinear on the averaging over long-term data for separate months of a year. Based on the analysis of the MVR statistics, AOCL unavailability estimates are suggested. It is expedient to consider a value of no less than 0.1% as a reasonable estimate of the annual average unavailability even for short (several hundred meters) lines. It is concluded that, in the general case, an increase of the optical transmitter power even by dozens of times does not result in a significant increase of the AOCL availability.

A basic framework for sub-transmission system health analysis

Abstract The reliability of supply in sub-transmission systems is usually quantified in terms of two sets of indices, the individual supply/load point indices (average failure rate, average outage duration and average annual unavailability) and the system performance indices (SAIFI, SAIDI, CAIDI, ASUI, ASAI, etc.). These probabilistic indices are very useful not only for assessing the severity of system failures in future reliability predictions but also in assessing the system’s past performance. Many utilities, however, continue to use deterministic methods (rule-of-thumb methods) to assess the reliability of their systems. This paper presents a method designated as system well-being analysis, which in addition to the conventional probabilistic risk index of supply point unavailability, also incorporates the specified deterministic criteria in defining additional system healthy and marginal states. The proposed method is illustrated in this paper to calculate the well-being indices of electric sub-transmission systems. The proposed technique, which can be used to evaluate the adequacy of sub-transmission systems, is applied in this paper to a small but comprehensive test system to show the effects of some pertinent factors and deterministic criteria on the system well-being indices.

Time-dependent unavailability of aging standby components based on nuclear plant data

The time-dependent unavailability of periodically tested and repaired aging components which have first failure densities satisfying the normal and the Weibull distributions with aging threshold are investigated using a generalized formula for surveillance testing and repair. The formalism is applied to the case of periodic, good-as-old surveillance testing with good-as-new repair. Actual aging data are used. The results show that aging can have significant impacts on the availability and reliability of a component and the system containing the component. More specifically: a) the time dependent unavailability of aging components can go through large swings with varying magnitude in time before stabilizing to the standard saw-tooth behavior of periodically tested components with constant failure rates, and b) approximating the unavailability by a constant failure rate can lead to large differences even when an average unavailability is calculated.

Cause-effect failure analysis for measure channels with computer process units

The impact of computer process unit inclusion in redundant measure channels is studied by means of a multiplier ß factor that deals with average unavailabilities relation between a computer process unit attachment channel and a normal one. Total active and passive channel failure modes by maximum and minimum limit value are analysed.

Optimization of test strategies: a general approach

A general approach to optimizing the test schedules of the standby system is proposed. The system consists of interrelated component groups with different test intervals. Fault-tree analysis and Markov chains were used to estimate the unavailability of the system. In three partial cases, the average unavailability of the system was calculated through the average unavailability of its components. For a system where tests were started randomly, the problem was reduced to a nonlinear programming problem, for which the numerical technique (gradient methods) is proposed and tested with some examples. In the general case a technique to calculate the average unavailability is proposed, and the problem is reduced to a nonsmooth optimization problem

Time-dependent unavailability analysis of standby components incorporating arbitrary failure distributions and three inspection/maintenance policies

Abstract Standby components suffer a certain type of faults defined as ‘unrevealed’ faults. For this purpose, they must be periodically tested to insure their availability for use when needed. The paper presents an effective computational methodology for the time dependent unavailability analysis of standby components. The methodology consists of a set of recursive equations which have been developed assuming an arbitrary probability distribution for component lifetime and considering three commonly used inspection/ maintenance policies . This set of equations has a general form and incorporates practical operating features of standby redundant systems. The indices evaluated are the exact point, interval and average unavailabilities for each component under consideration. An availability analysis of standby systems with multiple components can also be conducted by allowing staggered inspection of different sets of components within the same system to be handled by the methodology. Finally, a typical standby system is analyzed for various case studies.

Reliability of on-line versus standby safety systems in process plants: a comparative assessment of two systems for controlling accidental gas releases

This paper presents a method for reliability assessment of on-line and standby control and safety systems in process plants, based on the principles of Markovian reliability analysis. Safety or control systems in process plants aim to prevent and/or mitigate possible deviations from normal operating conditions that could lead to accidents. On-line control systems operate continuously while standby systems are triggered by the onset of an accident. Two alternative designs for controlling accidental releases of hydrogen selenide (H 2 Se) and hydrogen sulphide (H 2 S) in the manufacturing of photovoltaic cells are compared. The on-line system, which consists of a Venturi scrubber, a packed bed scrubber, and a carbon adsorption bed, operates continuously and its failure is immediately detectable. The standby system is triggered by a toxic gas release, and failure is detectable only through demands (actual or tests). It consists of a containment (high pressure vessel), a scrubbing vessel and a carbon adsorption bed. The average unavailability over a one year period is calculated for both systems as a function of the failure rates, the repair rates, the frequency of testing and the probability of human errors. Regions of the parameter values within which each alternative design exhibits lower average unavailability are provided.