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Email Address. Sign In. Reliability Analysis for Multi-Component Systems Subject to Multiple Dependent Competing Failure Processes Abstract: For complex multi-component systems with each component experiencing multiple failure processes due to simultaneous exposure to degradation and shock loads, we developed a new multi-component system reliability model, and applied two different preventive maintenance policies.

This new model extends previous research, and is different from related previous research by considering an assembled system of degrading components with s-dependent failure times resulting from shared shock exposure.

Previous research primarily pertained to a single component or simple system, or systems with s-independent failure processes and failure times. In our new system model, the individual failure processes for each component and the component failure processes are all s-dependent. These models can be applied directly, or customized for many complex systems with multiple components that experience s-dependent competing failure processes.

In this model, each component can fail due to a soft failure process, or a hard failure process. These two component failure processes are mutually competing and s-dependent. If one component fails relatively frequently, it is likely that the number of shocks is relatively large, and these shocks impact all components potentially causing them to fail more often as well.

Therefore, failure processes of all components are also s-dependent. An age replacement policy and an inspection-based maintenance policy are applied for a system with multiple components.

The optimal replacement interval or inspection times are determined by minimizing a cost rate function. The model is demonstrated on several examples.

### Reliability of Systems

Article :. Date of Publication: 24 January DOI: Need Help?We have already discussed reliability and availability basics in a previous article. This article will focus on techniques for calculating system availability from the availability information for its components. System Availability is calculated by modeling the system as an interconnection of parts in series and parallel.

The following rules are used to decide if components should be placed in series or parallel:. As stated above, two parts X and Y are considered to be operating in series if failure of either of the parts results in failure of the combination. The combined system is operational only if both Part X and Part Y are available. From this it follows that the combined availability is a product of the availability of the two parts. The combined availability is shown by the equation below:. The implications of the above equation are that the combined availability of two components in series is always lower than the availability of its individual components.

Consider the system in the figure above. Part X and Y are connected in series. The table below shows the availability and downtime for individual components and the series combination. From the above table it is clear that even though a very high availability Part Y was used, the overall availability of the system was pulled down by the low availability of Part X.

This just proves the saying that a chain is as strong as the weakest link. More specifically, a chain is weaker than the weakest link. As stated above, two parts are considered to be operating in parallel if the combination is considered failed when both parts fail.

The combined system is operational if either is available. From this it follows that the combined availability is 1 - both parts are unavailable.

## RBDs and Analytical System Reliability

The implications of the above equation are that the combined availability of two components in parallel is always much higher than the availability of its individual components.

Two instances of Part X are connected in parallel. The table below shows the availability and downtime for individual components and the parallel combination. From the above table it is clear that even though a very low availability Part X was used, the overall availability of the system is much higher.

Thus parallel operation provides a very powerful mechanism for making a highly reliable system from low reliability. For this reason, all mission critical systems are designed with redundant components.

Different redundancy techniques are discussed in the Hardware Fault Tolerance article. Consider a system like the Xenon switching system. The system has been designed to incrementally add XEN cards to handle subscriber load. Now consider the case of a Xenon switch configured with 10 XEN cards. Should we consider the system to be unavailable when one XEN card fails? In such systems where failure of a component leads to some users losing service, system availability has to be defined by considering the percentage of users affected by the failure.

This translates to 3 XEN cards out of 10 failing. We need a formula to calculate the availability when a system with 7 XEN cards is considered as available. Consider a system with N components where the system is considered to be available when at least N-M components are available i.

As a first step, we prepare a detailed block diagram of the system. This system consists of an input transducer which receives the signal and converts it to a data stream suitable for the signal processor. This output is fed to a redundant pair of signal processors. The active signal processor acts on the input, while the standby signal processor ignores the data from the input transducer. Standby just monitors the sanity of the active signal processor. The output from the two signal processor boards is combined and fed into the output transducer.

Again, the active signal processor drives the data lines.Many objects consist of more components. The mutual arrangement of the individual elements influences the resultant reliability. The formulae are shown for the resultant reliability of series arrangement, as well as for parallel and combined arrangement. The possibility of reliability increasing by means of redundancy is explained, and also the principle of optimal allocation of reliabilities to individual elements.

Everything is illustrated on examples. Concise Reliability for Engineers. Many objects consist of more parts or elements. From reliability point of view, an element is any component or object that is considered in the investigated case as a whole and is not decomposed into simpler objects.

An element can be a lamp bulb, the connecting point of two electric components, a screw, an oil hose, a piston in an engine, and even the complete engine in a diesel locomotive. Also, the individual operations or their groups in a complex manufacturing or building process can be considered as elements. An example of a simple system is an electric lamp made by a light bulb, socket, switch, wires, plug, and the lamp body.

An extremely complex system is an aircraft, containing tens of thousands of mechanical, hydraulic, or electric elements. Each of them can fail. This increases the probability that the whole system fails. The resultant reliability depends on the reliability of the individual elements and their number and mutual arrangement. A suitable arrangement can even increase the reliability of the system. In this chapter, important cases will be shown together with the formulas for the calculation of resultant reliability.

Two basic systems are series and parallel, and their combinations are also possible. From reliability point of view, a series system Fig.

For example, a motorcycle cannot go if any of the following parts cannot serve: engine, tank with fuel, chain, frame, front or rear wheel, etc. All these elements are thus arranged in series. Elements are also screws and many other things. If failure of any component does not depend on any other component, the reliability of the system is obtained simply as the product of the reliabilities of individual elements.

This is less than the reliability of the weaker component no. The probability of failure has increased to 1 â€” 0. What will be the reliability of a system composed of a 2 components, b 10 components, c 50 components, and d components? One can see that the drop of reliability is significant especially for high numbers of components. Complex large systems must therefore be assembled from very reliable elements.Skip to search form Skip to main content You are currently offline.

Some features of the site may not work correctly. DOI: Lisnianski and G. LisnianskiG. Levitin Published in Series on Qualityâ€¦. View PDF. Save to Library. Create Alert. Launch Research Feed. Share This Paper. Topics from this paper. Portable Document Format. Citation Type. Has PDF. Publication Type. More Filters. Research Feed. View 1 excerpt, cites methods. Dynamic performance and cost measures with setup determination under state-age-dependent deterioration.

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I Jan. BoxJeddah,Saudi Arabia Abstract: This paper employs multi-valued logic in the reliability analysis of a multi-state system. The paper expresses each instance of the multi-valued output of the system as an explicit function of the multi-valued inputs of the system. The paper demonstrates its proposed technique in terms of a standard commodity-supply system, and obtains numerical results that exactly agree with those obtained by earlier methods.

As a bonus, the paper utilizes the MVKM representation of the solved coherent multi-state system to illustrate its features of causality, monotonicity and relevancy. Introduction We propose a novel method for the reliability analysis of a multi-state system via multi-valued logic. This method seems to be the most natural and direct way to achieve this purpose, since it seeks to express each instance of the multi-state system as an explicit function of the multi-valued inputs of the system.

The ultimate output of the method is an aggregated or collective tabulation of the resulting functions. This tabulation is conveniently achieved as a Multi-Valued Karnaugh Map MVKMwhich serves as a natural, unique, and complete representation of the multi-state system.

The paper presents a detailed analysis of a standard commodity supply multi-state system, and provides a complete solution for it in MVKM form. This manually-obtained solution agrees exactly with other solutions obtained earlier via automated techniques [1, 2] or via different manual techniques [3, 4].

To construct our MVKM complete solutions, we could have followed among several possibilities either of the following two options. Option 1 is to use exhaustive enumeration, i. However, it decomposes the initial problem into individual problems, in which a verbal statement of the problem together with full specification of the individual inputs lead immediately to a selection of the output value from amongst its possible multitude of values. We use the choice of algebraic quantities herein and delegate the choice of CKMs to another forthcoming paper [14].

The organization of the remainder of this paper is as follows. Section II gives a verbal and a mathematical description of the problem to be solved.A business imperative for companies of all sizes, cloud computing allows organizations to consume IT services on a usage-based subscription model. The promise of cloud computing depends on two viral metrics, service reliability and availability, to evaluate the dependability of a system.

Vendors offer service level agreements SLAs to meet specific standards of reliability and availability. An SLA breach not only incurs cost penalty to the vendor but also compromises end-user experience of apps and solutions running on the cloud network. Though reliability and availability are often used interchangeably, they are different concepts in the engineering domain. Reliability is the probability that a system performs correctly during a specific time duration.

During this correct operation, no repair is required or performed, and the system adequately follows the defined performance specifications.

Reliability follows an exponential failure law, which means that it reduces as the time duration considered for reliability calculations elapses. In other words, reliability of a system will be high at its initial state of operation and gradually reduce to its lowest magnitude over time.

Availability refers to the probability that a system performs correctly at a specific time instance not duration. The service must be operational and adequately satisfy the defined specifications at the time of its usage. Availability is measured at its steady state, accounting for potential downtime incidents that can and will render a service unavailable during its projected usage duration.

For example, a Before discussing how reliability and availability are calculated, an understanding of incident service metrics used in these calculations is required. These metrics are computed through extensive experimentation, experience, or industrial standards; they are not observed directly.

Therefore, the resulting calculations only provide relatively accurate understanding of system reliability and availability. The graphic, below, and following sections outline the most relevant incident and service metrics:. The frequency of component failure per unit time.

In reliability engineering calculations, failure rate is considered as forecasted failure intensity given that the component is fully operational in its initial condition.

The formula is given for repairable and non-repairable systems respectively as follows:. The frequency of successful repair operations performed on a failed component per unit time.

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Repair rate is defined mathematically as follows:. The average time duration before a non-repairable system component fails. The following formula calculates MTTF:. The average time duration between inherent failures of a repairable system component.

The following formulae are used to calculate MTBF:. The average time duration to fix a failed component and return to operational state. This metric includes the time spent during the alert and diagnostic process before repair activities are initiated.

The average time solely spent on the repair process is called mean time to repair. The calculations below are computed for reliability and availability attributes of an individual component. IT systems contain multiple components connected as a complex architectural. The effective reliability and availability of the system depends on the specifications of individual components, network configurations, and redundancy models.

The configuration can be series, parallel, or a hybrid of series and parallel connections between system components. Redundancy models can account for failures of internal system components and therefore change the effective system reliability and availability performance.

A reliability block diagram RBD may be used to demonstrate the interconnection between individual components. Alternatively, analytical methods can also be used to perform these calculations for large scale and complex networks.

RBD demonstrating a hybrid mix of series and parallel connections between system components is provided:. The effective failure rates are used to compute reliability and availability of the system using these formulae:.Chapter 1: Basics of System Reliability Analysis.

Available Software: BlockSim. Generate Reference Book: File may be more up-to-date. In life data analysis and accelerated life testing data analysis, as well as other testing activities, one of the primary objectives is to obtain a life distribution that describes the times-to-failure of a component, subassembly, assembly or system.

This analysis is based on the time of successful operation or time-to-failure data of the item componenteither under use conditions or from accelerated life tests. For any life data analysis, the analyst chooses a point at which no more detailed information about the object of analysis is known or needs to be considered.

At that point, the analyst treats the object of analysis as a "black box. In system reliability analysis, one constructs a "System" model from these component models.

There are many specific reasons for looking at component data to estimate the overall system reliability. Many other benefits of the system reliability analysis approach also exist and will be presented throughout this reference. The types of components, their quantities, their qualities and the manner in which they are arranged within the system have a direct effect on the system's reliability. The relationship between a system and its components is often misunderstood or oversimplified. Unfortunately, poor understanding of the relationship between a system and its constituent components can result in statements like this being accepted as factual, when in reality they are false.

Block diagrams are widely used in engineering and science and exist in many different forms. They can also be used to describe the interrelation between the components and to define the system. When used in this fashion, the block diagram is then referred to as a reliability block diagram RBD. A reliability block diagram is a graphical representation of the components of the system and how they are reliability-wise related connected.

It should be noted that this may differ from how the components are physically connected. An RBD of a simplified computer system with a redundant fan configuration is shown below. RBDs are constructed out of blocks. The blocks are connected with direction lines that represent the reliability relationship between the blocks. A block is usually represented in the diagram by a rectangle. In a reliability block diagram, such blocks represent the component, subsystem or assembly at its chosen black box level.

The following figure shows two blocks, one representing a resistor and one representing a computer. It is possible for each block in a particular RBD to be represented by its own reliability block diagram, depending on the level of detail in question. For example, in an RBD of a car, the top level blocks could represent the major systems of the car, as illustrated in the figure below. Each of these systems could have their own RBDs in which the blocks represent the subsystems of that particular system.

This could continue down through many levels of detail, all the way down to the level of the most basic components e. The level of granularity or detail that one chooses should be based on both the availability of data and on the lowest actionable item concept. To illustrate this concept, consider the aforementioned computer system shown earlier. When the computer manufacturer finds out that the hard drive is not as reliable as it should be and decides not to try to improve the reliability of the current hard drive but rather to get a new hard drive supplier, then the lowest actionable item is the hard drive.

The hard drive supplier will then have actionable items inside the hard drive, and so forth. This information will allow the reliability engineer to characterize the life distribution of each component. Data can be obtained from different sources, including:.

For example, consider a resistor that is part of a larger system to be analyzed. Failure data for this resistor can be obtained by performing in-house reliability tests and by observing the behavior of that type of resistor in the field.

As shown below, a life distribution is then fitted to the data and the parameters are obtained. The parameters of that distribution represent the life distribution of that resistor block in the overall system RBD.