Reliability Modeling and Calculation of Balanced Systems with Multiple Failures

doi:10.12005/orms.2024.0085

Abstract

Abstract: The reliability theory originated in the 1930s, and the reliability problem was emphasized before and after the Second World War. With the development of society, the performance of military equipment has been greatly enhanced, but the increase in complexity has also increased the failure rate. Driven by actual demand, since the 1950s, the application of reliability has gradually expanded from the field of military technology to many fields such as national economy and people’s livelihood. In the fields of new energy storage, aerospace, machinery manufacturing, etc., balance characteristics are the basic requirements for the normal operation of many key systems, and based on the system perspective, such systems are usually called balanced systems. If they have performance imbalance or failure, it will accelerate system degradation or directly lead to system damage, resulting in serious consequences. The study of system reliability can effectively prevent or reduce the occurrence of system failures and accidents. Reliability modeling and related index calculation of equilibrium system is one of the research hot spots in reliability theory and engineering field.
For the series balance system composed of multiple components, it is assumed that each component gradually degrades under the environmental impact and presents multiple states. The performance balance of the system depends on the state of the components and their arrangement position, that is, when the parts of the system whose degradation degree exceeds a certain threshold are distributed in a certain area, the system will lose the performance balance. Considering single component failure leading to system failure and three types of system performance imbalance leading to system failure and four types of failure behaviors, when the number of continuous components with sparse d_l that are greater than or equal to a certain state threshold is greater than or equal to b_l, the system will lose performance balance. When the number of continuous components that are greater than or equal to a certain status threshold is greater than or equal to b_t, the system will lose performance balance. When the cumulative number of components greater than or equal to a certain state threshold is greater than or equal to b_w, the system will lose performance balance, so a balanced system reliability model considering multiple failure behaviors is constructed. Through the two-step finite Markov chain embedding method, the survival probability of the component in any state is obtained first, and then the reliability of the performance balance system is obtained according to the survival probability analytic formula of the single component.
Hydraulic support is an important part of fully mechanized coal mining equipment, widely used in coal seam mining face roof support, and the running state of hydraulic support is an important indicator of the safety of the whole face operation. After the impact of the hydraulic support system, because each component is damaged to different degrees, according to the different placement of the damaged parts, the system is at different levels of operation. If one of the brackets fails, the entire system will fail. Therefore, it is very important to study the reliability of the engineering equipment. The research object of this paper is the system composed of multi-state components, which is composed of multiple components. If the arrangement position of the components exceeding the threshold value is concentrated on a certain range or the failure of a single component leads to the failure of the system, the reliability model will be constructed and the reliability of the system solved. The research shows that the greater the value in an impact environment, the stronger the bearing capacity of the components, and the higher the reliability of the system. The effectiveness of the proposed model and method is verified.

Key words: balanced system, shock environment, finite Markov chain embedding method, reliability, variety of states, failure of competition

摘要： 平衡系统的可靠性建模与相关指标计算是可靠性理论与工程领域的研究热点之一。针对由多部件构成的串联平衡系统,假设每个部件受环境冲击影响逐渐退化,呈现出多种状态;系统的性能平衡取决于部件的状态及其排列位置,即当系统中退化程度超过某一阈值的部件分布在某一特定区域时,系统失去性能平衡。考虑单部件失效导致系统失效和三类系统性能失衡导致系统失效四类失效行为,构建了考虑多失效行为的平衡系统可靠性模型。运用有限马尔可夫链嵌入法推导了部件的相关概率指标以及系统可靠度。最后以液压支架系统为例,验证了所提出模型与方法的有效性。

关键词: 平衡系统, 冲击环境, 有限马尔可夫链嵌入法, 可靠性, 多状态, 竞争失效

CLC Number:

F272

DONG Qinglai, WANG Weiwei. Reliability Modeling and Calculation of Balanced Systems with Multiple Failures[J]. Operations Research and Management Science, 2024, 33(3): 104-110.

董庆来, 王伟伟. 考虑多失效行为的平衡系统可靠性建模与计算[J]. 运筹与管理, 2024, 33(3): 104-110.

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