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系列组件的 MTBF

1960

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For a system of components in series, where any single failure causes system failure, the overall failure rate is the sum of individual rates. The system’s MTBF is the reciprocal of this sum: [latex]MTBF_{system} = (\sum_{i=1}^{n} \lambda_i)^{-1} = (1/MTBF_1 + 1/MTBF_2 + … + 1/MTBF_n)^{-1}[/latex]. This implies the system’s MTBF is always less than the lowest individual component’s MTBF.

This principle highlights a critical aspect of system design: a chain is only as strong as its weakest link. When components are arranged in series, the overall system reliability is always lower than the reliability of the least reliable component. For example, consider a system with two components in series. Component 1 has an MTBF of 10,000 hours ([latex]\lambda_1 = 10^{-4}[/latex] failures/hour) and Component 2 has an MTBF of 20,000 hours ([latex]\lambda_2 = 0.5 \times 10^{-4}[/latex] failures/hour).

The total system failure rate is [latex]\lambda_{system} = \lambda_1 + \lambda_2 = 10^{-4} + 0.5 \times 10^{-4} = 1.5 \times 10^{-4}[/latex] failures/hour. The system’s MTBF is then [latex]MTBF_{system} = 1 / \lambda_{system} = 1 / (1.5 \times 10^{-4}) \approx 6,667[/latex] hours. This is significantly lower than the MTBF of either individual component.

This calculation is foundational to the use of Reliability Block Diagrams (RBDs), a graphical method for analyzing system reliability. In an RBD, components in series are drawn in a line, visually representing that all must function for the system to succeed. This analysis drives engineers to identify critical components and focus reliability improvement efforts, such as selecting higher-quality parts or introducing redundancy (parallel components).

可靠性设计（DfR）, 故障率, 平均故障间隔时间 (MTBF), 流程改进, 质量管理, 可靠性、可用性、可维护性和安全性（RAMS）, 可靠性工程, 风险管理, 系统设计

UNESCO Nomenclature: 2212

– Systems engineering

类型

抽象系统

中断

实质性

使用方法

广泛使用

前体

boolean algebra developed by george boole
network flow theory
graph theory principles
early circuit analysis techniques

应用

electronic circuit design reliability analysis
risk assessment in complex industrial processes
supply chain vulnerability analysis
software architecture design, where modules are in series

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Related to: series components, system reliability, failure rate, reliability block diagram, weakest link, system design, risk assessment, electronics.