| 陈玉阳,吴和成,胡明月.仅知失效数的指数型元件失效率的估计[J].装备环境工程,2019,16(5):59-64. CHEN Yu-yang,WU He-cheng,HU Ming-yue.Estimation on Failure Rate of Exponential Elements When Only the Failure Number is Known[J].Equipment Environmental Engineering,2019,16(5):59-64. |
| 仅知失效数的指数型元件失效率的估计 |
| Estimation on Failure Rate of Exponential Elements When Only the Failure Number is Known |
| 投稿时间：2019-01-03 修订日期：2019-05-25 |
| DOI：10.7643/ issn.1672-9242.2019.05.012 |
| 中文关键词: 失效率 指数分布 条件中位数 可靠性 |
| 英文关键词:failure rate exponential distribution conditional median reliability |
| 基金项目: |
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| Author | Institution |
| CHEN Yu-yang | 1. School of Petroleum and Chemical Engineering, Dalian University of Technology, Panjin, 124221, China; 2. a. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China |
| WU He-cheng | 2. a. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China |
| HU Ming-yue | 2. b. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China |
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| 中文摘要: |
| 目的 基于仅知失效元件数而不知其确切寿命的试验数据，对指数型元件的失效率进行估计。方法 设在时刻t0=0以n个指数型元件进行寿命试验，但仅在时刻t0< t1<…< tk记录失效的元件数，即在[t0, t1],[t1, t2],…,[tk-1, tk]内可以观测到失效的元件数，但失效元件的确切寿命未知，将各时间段内的失效元件数分别记为r1,r2,…,rk，在tk时刻未失效的元件数记为rk+1。采用改进的条件中数的方法，计算元件在[t0, t1],[t1, t2],…,[tk-1, tk],[tk, ∞]的条件中位寿命分别为μ1, μ2,…, μk, μk+1，将[ti-1, ti]内失效的ri个元件的寿命均近似看作μi，未失效的rk+1个元件的寿命近似看作(tk+μk+1)/2，进而估计元件的失效率，并对此方法进行仿真。结果 仿真结果表明，改进后的估计结果得到改善。结论 对于此类数据，改进的条件中位数方法可以有效估计元件的失效率，并可应用于实际。 |
| 英文摘要: |
| Objective To estimate the failure rate of exponential components based on the test data that only the number of failure elements is known and the exact life is unknown. Methods A life test on n components was conducted at the time t0=0 and the number of failure components was only recorded at the time t0< t1<…< tk, that is to say, failure components can be observed in [t0, t1],[t1, t2],…,[tk-1, tk]. But the exact lifetime of the failure components was unknown. The number of failure components in each time period was denoted as r1,r2,…,rk and the number of valid components at the time tk was denoted as rk+1. An improved conditional median method for estimating the failure rate for such data was adopted. The conditional median life in [t0, t1],[t1, t2],…,[tk-1, tk],[tk, ∞] was calculated as μ1, μ2,…, μk, μk+1 respectively. The lifetime of the ri elements in [ti-1, ti] was approximately considered as μi. The lifetimes of the rk+1components that were not invalidated were approximately considered as (tk+μk+1)/2. Then the failure rate of components was estimated and the method was simulated. Results It is shown that the improved evaluation method was more accurate. Conclusion For this kind of data, the improved conditional median method can effectively estimate the failure rate of components and can be applied to practice. |
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