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| Estimation on Failure Rate of Exponential Elements When Only the Failure Number is Known |
| Received:January 03, 2019 Revised:May 25, 2019 |
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| DOI：10.7643/ issn.1672-9242.2019.05.012 |
| KeyWord:failure rate exponential distribution conditional median reliability |
| Author | Institution |
| CHEN Yu-yang |
1. School of Petroleum and Chemical Engineering, Dalian University of Technology, Panjin, , China; 2. a. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing , China |
| WU He-cheng |
2. a. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing , China |
| HU Ming-yue |
2. b. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing , China |
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| Abstract: |
| 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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