Study on Processing Method and Engineering Application of Censored Data
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TECHNICAL ARTICLE—PEER-REVIEWED
Study on Processing Method and Engineering Application of Censored Data Yuanyuan Ma . Liyang Xie
Submitted: 21 October 2016 / Accepted: 10 February 2017 / Published online: 28 February 2017 ASM International 2017
Abstract The method and effects of extracting information from different fatigue test data were analyzed and compared according to the test data in engineering in this paper. By probability statistical analysis, the life data of ignored censored data were collected and analyzed to fit the distribution types and P–S–N curves. Otherwise, the life data including censored data were estimated by maximum likelihood estimation and K–S test. It is shown that the practice of simply ignoring censored data will underestimate the fatigue performance of the test sample in different degrees after analysis and comparison of the two results. Therefore, according to different types of test data, the influence of censored data should be considered fully in order to select the appropriate treatment method. Censored data in engineering usually should not be ignored. Keywords Reliability method Censored data Maximum likelihood estimation (MLE) K–S test
Introduction Load, strength, life are important parameters involved when a reliability method is used to solve practical engineering problems. These parameters are random variables obtained generally by fatigue test with statistical law and in Y. Ma (&) School of Mechanical Engineering and Automation, Liaoning University of Technology, Jinzhou 121001, China e-mail: [email protected] L. Xie School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China e-mail: [email protected]
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certain distribution form of obeying or approximately obeying [1–3]. Based on reliability theory, relevant test data need be collected and analyzed to determine the distribution form of random variables involved and the parameter characteristics [4, 5]. Besides, a lot of data in engineering are censored data (for example, the number of cycles in the fatigue test [107 is viewed as censored data), so the test or observational data need to be processed to estimate its distribution parameters, which will make it more practical to apply in engineering. Life tests are divided into complete tests and censored tests according to the non-activeness of samples. Due to constraints of time and financial, it is difficult to get complete samples. Therefore, censored samples are widely used [6–9]. Censoring refers to the truncating process of life data at fixed time, or with fixed number, or randomly according to certain criteria. In this way, from the data obtained, it is known that only part of samples observed has exact life, while that of the remaining part is only known to exceed certain value. Parameter estimation method of mathematical statistics is usually adopted to analyze and process censored data. That is to say, one or more unknown parameters are estimated by collecting and inferring the known population distribution. Maximum li
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