<p>Degradation models are more and more used in reliability analysis. Among the most classical models, one can cite the Wiener process with a linear drift and the gamma process. Such models can be used to define complex maintenance policies, for instance. However, up to now, no goodness-of-fit test has been proposed formally for a general sampling scheme. In this paper, we first derive a moments method estimator for independent and gamma distributed random variables with common rate parameter (the shape being possibly different for each random variables) for which we provide asymptotic properties. Next, we consider a goodness-of-fit test for such sequence of random variables. This is an extension of a test derived by Villaseñor and González-Estrada (Villaseñor and González-Estrada <CitationRef CitationID="CR18">2015</CitationRef>). This result is used to propose a goodness-of-fit test for homogeneous gamma processes under a general sampling scheme. We have applied this test to a real data set and then we have studied numerically the performance of our test in terms of coverage probabilities and power.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Goodness-of-fit test for homogeneous gamma process under a general sampling scheme

  • Christian Paroissin

摘要

Degradation models are more and more used in reliability analysis. Among the most classical models, one can cite the Wiener process with a linear drift and the gamma process. Such models can be used to define complex maintenance policies, for instance. However, up to now, no goodness-of-fit test has been proposed formally for a general sampling scheme. In this paper, we first derive a moments method estimator for independent and gamma distributed random variables with common rate parameter (the shape being possibly different for each random variables) for which we provide asymptotic properties. Next, we consider a goodness-of-fit test for such sequence of random variables. This is an extension of a test derived by Villaseñor and González-Estrada (Villaseñor and González-Estrada 2015). This result is used to propose a goodness-of-fit test for homogeneous gamma processes under a general sampling scheme. We have applied this test to a real data set and then we have studied numerically the performance of our test in terms of coverage probabilities and power.