Renewal Function and Interval Availability: A Numerical Monte-Carlo Study
Renewal Function and Interval Availability: A Numerical Monte-Carlo Study
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DOI：
10.1081/sta-120028689
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发表时间：
2004-01
期刊：
影响因子：
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通讯作者：
I. Gertsbakh;Y. Shpungin
中科院分区：
文献类型：
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作者：
I. Gertsbakh;Y. Shpungin
摘要 我们考虑更新函数的蒙特卡罗估计，该更新函数等于区间[0, T]上系统更新的平均次数，适用于两种情况：（1）系统在故障后立即被相同的系统替换； (2)每个系统运行期之后都有一个修复期。我们的方法基于模拟 P(τ1 + ċ + τ n ≤ T) 类型卷积的无偏估计。我们证明了 Gertsbakh 和 Shpungin [Gertsbakh, I., Shpungin, I. (1999) 中提出的所谓产品类型估计器。卷积的乘积类型估计器。见：Janssen, J.、Limnios, N.，编辑。半马尔可夫模型和应用。 Kluwer 学术出版社，第 201-206 页]比粗略的蒙特卡罗和布朗估计更准确，Brown 等人。 [布朗，M.，所罗门，H.，史蒂文斯，M.A.（1981）。更新函数的蒙特卡罗模拟。 J.应用程序。很可能。 426–434]。我们展示了如何使用建议的卷积估计器来计算区间可用性。
Abstract We consider Monte-Carlo estimation of renewal functions which are equal to the mean number of system renewals on interval [0, T], for two cases: (1) the system is immediately replaced after its failure by an identical one; (2) each system operation period is followed by a repair period. Our method is based on simulating unbiased estimates of convolutions of type P(τ1 + ċ + τ n ≤ T). We demonstrate that so-called product-type estimators suggested in Gertsbakh and Shpungin [Gertsbakh, I., Shpungin, I. (1999). Product-type estimator of convolutions. In: Janssen, J., Limnios, N., eds. Semi- Markov Models and Applications. Kluwer Academic Publishers, pp. 201–206] are more accurate than the crude Monte Carlo and Brown's estimators, Brown et al. [Brown, M., Solomon, H., Stevens, M. A. (1981). Monte Carlo simulation of the renewal Function. J. Appl. Probab. 426–434]. We show how to compute the interval availability using the suggested convolution estimators.