A semi-Markov process with an inverse Gaussian distribution as sojourn time |
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Authors: | Mario Lefebvre Simona Perotto |
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Affiliation: | 1. Department of Mathematics and Industrial Engineering, École Polytechnique, C.P. 6079, succ. Centre-ville, Montréal, Québec, Canada H3C 3A7;2. MOX – Modeling and Scientific Computing, Department of Mathematics “F. Brioschi”, Politecnico of Milano, via Bonardi 9, I-20133 Milano, Italy |
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Abstract: | Let Xn denote the state of a device after n repairs. We assume that the time between two repairs is the time τ taken by a Wiener process {W(t), t ? 0}, starting from w0 and with drift μ < 0, to reach c ∈ [0, w0). After the nth repair, the process takes on either the value Xn?1 + 1 or Xn?1 + 2. The probability that Xn = Xn?1 + j, for j = 1, 2, depends on whether τ ? t0 (a fixed constant) or τ > t0. The device is considered to be worn out when Xn ? k, where k ∈ {1, 2, …}. This model is based on the ones proposed by Rishel (1991) [1] and Tseng and Peng (2007) [2]. We obtain an explicit expression for the mean lifetime of the device. Numerical methods are used to illustrate the analytical findings. |
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