Consider two components and three types of shocks. A type 1 shock ca.pdf
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Consider two components and three types of shocks. A type 1 shock ca.pdf
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Consider two components and three types of shocks. A type 1 shock causes component 1 to fail, a type 2 shock causes component 2 to fail, and a type 3 shock causes both components 1 and 2 to fail. The time until shocks 1, 2 and 3 occur are independent exponential random variables with rates 1, 2, and 3, respectively. Let Xi denote the time at which component i fails, for i = 1, 2. (a) Find P{X1 > s,X2 > t}. (b) Find the CDF of X1, Fx1 (s). Solution One idea is suggested in Yan, Carpenter and Diawara (2006) and in Diawara and Carpenter (2008) in their papers from AJMMS. Please check it out, and let me know if you have questions..
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Consider two components and three types of shocks. A type 1 shock ca.pdf
- Consider two components and three types of shocks. A type 1 shock causes component 1 to fail, a type 2 shock causes component 2 to fail, and a type 3 shock causes both components 1 and 2 to fail. The time until shocks 1, 2 and 3 occur are independent exponential random variables with rates 1, 2, and 3, respectively. Let Xi denote the time at which component i fails, for i = 1, 2. (a) Find P{X1 > s,X2 > t}. (b) Find the CDF of X1, Fx1 (s). Solution One idea is suggested in Yan, Carpenter and Diawara (2006) and in Diawara and Carpenter (2008) in their papers from AJMMS. Please check it out, and let me know if you have questions.