Hello everyone! This is my inaugural post on this platform. Through a reliability training, I have come across the concept of equivalent Mean Time Between Critical Failures (MTBCF) for a dual-parallel setup. The formula for calculating MTBCF is MTBCF=(m+3FR)/2(FR*FR), where m=1/MTTR and FR represents the failure rate of each of the two identical components. I have referenced the "IEEE Transactions on Reliability" by A. Kullstam for general formulas, but I am still seeking clarification on how the MTBCF for a dual-parallel configuration is derived. Any insights would be greatly appreciated. Thank you!
Is it really that challenging?
This outcome was achieved through Markov chains under the assumption of random TTF and TTR following an exponential distribution. Personally, I find Monte Carlo simulation to be more preferable. With this approach, input variables can take on any value and adhere to any distribution that is deemed most suitable. As a result, the outputs generated are more accurate and reliable.
Hello Rui, I appreciate your response. I am in search of a thorough and definitive proof, would you be able to assist me with this? Thank you.
CoB inquired: "Hello Rui, thank you for your response. I am still in need of a rigorous proof. Could you assist me, please? Best regards." Hello CoB, I recommend checking out a reliable source for information by Charles E. Ebeling on Amazon. The reference I have from 1997 can be found here: http://www.amazon.co.uk/Introd...+engineering+ebeling. Take a look at pages 207 and 208. Keep in mind that Ebeling also has a more recent edition from 2009, which may be more current. Consider purchasing the book for a deeper dive into advanced mathematics topics like Markov chains, differential equations, Laplace transforms, and Cramer's rule. Regards.
Hello and welcome to the forum! The MTBCF in a dual-parallel setup is essentially derived from the concepts and mathematical formulations of reliability engineering. With two identical components operating in parallel, you have a redundancy. The failure rate of the system is decreased because if one component fails, the other continues operating, essentially picking up the slack which results in a lower effective failure rate. Keep in mind, though, that MTBCF doesn't just involve gross failure of components, but any critical failure that stops the workflow. It could be hardware, software, a network glitch, etc. It's a potent tool for overall system reliability planning and a key metric to evaluate system robustness. If you’re still having trouble grasping it, I recommend looking into system reliability engineering resources or seeking guidance from a system reliability engineer. They should be able to break it down in layman's terms for you.
Welcome to the forum! Great to see you diving into such a technical topic. The derivation of MTBCF for a dual-parallel setup typically considers how the redundancy in the configuration affects overall system reliability. In essence, while each component has its own failure rate, the parallel setup allows one to continue functioning if the other fails, which is why you see the formula you mentioned. It’s modeling the chances of both components failing simultaneously, which decreases the overall failure rate compared to a single unit. If you haven't already, I'd suggest looking into failure distribution functions like the exponential distribution to get a clearer understanding, as they can be helpful in breaking down the probabilities involved. Hope this helps!
Hi there! Welcome to the forum! I can see why the MTBCF for a dual-parallel setup would be a bit confusing—it’s definitely a crucial concept in reliability engineering. The idea behind the formula you mentioned is rooted in the redundancy of having two identical components that can take over if one fails. Essentially, since only one component needs to function for the system to operate, the failure rate is effectively reduced, and that’s where the m and FR values come into play. If you think of it this way, you end up factoring in both components working in tandem, which contributes to that ‘3FR’ in your formula. If you’re looking for a deeper dive, perhaps some reliability textbooks or specific case studies could illuminate how the parallel model's unique characteristics come into play. Good luck, and feel free to share your findings!
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Answer: - MTBCF is a measure of reliability and is calculated using the formula MTBCF=(m+3FR)/2(FRFR), where m=1/MTTR and FR represents the failure rate of each of the two identical components in a dual-parallel configuration.
Answer: - The "IEEE Transactions on Reliability" by A. Kullstam is a recommended reference for general formulas related to MTBCF calculations.
Answer: - The MTBCF for a dual-parallel setup is derived using the formula MTBCF=(m+3FR)/2(FRFR), where m=1/MTTR and FR represents the failure rate of each component. This formula accounts for the redundancy and reliability of the parallel components.
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