System Reliability Calculation | Physical Significance of Calculating System Reliability Probability

Summary

This video explains the fundamental concepts of maintenance and reliability, focusing on how reliability is calculated using a formula based on failure rate and time. It covers key concepts like failure rate, mean time between failures (MTBF), and inherent reliability. The script demonstrates how reliability varies over time, with practical examples of a pump's failure rate and its reliability over different operating periods. The video emphasizes the importance of using historical data with similar operating conditions and highlights the limits of machine reliability, which can only be improved through redesign, not maintenance.

Takeaways

• 😀 Reliability is a measure of how trustworthy a machine is to perform without failure over a certain period of time under specific conditions.
• 📊 Reliability is calculated using Euler's number (2.7182) raised to the power of the product of the failure rate (Lambda) and the time interval for which reliability is being calculated.
• ⏱️ The failure rate (Lambda) represents the rate at which a machine fails, typically measured in failures per hour or per another time unit.
• 🔄 MTBF (Mean Time Between Failures) is the inverse of the failure rate, showing the average time between failures of a machine.
• 🔧 A machine’s failure rate can be determined from historical maintenance data, for example, a pump with 10 failures in 10,000 hours would have a failure rate of 0.001.
• 💡 The reliability of a machine decreases as the operational time increases, especially for machines with high failure rates.
• 📉 For a machine with a failure rate like the pump example, the likelihood of not failing over 12,000 hours is only 0.615%, indicating almost certain failure over this period.
• ⏳ On the other hand, the reliability of the same pump increases to over 60% for an operating time of just 500 hours.
• ⚙️ When calculating reliability, it is crucial to use the failure rate of machines operating under the same or similar conditions to ensure accuracy.
• 🔒 Inherent or intrinsic reliability represents the best-case scenario of a machine’s reliability under ideal conditions, and no maintenance can exceed this limit. Improving it requires redesigning the system.

Q & A

What is the formula for calculating reliability?

The formula for calculating reliability is R(t) = e^(-λ * t), where 'e' is Euler's number (2.7182), 'λ' is the failure rate, and 't' is the time interval over which reliability is being calculated.

What does the failure rate (λ) represent?

The failure rate (λ) represents the rate at which a machine fails, typically measured as failures per unit of time (e.g., failures per hour or failures per month).

How is the mean time between failures (MTBF) related to the failure rate?

MTBF is the inverse of the failure rate. It is calculated as 1/λ, and it represents the average time between two consecutive failures of a machine.

If a pump has 10 failures in 10,000 hours of operation, what is its failure rate?

The failure rate of the pump would be 0.001, as calculated by dividing 10 failures by 10,000 hours (10/10,000).

How is reliability calculated for a machine with a failure rate of 0.001 over 12,000 hours?

The reliability for 12,000 hours is calculated using the formula R(t) = e^(-λ * t). With λ = 0.001 and t = 12,000 hours, the reliability turns out to be 0.615%, meaning there is a 0.615% chance that the pump will not fail during the next 12,000 hours.

What does a reliability of 0.615% indicate for the pump?

A reliability of 0.615% indicates that there is a very low probability (0.615%) that the pump will not fail during the next 12,000 hours of operation. Given the pump's high failure rate, it is likely to fail multiple times during this period.

Why does the reliability of a machine decrease over time?

Reliability decreases over time because the likelihood of failure increases as the machine continues to operate, especially if the machine has a high failure rate.

What is the importance of using historical data when calculating reliability?

It is crucial to use historical data from machines with similar operating conditions when calculating reliability. This ensures that the failure rate is accurately represented and reflects the actual performance under specific conditions.

What is meant by intrinsic reliability, and how is it different from regular reliability?

Intrinsic reliability refers to the inherent reliability of a machine under ideal conditions, based on its design. It represents the maximum reliability a machine can achieve and cannot be improved through maintenance; only redesigning the machine can improve its intrinsic reliability.

How do companies use reliability calculations in product warranty decisions?

Companies use reliability calculations to determine the optimal warranty period for their products. By understanding the likelihood of failure over time, they can set a warranty duration that minimizes the risk of excessive warranty claims while ensuring customer satisfaction.