How to Calculate Reliability Given 3 Different Distributions

How to Calculate Reliability Given 3 Different Distributions

On occasion, we want to estimate the reliability of an item at a specific time.

Maybe we are considering extending the warranty period, for example, and want to know the probability of no failures over one year instead of over the current 3 months.

Or, let’s say you talked to a bearing vendor and have the Weibull parameters and wish to know the reliability value over 2 years.

Whatever specific situation, you have the life distributions parameters. You just need to calculate reliability at a specific time. We can do that and let’s try it with three distributions using their respective reliability functions: exponential, Weibull, and lognormal.

The Exponential Reliability Function

Let’s say the motor driver board has a data sheet value for θ (commonly called MTBF) of 50,000 hours. Let’s say we are interested in the reliability (probability of successful operation) over a year or 8,760 hours.

The reliability function for the exponential distribution is:

$$ \displaystyle\large R(t)={{e}^{-{}^{t}\!\!\diagup\!\!{}_{\theta }\;}}={{e}^{-\lambda t}}$$