B10 Life Exponential Distribution

This video from the Institute of Quality and Reliability explains how to calculate the B10 life (the time by which 10% of items are expected to fail) for an exponential distribution.

We suggest to view our video on Exponential Distribution for better learning experience. Here is the link to the video:  Remember this Memoryless Exponential Distribution . Your feedback is welcome!

Here’s a summary of the key points:

• Exponential Distribution: Used when the failure rate (Lambda) is constant. The mean time to failure (MTTF or Theta) is the reciprocal of the failure rate (θ=1/λ).
• Reliability Function: The probability of an item functioning at time T is given by R(T)=e^−λT=e^−T/θ.
• BX Life: The time by which X percent of items are expected to fail. B10 life specifically refers to the time at which 10% of items will have failed, meaning the reliability at this time is 90% or 0.9.
• Calculating B10 Life:
  • Using the reliability function: ln(R(T))=−λT.
  • For B10 life, R(T)=0.9, so ln(0.9)=−λT=−T/θ.
  • Therefore, T=−ln(0.9)×θ (or MTTF).
• Example: For an electronic item with an MTTF of 20,000 hours, the B10 life is calculated as −ln(0.9)×20000≈2107 hours.
• Excel Calculation: The video demonstrates how to use Microsoft Excel to perform this calculation using the MTTF value. By inputting the percentage of failure (e.g., 10% for B10), Excel can calculate the corresponding BX life.
• Generalization: The method can be used to calculate BX life for any percentage X by adjusting the reliability value (e.g., for B1 life, reliability is 0.99).