## Basics of Probability for Data Science explained with examples.

The constant failure rate of the exponential distribution would require the assumption that the automobile would be just as likely to experience a breakdown during the first mile as it would during the one-hundred-thousandth mile. Clearly, this is not a valid assumption. However, some inexperienced practitioners of reliability engineering and life data analysis will overlook this fact, lured.

In order to do this, you calculate the probability of success and multiply it by the outcome associated with success. You then calculate the probability of failure and multiply it by the outcome associated with failure. By adding your two answers, you will have the expected average value of the payoff.

Fault tree analysis (FTA) is a top-down, deductive failure analysis in which an undesired state of a system is analyzed using Boolean logic to combine a series of lower-level events. This analysis method is mainly used in safety engineering and reliability engineering to understand how systems can fail, to identify the best ways to reduce risk and to determine (or get a feeling for) event.

The hard part is with only MTBF you can only estimate the expected number of failures or the probability of failure over some duration. You need to be sure the MTBF value is valid over the time period of interest. IF the value is based on the first year of operation, it may not be accurate for the second year, and very inaccurate for the 10th year.

Probability of Failure on Demand (PFD) Reliability, as previously defined, is the probability a component or system will perform as designed. Like all probability values, reliability is expressed a number ranging between 0 and 1, inclusive.

How to calculate total probability of failure from conditional probability? Let's say A has a 20% chance of occurring next year. If it does occur, it won't occur the year after.

So, we calculate the probability of it, being in a range. We calculate the probability of rainfall being in the range of 2 cm to 2.01 cm. It will be the sum of probabilities for all values between 2 and 2.01. The area under the probability density function with limits 2 and 2.01 will give us that.