3 Lifetime Distributions
Chapter Overview and Learning Objectives
To understand the basic concepts of the probability distributions.
- To learn the discrete and continuous probability distributions.
- To apply the probability distributions to the reliability concepts.
- To understand the fundamental concepts of the failure rate.
- To learn parameters and failure characteristics of various distributions, including exponential, Weibull, normal, and lognormal distributions.
- To apply Excel, Minitab, and Python functions to efficiently calculate the values related to the probability distributions.
3.1 Probability Distributions
The probability distribution gives the probabilities of occurrences of different possible outcomes. Figure 3.1 shows the probability distribution of the number of cars sold per day. The highest probability is to sell three cars per day, and the lowest probability is to sell five cars per day.
Figure 3.1 Probability distribution of the number of cars sold per day.
3.1.1 Random Variables
A random variable is an outcome from a random experiment. These values could vary depending on the results of a random experiment. The random variable can be categorized into discrete and continuous variables.
Discrete random variable
A discrete random variable accounts for countable values or distinct values. A finite number of distinct values is expected. Examples include:
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