Reliability is heavily dependent on Probability and Statistics for measuring and describing its characteristics.

To further explore this topic, there are certain terms you need to understand such as:

• Failure Distribution: This is a representation of the occurrence failures over time usually called the probability density function, PDF, or f(t)
• Cumulative Failure Distribution: The cumulative version of the PDF called the CDF, or F(t)
• Reliability: If we can call the CDF the unreliability of a product, then 1-F(t) must be the reliability.

An important part of reliability is identifying, understanding, and optimizing the type of statistical distribution that represents the product.

Binomial Distribution, for example, is used to represent situations where there are two possible outcomes, success or failure and the probability of one of the types of outcomes is known, whereas, Normal Distribution usually represents wearout situations.

Another type of distribution, Weibull Distribution, can be used to represent a number of other distributions such as the Normal, the Exponential, and others (usually 2 parameter but can be 3 parameter).

The Weibull can be used to represent the three regions of the classic reliability “Bathtub” curve: (Region 1) the decreasing failure rate associated with infant mortality, (Region 2) the constant failure rate of useful life, and (Region 3) the wearout period of increasing failure rate.

The Weibull parameters β, called the Weibull Shape Parameters, for the three Bathtub regions are respectively <1.0, =1.0, and >1.0.

The use of reliability is especially important to the Department of Defense because a high percentage of defense systems fail to meet their reliability requirements. This is a serious problem for the DOD, as well as the nation.

Those systems are not only less likely to successfully carry out their intended missions, but they also could endanger the lives of the operators. Furthermore, reliability failures discovered after deployment can result in costly and strategic delays and the need for expensive redesign, which often limits the tactical situations in which the system can be used.

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