Read the following: Reliability Engineering/ERAU Hunt Library – O’Reilly Chapter

Read the following:
Reliability Engineering/ERAU Hunt Library – O’Reilly
Chapter 2 (Sections 2.2), Hazard Rate
An idealized (though rarely occurring) shape of the hazard rate of a product is the bathtub curve. The bathtub curve is a model for system reliability, including early life burn-in and eventual wear-out at the system’s end of life.
The ‘bathtub’ refers to the shape of a line that curves up at both ends, similar in shape to a bathtub. The bathtub curve has 3 regions:
The first region has a decreasing failure rate due to early failures.
The middle region is a constant failure rate due to random failures.
The last region is an increasing failure rate due to wear-out failures.
Considering the above diagrams and considering the piecewise linear bathtub hazard function defined over the three regions of interest given below. The constants in the expressions are determined to satisfy the normal requirements for h(t) to be a hazard function.
Address the following questions in this discussion:
Briefly describe each region of the bathtub curve.
Develop the equations for the reliability function and the probability density function for the time to failure random variable based on the above hazard function.
How does the bathtub curve concept, which encompasses phases of early failures, random failures, and wear-out failures, relate to and impact the reliability of a system? Additionally, demonstrate your understanding by applying statistical techniques to model system reliability based on the given hazard function.
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