Decreasing Constant Increasing {} Failure Failure Failure Rate Rate Rate Early Observed Failure ."Infant Rate Failure Rate "Mortality" Failure Wear Out Fallures Constant (Random] Failures Time 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. hi(t) = bi - cit for 0 < t_ t1 h(t) = h2(t) - bi - citi - c2(t ti) forti < t < t, ha (t) = b1 - citi c2 (t2 - t1 ) + c3 (t - t2) for tz < t < co Address the following questions in this discussion: 1. Briefly describe each region of the bathtub curve. 2. 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. 3. 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