3. A machine has n components, the lifetimes of which are independent. However the wholemachine will fail if any component fails. The hazard functions for the components arenh1(t),..., hn(t). Show that the hazard function for the machine ish:(t).4. Suppose that the lifetime distributions of the components in Exercise 3 are Weibull distributionswith scale parameters p1,..., Pn and a common index (i.e. "shape parameter") y so that thehazard function for component i is yp:(pit)"-1. Find the lifetime distribution for the machine.

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Answered: 3. A machine has n components, the…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 4E

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Heights (om) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 188 cm and weights of 41 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x 167.74 cm, y 81.46 ko, r0.239, Pvalue 0.017, and y - 106 + 1,15x. Find the best predicted value of y (weight) given an adult male who is 153 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 153 cm tall is kg. (Round to two decimal places as needed.)
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3. A machine has n components, the lifetimes of which are independent. However the whole machine will fail if any component fails. The hazard functions for the components are h1(t),..., hn(t). Show that the hazard function for the machine is h(t).