Problem 8-32 You are conducting a reliability analysis for a new product. Based on prior testing with a similar product, you bel
ieve the Weibull failure-time distribution, with parameter lambda=.200 per year, applies. But you have no basis for establishing beta. Compute at a time span of 5 years (1) the failure rate and (2) the survival probability assuming that
(a) beta=0.1
failure rate=
survival probability=
(b) beta=1
failure rate=
survival probability=
(c) beta=1.9
failure rate=
survival probability=
(d) beta=2.2
failure rate=
survival probability=
(a) beta=0.1
failure rate=
survival probability=
(b) beta=1
failure rate=
survival probability=
(c) beta=1.9
failure rate=
survival probability=
(d) beta=2.2
failure rate=
survival probability=
1 answer:
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Answer:
1. Equilibrium solution: y= -3
2. Equilibrium solution y= ±1.414
Step-by-step explanation:
Thinking process:
The equilibrium solution can only be derived when
1. Let's look at the first equation:
equating to the expression
gives
y + 3 = 0
y = -3
Therefore, the equilibrium solution occurs at y = -3
2. Let's look at the second solution:
dividing each side by (t²-1) gives
1/(t²-1) = (y²-2)/ (y²-4)
factorizing the right hand side gives:
at equilibrium: , then
y² - 2 = 0
solving for y gives y = ±√2
= ±1.414