A system has two failure modes. One failure mode, due to external conditions, has a constant failure rate of 0.07 failures per year. The second, attributed to wear out, has a Weibull distribution with a characteristic life of 10 yr and a shape parameter of 1.8. Determine the system reliability for a design life of 1 yr. (four decimals)

0.9177

Step-by-step explanation:

let us first represent the two failure modes with respect to time as follows

R₁(t) for external conditions

R₂(t) for wear out condition ( Wiebull )

Now,

where t = time in years = 1,

n = failure rate constant = 0.07

Also,

where t = time in years = 1

where Q = characteristic life in years = 10

and B = the shape parameter = 1.8

Substituting values into equation 1

Substituting values into equation 2

let the system reliability for a design life of one year be Rs(t)

hence,

Rs(t) = R1(t) * R2(t)

t = 1

Rs(1) = 0.9177 (approx to four decimal places)

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is