Reliability Engineering 1st. Edition by Kailash C. Kapur, Michael Pecht | 9781118140673 | 1118140672 | Holooly

Aircraft Design

Reliability Engineering

63 SOLVED PROBLEMS

Question: 2.9

The failure rate per year of a component is given by: h(t) = 0.003t², t≥0. (a) Find an expression for the reliability function and the probability density function for the time to failure of the component. (b) Find the B20 (the 20th percentile) for the life of the component (c) Find the expected ...

Verified Answer:

(a)

R(t)=\exp \left(-\int_0^t h(\tau) d \ta...

Question: 17.9

Compute the reliability of an active redundant configuration system with two out of three units (all with identical reliability R) required for success. ...

Verified Answer:

In this case, n = 3 and k = 2. The reliability for...

Question: 2.8

For the triangular life distribution given in Example 2.3, calculate the E[T], V[T], and standard deviation ...

Verified Answer:

We have

f(t)= \begin{cases}\frac{t}{5,000},...

Question: 2.7

The failure rate or hazard rate of a component is: h(t) = 0.02t^1.7, t≥0. The failure rate is in failures per year. (a) What is the reliability function of this component and what is the value of the reliability for a period of 2 years? (b) What is the median life or B50 life of this component? ...

Verified Answer:

(a)

R(t)=\exp \left[-\int_0^t h(\tau) d \ta...

Question: 2.6

If T is a random variable representing the hours to failure for a device with the following pdf: f(t) = texp (-t²/2), t>=0. (a) Find the reliability function (b) Find the hazard function. (c) If 50 devices are placed in operation and 27 are still in operation 1 hour later, find approximately ...

Verified Answer:

(a) To develop the reliability function, R(t), we ...

Question: 2.5

The reliability function for a system is assumed to be an exponential distribution (see Chapter 3) and is given by R(t) = e-λ0t, where λ0 is a constant (i.e., a constant hazard rate). Calculate the reliability of the system for mission time, t, given that the system has already been used for 10 ...

Verified Answer:

Using Equation 2.39

R(t, 10)=\frac{R(t+10)}...

Question: 2.4

The failure or hazard rate of a component is given by (life is in hours): Thus, the hazard rate is piecewise constant. Find an expression for the reliability function of the component ...

Verified Answer:

Using Equation 2.18 or Equation 2.33, we have [lat...

Question: 2.3

A product has a maximum life of 100 hours, and its pdf is given by a triangular distribution, as shown in the figure below. Develop the pdf, cdf, and the reliability function for this product. ...

Verified Answer:

Its pdf, cdf, and reliability function, respective...

Question: 2.2

From the histogram in Figure 2.4: (a) Calculate the unreliability of the product at a time of 30 hours. (b) Also calculate the reliability ...

Verified Answer:

(a) For the discrete data represented in this hist...

Question: 2.1

A semiconductor fabrication plant has an average output of 10 million devices per week. It has been found that over the past year 100,000 devices were rejected in the final test. (a) What is the unreliability of the semiconductor devices according to the conducted test? ...

Verified Answer:

The total number of devices produced in a year is:...

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