Tarea Ingenieria confiabilidad, problemas 2.24, 2.28, 3.5, 3.14, 3.20, 3.36, 3.44 Libro Reliability Engineering and Risk Analysis, A Practical Guide

Gestión de Activos Físicos

Tarea #01

Solve the following exercises from “Reliability Engineering and Risk Analysis, A Practical Guide”, Modarres M, Kaminskiy K., Krivtsov V., Second Edition, CRC Press, 2009:

2.24) A company is studying the feasibility of buying an elevator for a building under construction. One proposal is a 10-passenger elevator that, on average, would arrive in the lobby once per minute. The company rejects this proposal because it expects an average of five passengers per minute to use the elevator.

1. Support the proposal by calculating the probability that in any given minute, the elevator does not show up, and 10 or more passengers arrive.
2. Determine the probability that the elevator arrives only once in a 5-minute period.

2.28) Use Eqn 2.73 and calculate mean and variance of a Weibull distribution.

3.5) Assume that t, the random variable that denotes life in hours of a specified component, has a cumulative density function (cdf) of

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Determine the following:

1. pdf f(t)
2. Reliability function R(t)
3. MTTF (Using a practical upper limit of 1 million hrs to avoid trivial solution) 3.7) Consider the Rayleigh distribution:

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1. Find the hazard rate h(t) corresponding to this distribution.
2. Find the Reliability function R(t)
3. Find the MTTF
4. For which part of the bathtub curve is this distribution adequate?

3.14) A manufacturer uses exponential distribution to model number "cycle-to-failure" of its products. In this case, r.v. T in the exponential pdf represents the number of cycles to failure l = 0.003 f/cycle.

1. What is the mean number of cycles to failure for this product?
2. If a component survives for 300 cycles, what is the probability that it will fail sometime after 500 cycles? Accordingly, if 1,000 components have survived 300 cycles, how many would one expect to fail after 500 cycles?

3.20) The average life of a certain type of small motor is 10 years, with a standard deviation of 2 years. The manufacturer replaces free of charge all motors that fail while under warranty. If the manufacturer is willing to replace only 3% of the motors that fail, what warranty period should be offered? Assume the time to failure of the motors follows a normal distribution.

3.36) The cycle-to-failure T for a certain kind of component has the instantaneous failure rate l = 2.5x10-5t2 per cycles. Find the MCTF (mean-cycle-to-failure), and the reliability of this component at 100 cycles.

3.44) The time to failure of a solid state power unit has a hazard function in the form of

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1. Compute reliability at 50h.
2. Determine design life if a reliability of 0.99 is desired.
3. Compute MTTF
4. If the unit has operated for 50 hrs, what is the probability that the unit will operate for another 50 hrs.
5. What is the mean residual time to failure at t = 50 hrs? Compare it with the results shown at part c.

Gestión de activos físicos.  Solucion

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