ENG 622

Table 1 below shows failure data for 250 germanium chips, all of which failed during the test period. Calculate and plot the probability of failure (unreliability) and probability of success (reliability) as a function of time to failure.

Table 1 failure data for chips

Time to Failure (min) t

Cumulative Failures , n(t)

0 0

20 9

40 23

60 50

90 83

160 113

230 143

400 160

900 220

1200 235

2500 240

2500 250

Figure below shows a chemical system in which the temperature increases with the feed rate of flow-controlled stream A. Heat is removed by water circulation through a water cooled heat exchanger. Normal reactor temperature is 200F, but a catastrophic runaway will start if the temperature reached 300F. In view of this situation:

1. The reactor temperature is monitored (by TE/TT 714).

2. Rising temperature is alarmed at 225F (see Horn).

3. An interlock shuts off stream A at 250F, stopping the reaction (SV-1).

4. The operator can initiate the interlock by punching the panic switch (NC).

a) Construct the fault tree for this system.

b) Obtain the minimal cut sets.

Load and strength are normally distributed (units in thousand-pounds) as follows:

Load ~ Normal(35, 8);

Strength ~ Normal (85, 8)

Note: Normal (35,8) indicates a mean value of 35 and standard deviation of 8.

Calculate the safety factor and safety index of the structural design.

How would the standard deviation on load and strength change if safety index is limited to a value of 3?

Consider the following system where all components are active during the life of the systems.

Satisfactory operation occurs if all parts in any one path function.

Find the system reliability of this system.

Conventional way of radiation treatment was to target cancer cells while some of the healthy sells also get affected. The instrument to provide radiation treatment cost $2 million and it is 90% reliable. The new concept targets only the cancer cells and the equipment costs only $1.25 million with unknown reliability since the equipment has not been used. The design-engineers assign a reliability value of 0.98 assuming all of the assumptions are correct. If all of the assumptions are not correct (equal likely probability), reliability is estimated only about 0.8. Since liability cost is $20 million, the engineer faces a decision for the following two alternates:

• Capture the opportunity of accomplishing cost saving and high reliability

• Assure a reasonable reliability by the conventional design

Set up a decision tree and determine the expected total cost of both designs. Which design would you prefer?

A plate fin heat exchanger for truck is designed to cool high temperature and high pressure oil using high pressure water. This heat exchanger on a recent trip from Miami to Cleveland developed an oil leak and it contaminated water. The plate fin heat exchanger uses gaskets to separate oil and water paths. Since this unit is used in trucks, vibration should also be considered. Run a FMEA analysis and suggest the possible solution to avoid future failure.

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