Applied Engineering Statistics Homework

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1. According to a financial monthly, disability causes 48% of all mortgage foreclosures. Given that 20 foreclosures were recently audited by a large lending institution, find a) the probability that five or fewer of the foreclosures are due to disability; b) the probability that at least three are due to disability. Use Binomial Probability function.

2. A sub-system assembly consists of a combination of three components each with a dimension of 3.44, 5.21 and 4.36 inches respectively. These dimensions are measured independently, yielding a random measurement with a standard deviation of 0.05 in. The total length of the assembly is the sum of the three dimensions. What is the estimated length and its uncertainty.

3. The production of a certain type of polymer fiber follows a normal distribution with a mean diameter of 20m and a standard deviation of 30m. Compute the probability that a measured value is greater than 80m. Compute the probability of a measured value between 50m and 80m.

4. Six items were tested to failure. Test cycles are 1025, 1550, 2232, 3786, 5608 and 7918 respectively.

a. Determine the failure rate

b. Determine the mean life, assuming that the failure rate is constant

c. Determine the reliability at t = 4250 cycles

d. If the mean life of the item is 3500 cycles with a standard deviation of 250 cycles, what is the reliability at 5500 cycles?

5. An antifriction bearing is to be mounted on a 6 in. diameter shaft. The inside diameter (hole) of the bearing is found to be 6.005 in. The manufacturing tolerance of the shaft is given to be 0.003 in. A minimum clearance fit of 0.001 in. is specified. Find the tolerance required in the bearing hole so that 0.1% of parts do not match (i.e., meet minimum requirements). Assume manufacturing variations are normally distributed.

6. A block diagram representation of a system is shown below. Determine the overall system reliability.

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