Reference no: EM132596120

Introduction to reliability

Question 1:

Table A1 shows reliability data for 100 gas discharge lamps.

(a) Plot a histogram of failure frequency for this data. It should be similar in style to Figure 1.6 in Study Guide 1 (page 10).

(b) Plot the cumulative percent failure against age of lamp. The graph should be similar to Figure 1.7 in Study Guide 1 (page 12).

(c) Use Weibull probability paper to plot this data. The graph should be similar to Figure 2.16 in Study Guide 2 (page 39).

(d) What type of failure (Burn-In, Random, Wearout) is exhibited by the Gas Discharge Lamps?

(e) By what age would you expect 10% of lamps of this type to fail?

Table A1: Gas discharge lamps failure data

Hours	Number of Failures
0-400	5
400-800	9
800-1200	6
1200-1600	5
1600-2000	7
2000-2400	6
2400-2800	8
2800-3200	2
3200-3600	6
3600-4000	6
4000-4400	4
4400-4800	2
4800-5200	0
5200-5600	0
5600-6000	12
6000-6400	0
6400-6800	0
6800-7200	0
7200-7600	0
7600-8000	8
Unfailed at 8000	14
Total	100

Question 2
When the number of failures is small the cumulative probability of failure associated with the ith failure from a population of N items is given by the Median Rank.

Median Rank is approximated by the formula:

Failure probability = (i - 0.3) / (N + 0.4)

Six bearings have been run for a period of time and the following ages at failure observed. Table A2: Bearings failure data

Bearing	Age of Failure (Weeks)
1	24
2	8
3	14
4	12
5	16
6	Not failed at 24 weeks

Use Weibull probability paper to determine the distribution of time to failure and estimate the mean life of the bearings.

Reliability analysis

Question 3: Confidence limits for the MTBF

Data relating to manpack radios is shown in the following table, use mid-points of the utilisation ranges:

Utilisation Hours	Number of Sets	Number of Failures
0-50	100	8
50-100	200	8
100-150	200	10
150-200	100	4

Use chi-squared tables to estimate the MTBF and give a 90% confidence interval. Show your full working.

Question 4: Maintainability
An aircraft maintenance check takes the following times in minutes to complete on six successive occasions:
49, 59, 43, 65, 55 and 58

Find a suitable distribution to fit these data and estimate the maintainability, given a maintenance constraint of 60 minutes. (Note: The maintainability is the probability that the maintenance is completed within the maintenance time constraint.)

Question 5:
State the conditions which must apply if the preventive replacement of a component or assembly is to be economically worthwhile.
Preventive replacement

Question 6:
Suppose that, on the average, 3 "strong" earthquakes occur in a certain region every 7 years. For this region,
a) Determine the probability of getting 3 strong earthquakes in 7 years.
b) What is the probability of having at least 2 strong earthquakes in 5 years?

Question 7:

Three nominally identical temperature sensing elements are connected to nominally the same point on a process plant. A shutdown signal is designed to be given if any one or more of these temperature sensors record a temperature above a certain prescribed level. The times to failure of each element are exponentially distributed with a mean value of 5,000 hours. What is the mean time to complete failure of the alarm system?
Financial analysis of capital equipment replacement

Question 8:
Canmade Limited wants to determine the capital replacement age for its turret sideloaders to minimise total discounted cost. Historical data analysis has produced the following information (all costs in present day dollars):

Year	Average Operating and Maintenance Cost ($/year)		Resale Value at End of Year ($)
1	16	000	100	000
2	28	000	60	000
3	46	000	50	000
4	70	000	20	000

The cost of a new turret sideloader is $150 000, and the interest rate for discounting purposes is 12%. Carry out calculations using a hand calculator to solve this problem. Show your detailed working.