A company which produces railway sleepers for rail infrastructure projects, is seeking to improve its product quality and reliability. The company has provided the following qualitative and quantitative data related to its current operation. Prepare an individual report to carry out
the evaluation and answer the following four questions.

Q1. The company has kept at one of its plants 24 months records of the total number of failures occurring each month, as shown in Table Q1. Produce the 3-month moving average and the 6-month moving average plots, together with the CUSUM plot (if the target value is 15).
Table Q1
Month Failures
1 18
2 20
3 16
4 10
5 12
6 18
7 15
8 11
9 13
10 15
11 15
12 22
13 12
14 17
15 15
16 14
17 9
18 13
19 13
20 17
21 16
22 18
23 14
24 21

Q2. A machine in the company has an MTBF of 380 hours and an MTTR of 20 hours.
1) Calculate its availability for the original system.
2) A second active parallel system will be acquired if the availability of the original system is lower than 99%. Do you think one additional will be sufficient? If so, what is the improved availability for the new system? Justify your answer.
3) If the additional machine costs £180,000 and the downtime costs £5000 per hour, what is the payback period of the additional machine?

Q3. Using the system reduction procedure, calculate the reliability of the independent system as shown in the form of a Reliability Block Diagrams below (Figure Q3). Illustrate how the Reliability Block Diagrams are simplified. The reliabilities of all units are shown in the diagram. Figure Q3

Q4. In a reliability test in the company, the time-to-failure values of ten mechanical items of the same design running under identical condition were recorded and are as given in the following table (Q4): Table Q4

Units 3, 5 and 10 had not failed at the end of the test period. Using the median rank method for estimating the failure probability and assuming that the
guaranteed life before failure is 1500 hours,
a) Calculate and tabulate the median ranks for the data supplied.
b) Plot the cumulative percent failure versus time to failure on the Weibull graph paper supplied.
c) Estimate the shape factor  and the characteristic time to failure  for the distribution. Infer from the value of  whether the failure is an early failure, a random failure or a wear-out failure.
d) Estimate the reliability of an item at 2300 hours, its failure probability between 2300 and 2400 hours, and the probability that the item that is functional at 2800 hours will fail before reaching 2900 hours.