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
ASSIGNMENT/COURSEWORK PROFORMA

Module code:

MN5554

Assessment title:

Quality Management and Reliability

Module tutors:

Main objectives of the assessment:

To enable students to demonstrate their in-depth knowledge of the principles of advanced techniques of reliability engineering and abilities to apply them to solve practical problems.

Brief Description of the assessment:

Prepare an individual report to complete the four questions. They are related to all the key topics of reliability.

Learning outcomes for the assessment (refer to the appropriate module learning outcomes)

Students will be able to demonstrate the following:

To gain comprehensive understanding of advanced techniques of reliability engineering;
To organise the collection of plant data and undertake an analysis of it which will facilitate the diagnosis of reliability problems and their effective elimination;
To apply and critically evaluate the most appropriate of the currently available techniques for reliability assessment.
Assessment criteria:

Q1. Initial data analysis (20%)

Q2. Basic reliability and availability calculation (20%)

Q3. Reliability calculation based on Reliability Block Diagram (20%)

Q4. Weibull analysis of lifetime data (40%)

Assessment method by which a student can demonstrate the learning outcomes:

Writing of a technical report comprising the solutions to the given questions related to reliability in an industrial company.

Weighting:

50% of module marks

Format of the assessment/coursework: (Guidelines on the expected format and length of submission): * Note: full reports may not exceed 10 pages (including appendices)

Format is a formal written report including diagrams, calculations (with data; formula; workings and assumptions) and discussion/ comments. Report to be written using Word in a 12 point font. Typical length of report is 1000 words.

Assessment date/submission deadline :

Please submit by Monday 24^{th} Jan 2022 via WISEflow

Indicative reading list:

Slack, N., Chambers, S. and Johnston, R. (2004). Operations Management, 4th Edition, Pearson Education.
O`Connor, P.D.T. and Kleyner, A. (2012). Practical Reliability Engineering, Wiley.
Bentley, J.P. (1998). An Introduction to Reliability and Quality Engineering (2nd Edition). Addison Wesley.
Ross, S.M. (2009). Introduction to Probability and Statistics for Engineers and Scientists. Elsevier Academic Press.
Other information

Tutor e-mails: Tao.Zhang@brunel.ac.uk

Use your student ids for anonymity (i.e. no student names on the assignment itself).

ASSIGNMENT

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

Unit No.

Time to failure (hours)

1

3280

2

2875

3*

2800

4

2480

5*

2960

6

4050

7

2750

8

3600

9

3100

10*

3550

* 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 b and the characteristic time to failure h for the distribution. Infer from the value of b 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.

Formulae that may be used for Question 4 are given below:

New _ increment = N + 1 - (Order _ number _ of _ previous _ failed _ item )

N + 1 - (Number _ of _ previous _ items )

Order _ number = New _ increment + previous _ order _ number

Median _ rank = Order _ number - 0.3

N + 0.4

where N is the total number of items in the sample.

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