ET ZC432 (EC-2 Regular) Page 1 of 2

Birla Institute of Technology & Science, Pilani

Distance Learning Programmes Division

Second Semester 2008-2009

Comprehensive Examination (EC-2 Regular)

Course No. : ET ZC432 Course Title : QUALITY CONTROL ASSURANCE & RELIABILITY Nature of Exam : Open Book Weightage : 60% Duration : 3 Hours Date of Exam : 04/04/2009 (FN)

Note: 1. Please follow all the Instructions to Candidates given on the cover page of the answer book. 2. All parts of a question should be answered consecutively. Each answer should start from a fresh page. 3. Mobile phones and computers of any kind should not be used inside the examination hall. 4. Use of any unfair means will result in severe disciplinary action.

Q.1 The mean time to assemble a product as found from a sample of size 40 is 10.4 min. the

standard deviation of the assembly times is known to be 1.2 minutes. (a) Find a two-sided 90% confidence interval for the mean assembly time, and

interpret it. (b) Find a two-sided 99% confidence interval for the mean assembly time, and

interpret it. (c) What assumptions are needed to answer parts a and b above? (d) The manager in charge of the assembly line believes that the mean assembly time

is less than 10.8min. Can he make this conclusion at a significant level α of 0.05? [8]

Q.2 A random sample of 50 observations of the mileage per gallon (mpg) of a particular brand

of gasoline is shown:

33.2 29.4 36.5 38.1 30.0

29.1 32.2 29.5 36.0 31.5

34.5 33.6 27.4 30.4 28.4

32.6 30.4 31.8 29.8 34.6

30.7 31.9 32.3 28.2 27.5

34.9 32.8 27.7 28.4 28.8

30.2 26.8 27.8 30.5 28.5

31.8 29.2 28.6 27.5 28.5

30.8 31.8 29.1 26.9 34.2

33.5 27.4 28.5 34.8 30.5

Construct a box plot. What insights do you get from this plot? [4]

Q.3 The tensile strength of non-ferrous pipes is of importance. Samples of size 5 are selected from the process output, and their tensile strength values are found. After 30 such samples, the process mean strength is estimated to be 3000 kg with a standard deviation of 50kg.

(a) Find the 1σ and 2σ control limits. For the 1σ limits, what is the probability of

concluding that the process is out of control when it is really in control? (b) Find the 3σ limits. (c) If rule1 and rule2 are simultaneously used to detect out-of-control conditions,

assuming independence, what is the overall probability of type-I error if 3σ control limits are used? [6]

No. of Pages = 2 No. of Questions = 9

ET ZC432 (EC-2 Regular) Page 2 of 2

ET ZC432 (EC-2 Regular) Second Semester 2008-2009 Page 2

Q.4 The bore size on a component to be used in assembly is a critical dimension. Samples of

size 4 are collected and the sample average diameter and range calculated. After 25 samples, we have,

25 _ Σ Xi = 107.5 i=1 25 Σ Ri = 107.5 i=1

The specifications on the bore size are 4.4 +- 0.2mm. The unit costs of scrap and rework are $ 2.40 and $ 0.75 respectively. The daily production rate is 1200.

(a) Find the X bar and R - chart control limits. (b) Assuming the process is in control, estimate its standard deviation. (c) Find the proportion of scrap and rework (d) Find the total daily cost of scrap and rework (e) If the process average shifts to 4.5mm, what is the impact on the proportion of

scrap and rework produced? [10]

Q.5 A building contractor subcontracts a job involving hanging wall paper to a local merchant. To have an idea of the quality level of the merchant’s work, the contractor randomnly selects 300ft2 and counts the number of blemishes. The total number of blemishes for 30 samples is 80. Construct the centre line and control limits for an appropriate chart. Is it reasonable for the contractor to set a goal of an average of 0.5 blemish per 100ft2? [10]

Q.6 A pharmaceutical company producing vitamin capsules desires a proportion of calcium content between 40 and 55 ppm. A random sample of 20 capsules chosen from the output yields a sample mean calcium content of 44 ppm with a standard deviation of 3 ppm. Find the natural tolerance limits of the process. If the process is in control at the present values of its parameters, what proportion of the output will be non conforming, assuming a normal distribution of the characteristics? Find the process capability index Cpk, and comment on process performance. [8]

Q.7 Construct the ATI curve for the sampling plan N=1200, n=50, c=1. Suppose the process

average non conforming rate is 3%. Explain the value of ATI for that level of non conformance. [5]

Q.8 A remote control unit has 40 components in series. The reliability of each component is 0.994. What is the reliability of the remote control unit? If a redesign has 25 components in series, what is the reliability of the unit? [4]

Q.9 Discuss the difficulty in measuring service quality. What are some remedial measures?

[5]

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