I‘IHITIIBIH UNIVERSITY

OF SCIENCE Rl'ID TECHI‘IOLOGY

FACULTY OF HEALTH AND APPLIED SCIENCES

DEPARTMENT OF MATHEMATICS AND STATISTICS

QUALIFICATION: BACHELOR OF SCIENCE IN APPLIED STATISTICS HONOURS

QUALIFICATION CODE: O8BSSH LEVEL: 8

COURSE CODE: SQC801S COURSE: STATISTICAL QUALITY CONTROL

SESSION: JULY 2017 PAPERzTHEORY

DURATION: 3 Hours MARKS: 85

SECOND OPPORTUNITY EXAMINATION QUESTION PAPER

EXAMINER Mr. J. J. SWARTZ

MODERATOR; PROF. A. SATHIYA SUSUMAN

INSTRUCTIONS

1. Answer all the questions in the booklet provided

2_ Show clearly all the steps used in the calculations.

PERMISSIBLE MATERIALS

1. Calculator

THIS QUESTION PAPER CONSISTS OF 4 PAGES (Including this front page)

Question 1 [18 marks]

1.1 What are the quality measures of quality used in attribute control charts and variable control

charts. [4]

1.2 Statistical quality control (SQC) is the term used to describe the set of statistical tools used by

quality professionals. Statistical quality control can be divided into three broad categories, state these

categories and explain each ofthem. [6]

1.3. Explain the term quality planning in statistical quality control. [4]

1.4. Explain the difference between an R — chart and a? — chart. [4]

Question 2 [24 marks]

2.1 Surface—finish defects in a small electric appliance occur at random with a mean rate of 0.1

defects per unit. Find the probability that a randomly selected unit will contain at least one surface-

finish defect. [4]

2.2 A batch of N=25 contains 3 non-conforming units. What is the probability that a sample of five

units selected at random contains one or more non-conformances. [5]

2.3 The tensile strength of a metal part is normally distributed with mean 40 lb and a standard

deviation of 5 lb. If 50 000 parts are produced, how many would you expect to fail to meet a

minimum specification limit of 35 lb tensile strength? [5]

2.4 Frozen orange juice concentrate is packed in 6—02 cardboard cans. These cans are formed on a

machine by spinning them from cardboard stock and attaching a metal bottom panel. By inspection

of a can, we may determine whether, when filled, it could possibly leak either on the side seam or

around the bottom joint. Such a nonconforming can has an improper seal on either the side seam

or the bottom panel. To establish the control chart, 30 samples of n = 50 cans each were selected at

half-hour intervals over a three—shift period in which the machine was in continuous operation. The

data are shown in the Table below.

Table: Frozen orange juice concentrate. Sample n = 50 cans

Number of

a

Number of

Sample Nonconforming Sample Fraction Sample NonconformingNumber Cans. D, Nonconforming. p, Number Cans, D,

l 12 0.24 17 10

2 15 0.30 18 5

3 8 0.16 19 13

4 10 0.20 20 1 1

5 4 0.08 21 '20

6 7 0.14 22 18

7 16 0.32 23 24

8 9 0.18 24 15

9 14 0.28 25 9

10 10 0.20 26 12

l 1 5 0.10 27 7

12 6 0.12 28 13

13 17 0.34 29 9

1:1» 12 0.24 30 6

15 22 0.44 347

0.1616.

8...1 .

2.4.1 Estimate the true fraction non-conforming for the given data

2.4.3 Calculate the upper and lower control limits

Question 3 [20 marks]

3.1 The output voltage of a power supply is assumed to be normally distributed. Sixteen

observations taken at random on voltage are as follows:

10.35 9.30 10.00 9.96 11.65 12.00 11.25 9.58

11.54 9.95 10.28 8.37 10.44 9.25 9.38 10.85

3.1.1 Test the hypothesis that the mean voltage equals 12 volts, using a two—sided test at 5%

level of significance.

3.1.2 Find the p-value for the test.

3.1.3 Construct a 95% confidence interval for the true mean diameter of bearings.

3.1.4 Test the hypothesis that 02 = 1 at 5% level of significance.

Question 4 [25 marks]

4.1. Compute the CPR measure of process capability for the following machine and interpret the

findings. What value would you have obtained with the Cp measure?

3

[3]

[7]

[5]

[5]

[5]

[5]

Machine Data:

USL = 110

LSL = 50

Process 0 = 10

Process [1= 60 [15]

4.2. Compute the CPR measure of process capability for the following machine and interpret the

findings. What value would you have obtained with the Cp measure?

Machine Data:

USL = 110

LSL = 50

Process 0 = 10

Process [1= 60 [10]

END OF EXAMlNATlON!