QUALITY AND RELIABILITY

Assignment 1
This assignment is worth 12.5%
Latest Due Date: Monday 10th November 5pm
Please ensure that all work is shown neatly.
Please make an individual attempt all all exercises. Copying will accrue you zero percent
Submission Type: Hardcopy only into my Pigeon Hole (bottom row. Two pigeon holes in)
Question 1
The data in the table below was collected in order to test a rumour that there were differences in
tensile strengths between the products from nominally identical plants owned by a single company.
The tensile strength values have been coded.
X= (Strength – 60.0) – 10
Plant A 22 24 0 1 4
Plant B 7 5 4 12 2
Plant C -4 -5 -4 14 -9
Plant D -11 -4 -12 -9 -7
Table 1.0 Tensile Strength of Product
Demonstrate manually the calculations and logic required build up an ANOVA table (to include Mean
Square, Sum of Squares, Degrees of Freedom and F value) for this problem. At the 1% level of
significance, what do you conclude about the rumour?
(25 Marks)
QUESTION 2
A GRR study on a measurement system was undertaken by three operators using ten parts. Each
part was measured three times for a particular characteristic. The results of that measurement are
on a .xls file on webcourses labelled GRRExampleMSA.xlsx. Using Minitab, conduct an appropriate
GRR study. Interpret the output from Minitab (please show relevant screen shots) and determine
whether this measurement system is fit for purpose.
(20 Marks)
Question 3.
Select the correct answer in each case
(a) Engineers at an electronics company want to test the resistance of a new batch of resistors.
The null hypothesis is that the mean resistance is 1,200 OHMS. The engineers use an alpha
of 0.05. Below is the output from the one-sample t test. What conclusions should the
engineers make?
1. Reject H0. The p value is greater than alpha
2. Reject H0. The t statistic is greater that alpha
3. Fail To Reject H0. The p value is greater than alpha
4. Fail To Reject H0. The p value is greater than alpha
(b) A research facility is considering a new training programme for new hires. Researchers test
the program’s effectiveness by administering a proficiency test before and after the training.
Which of the following questions can the researchers answer with a paired t test.
1. Do the post-test scores equal a target value
2. On average do trainees score differently on the pre-training test compared to the posttraining
test
3. Do the mean test scores of new hires differ from the mean test scores of seasoned
employees
4. Are the test scores of new hires more variable than the test scores of seasoned employees
(c) A factory operator uses a thermometer to measure the tap temperature of molten plastic. He
must be able to measure a tap with a true temperature of 265ºF to be between 260ºF and
270ºF. He takes eight measurements of the 265ºF tap and plots his results on an individual
value plot. The eight measurements range between 140ºF and 320ºF but have a mean of
224.78ºF. Which of the following best describe the measurement system?.
1. Accurate and precise
2. Precise but not accurate
3. Accurate but not precise
4. Not accurate and not precise
(d) A cell phone manufacturer hires a new supplier of rechargeable batteries. Engineers conduct
a 2-sample t-test to determine whether the current mean battery life (number of
discharge/charge cycles) of the new batteries is equal to the mean battery life of their
current supplier. Given the test output (see below (a=0.05)), what should engineers
conclude?
1. Reject H0. The standard deviation of the mean battery lives are different
2. Reject H0. The p value is less than a
3. Fail To Reject H0. The t-test statistic is greater than a
4. Fail To Reject H0. The p value is equal to zero.
(E) A supermarket uses a spring scale to measure the weight of produce. Which of the following
may affect precision?
1. Cashiers weigh different types of produce with the same scale multiple times
2. Cashiers weigh different types of produce with different scales multiple times
3. Cashiers follow different procedures when weighing the same apple with the same scale
multiple times
4. Cashiers follow different procedures when weighing the same apple with different scales
multiple times
(10 marks)
Question 4
Suppose that the boiling point of a particular coolant used in car engines is claimed by the
manufacturer to be 100 degrees centigrade. Further suppose that a series of accurate
measurements made in the lab using eight random samples of the coolant are recorded as
110.2°C 110.3°C 110.1°C 109.8°C 110.0°C 110.4°C 110.4°C 110.1°C
Based on these results, is it reasonable to claim that the boiling point of the coolant is greater than
the assumed true boiling point of 110 °C at the 5% level of significance. Please undertake this test
manually.
(15 marks)
Question 5
In a pad printing machine, X denotes the dry ink film thickness from a sample of 30 pushbuttons
produced during the first hour of production. Y is the dry ink thickness from a sample from a
population of pushbuttons produced during the last hour of production. Assume that the samples
have been obtained from two independent normal populations with equal but unknown variances. A
project team are looking for evidence that to support their claim that the dry ink film thickness
increases over time. Using an appropriate hypothesis test manually conducted, determine if there is
sufficient evidence to conclude that it has
Dry Ink Film Thicknesses for Pad Printing Study
Button X Y Button X Y Button X Y
1 10.0 12.4 11 9.2 7.7 21 9.7 10.0
2 11.2 10.9 12 8.4 12.7 22 9.4 8.4
3 8.1 10.4 13 6.4 10.2 23 8.6 10.0
4 8.3 10.3 14 8.3 10.2 24 10.4 11.5
5 10.8 10.6 15 8.2 8.6 25 8.3 11.4
6 10.3 9.6 16 7.0 8.4 26 8.0 11.7
7 9.5 9.7 17 10.8 9.5 27 8.7 10.7
8 8.2 9.6 18 7.5 7.8 28 9.6 10.8
9 10.0 9.8 19 7.4 11.5 29 8.9 9.4
10 10.1 10.3 20 9.5 10.0 30 8.9 10.7
(20 Marks)
Question 6
Using the file Diameters.MTW as input, use Minitab to draw scatter plot of the data and fit a linear
relationship to the data. Also find the R sqd. value and comment on its meaning in this case.
(10 marks)