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```Problem 1
a) Describe the seven basic tools of quality control very briefly. How should we
use these tools together?
Solution:
The seven tools of quality control are the cause-an-effect diagram,
flowchart, checklist, control chart, scatter diagram, Pareto chart and
histogram. The cause-and-effect diagram, or fishbone diagram, shows all
possible causes of one quality problem or defect type (effect), where the
causes are separated into categories (or bones) on the diagram. It is used
as a brainstorming tool to determine which causes to investigate. The
flowchart documents the flow of the materials or customer through the
steps of the process. The checklist lists the type of defects, along with a
tally of the frequency of each type. Control charts show plots of samples of
a product or service characteristic taken from the process over time. The
control chart helps us determine whether the process is in control, which
means that only random variation exists. Scatter diagrams are plots on an
x-y axis used to determine the relationship between two variables. Pareto
charts show the frequency and cumulative percentages of defect types
arranged from most frequent to least frequent defect types. This chart
demonstrates which defect types cause the majority of the quality
problems or complaints. A histogram shows the frequency of each quality
problem. The Pareto chart and cause-and-effect diagram can be effectively
used in combination. First, the Pareto chart is used to identify the
problem(s) that cause the highest number of actual defects or complaints.
Next, a common problem becomes the effect on the cause-and-effect
diagram. This diagram then helps us identify causes to investigate in order
to solve the problem.
The tools should be applied as follows: First, a flow chart is used to get a
big picture look at a process. From this big picture, critical points along the
process are selected for data collection, which is accomplished with a
check sheet. The data collected by a check sheet are analyzed with
histograms, scatter plots and control charts. Once some analysis is done, a
cause and effect diagram can be used to surface causes of the primary
problem and finally a Pareto chart can be used to prioritize causes for
mitigation.
b) Who developed these tools?
Solution: Kaoru Ishikawa identified seven tools that when used together,
provide a path to continuing quality improvement.
c) Describe Pareto Analysis in more detail.
Solution: Joseph Juran identified an economic concept that he applied to
quality problems. This economic concept is called Pareto's law or the 80/20
rule, and is named after the Italian economist Vilfredo Pareto. Pareto found
that 80 percent of the wealth in Milan was held by 20% of the population.
Using Pareto's law, we can see that the majority of quality problems are
caused by relatively few causes.
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d) Explain the differences between x-bar and R-charts. How can they be used
together and why would it be important to use them together?
Solution: The x-bar chart is used to detect variations in the mean of the
process, while the R-chart is used to detect changes in the variability of the
process. The x-bar and R-charts are used when the data is a variable,
meaning that we can collect data using decimal points, such as 16.5
ounces. Examples of variables are weight, height and temperature. The xbar and R-charts should be used together. Think about preparing a
Thanksgiving turkey in the oven. What can go wrong with the temperature
of the oven if it is set at 350 degrees? The average temperature during
cooking could be 250 degrees instead. On the other hand, the temperature
could average 350 degrees, but actually fluctuate during cooking time
between 200 and 500 degrees. Either way, the turkey will not be properly
cooked in the oven. The inaccurate average temperature would have been
detected by the x-bar chart. The changes in the temperature would have
been detected by the R-chart. We use these charts together by plotting the
average of the sample on the x-bar chart and the range (high temperature
in the sample minus the low temperature) on the R-chart. Then, we first
interpret the R- chart. If it is out of control, then the process variation is out
of control. The next step would be to investigate the cause of this problem.
There is no need to interpret the x-bar chart if the R-chart is out of control.
If the variation is out of control, it is not possible to make conclusions
about the average because the variation would probably change the
average. If the R-chart is in control, then we interpret the x-bar chart. If it is
out of control, then the process average is out of control.
e) Draw a simply flow chart to help quality improvement teams select the
appropriate form of control chart to suit each situation to be monitored.
Include the following charts: x-bar-, R-, p-, and c-chart.
Solution: See lecture notes.
f) Explain what is meant by process capability. Why is it important?
What does it tell us? How can it be measured?
Solution: Management or regulations set acceptable levels of variation in
order to determine if a product is defective or not. For example, a product
is not defective if it is filled to 16 ounces plus or minus one ounce. For this
product, the upper specification limit would be 17 ounces, while the lower
specification limit would be 15 ounces. Process capability tells us whether
or not the process itself is capable of manufacturing product that has a
high probability of falling within the specification limits (is not defective). It
is important for a company to produce quality products. Process capability
is measured by comparing the specifications to the actual variation in the
process. The process capability index is the width of the specifications
divided by the width of the process variation. If the process capability
index is less than one, then the process is not capable of producing within
specifications. The higher the index, the more capable the process. The
index can be used to determine how many defects are produced on
average.
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g) Determine the process capability for the following machine and interpret the
findings. USL = 100, LSL = 70, Process standard deviation sigma = 5, Process
mean mu = 80. Would looking at Cp alone be sufficient?
Solution:
This process is not capable since the Cpk value is less than 1. Looking at
the Cp index by itself would lead us to believe that the machine is capable.
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