MFE3100
Quality Management and Control
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© E.Francalanza MFE 3100 – Quality Management and Control
© E.Francalanza MFE 3100 – Quality Management and Control
• Set your Mobile Phones to Silent
• Respect your colleagues – no private
conversations
• Be on time
MFE3100
Quality Management and Control
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© E.Francalanza MFE 3100 – Quality Management and Control
• SPC for Attribute Data
• Tutorial Overview
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Quality Management and Control
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© E.Francalanza MFE 3100 – Quality Management and Control
© E.Francalanza MFE 3100 – Quality Management and Control
• The quality of many products and services is dependent upon characteristics which cannot be measured as variables.
• These are called attributes and may be counted, having been judged simply as either present or absent, conforming or non-conforming, acceptable or defective
• Attribute Chart data is more easily assessed. Variables are sometimes converted to attributes for assessment.
• Attributes are not so sensitive a measure as variables, and therefore detection of small changes is less sensitive.
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Quality Management and Control
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Attribute Data
Non-Conforming
Units
Non-Conformities
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• Non-Conforming Units
– Can be wholly described as failing or not
failing, acceptable or defective, present or not
present.
– Examples: Ball-Bearings, Invoices, Workers.
• For 100 Ball-Bearings we can state how many are
defective or non-conforming. If 2 Ball-Bearings are
classified as unacceptable or defective, 98 will be
acceptable.
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• Non-Conformities
– Used to describe a product or service.
– Examples: Errors, Sales Calls, Truck
Deliveries.
• For a product such as a Windscreen which is being
examined for defects such as scratches or
bubbles, one can only measure the number of non-
conformities present, and one cannot imply on
defects which are not present.
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Name Sample Size Defect Type
The p-chart Varied Defective
The np-chart Constant Defective
The u-Chart Varied Defects
The c-Chart Constant Defects
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Quality Management and Control
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Check on
sample size (n)
Is n
constant
?
Check on type
of item
Is the item
a defective
unit rather
than a
defect?
Check on type
of item
Is the item
a defective
unit rather
than a
defect?
u-Chart
No Yes
p-Chart c-Chart np-Chart
No Yes No Yes
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• If process control is going to be effective, it
is off utmost importance to clarify what
constitutes a defective, non-conformance,
defect or error.
• Judgments can vary, leading to heated
discussions, therefore control samples
have to be set up.
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Quality Management and Control
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• Most Popular Chart
• Used for process control of defective units,
when it is not possible to take a sample of
a constant sample size
• Data Required:
– Sample Size
– No. Of Defectives per Sample
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Quality Management and Control
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• Company ABC wants to carry out an SPC
study on the delivery of Textile
Components (ex. Shirts).
• The Textiles are delivered in varying
batches. Samples are taken in proportion
to the batches, and the number of rejects
(ex. due to tears) is recorded for 24
deliveries.
• Data is presented in the next slide.
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Issue Size Number of
Rejects Proportion
Defective 1135 10 0.009
1405 12 0.009
805 11 0.014
1240 16 0.013
1060 10 0.009
905 7 0.008
1345 22 0.016
980 10 0.010
1120 15 0.013
540 13 0.024
1130 16 0.014
990 9 0.009
1700 16 0.009
1275 14 0.011
1300 16 0.012
2360 12 0.005
1215 14 0.012
1250 5 0.004
1205 8 0.007
950 9 0.009
405 9 0.022
1080 6 0.006
1475 10 0.007
1060 10 0.009
p
Mean: Mean:
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Quality Management and Control
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• Similar to a p-chart but the sample size is
constant.
• The data values plotted are the actual
number of defective items per sample
rather than the proportion.
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• A manufacturer of ball-point pens takes 50
samples of size 100 are taken every hour
from the production process to check for
defective products.
• The number of defects found in each
sample is recorded using a tally chart and
a Histogram is plotted with the results
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Sample No. No of Defective
Parts per Sample Sample No.
No of Defective
Parts per Sample
1 2 26 0
2 4 27 3
3 1 28 1
4 0 29 2
5 0 30 1
6 4 31 2
7 5 32 1
8 3 33 5
9 2 34 3
10 3 35 0
11 2 36 2
12 3 37 2
13 0 38 1
14 3 39 3
15 1 40 1
16 2 41 1
17 3 42 3
18 1 43 0
19 2 44 2
20 1 45 1
21 2 46 2
22 4 47 0
23 2 48 4
24 1 49 2
25 6 50 1
Total Defective:
Step 1: Calculate
Total No. of
Defectives 100
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p = 0.02
n = 100.00
np = 2.00
UCL 6.40
LCL 0.00
Step 2: Calculate np
Step 3: Calculate
UCL & LCL
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Quality Management and Control
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0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435363738394041424344454647484950
Step 4: Plot Graph
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• The u-chart is used for process control for defects when it is not possible to take a sample of constant sample size. This is similar to the p-chart, where the data values plotted on the chart are the proportion of faults per sample.
• Note however the difference that it is the number of non-conformities per item within the sample that is being monitored, and not the number of items per sample which have been rejected.
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Quality Management and Control
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• Considering a process which manufactures cooling fan blades.
• Each blade has a possible 17 measurements made on it. If variable charts had to be plotted and analyzed in detail this would take up a lot of time.
• Instead dimensions read are compared to the tolerance specifications and the number of defects (i.e. dimensions out of tolerance) are listed.
• The next table shows data gathered from 20 different batches.
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Number of Blades in
Sample Number of defects in
Sample Number of Defects
per Unit (u)
85 40 0.47
88 82 0.93
92 95 1.03
83 78 0.94
78 125 1.60
75 50 0.67
80 105 1.31
72 35 0.49
80 72 0.90
92 85 0.92
75 68 0.91
81 77 0.95
43 75 1.74
80 46 0.58
125 120 0.96
120 105 0.88
155 250 1.61
81 152 1.88
45 17 0.38
50 13 0.26
u
Mean: Mean:
𝒖
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Quality Management and Control
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• The c-chart is used for process control of
defects when it is possible to take samples
at a constant sample size.
• The data which is plotted on the chart are
the number of defects c in each sample.
© E.Francalanza MFE 3100 – Quality Management and Control
• In a polythene film process, the number of
defects – fisheyes – on each identical
length of film are being counted.
• The following chart portrays the variation
of the number of fisheyes which have
been found on inspecting 50 lengths,
randomly selected, over a 24-hour period.
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• If the chart is now used to control the
process, we may examine what happens
over the next 25 lengths, take over a
period of 12 hours.
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Quality Management and Control
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• What elements make up the main
components of the ISO 9001 Management
System, and how does this system work?
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• A laptop manufacturer sells 10,000 products per year. The costs for
the products sold are detailed in the table below. The products are
sold at the price of €1,200 per laptop. Analyze these costs. All the
costs listed are in (x103) €.
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Preventive € 500,000
Appraisal € 700,000
Failure € 700,000
Cost of Quality € 1,900,000 24%
Manufactuirng € 6,050,000 76%
Total Cost € 7,950,000
No. Sales 10000
Price/unit € 1,200
Sales € 12,000,000
Cost € 7,950,000
Profit € 4,050,000 34%
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• What are the types of variation that are encountered when analyzing a process?
– Common causes of variation
– Special causes of variation
• Give some examples of common and special causes of variation.
– Common causes – inherent process instability, such as vibrations.
– Special causes – chattering, tool wear, mis-alignments
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• Why do we need to use these ‘old’ quality tools in problem solving?
– Promotes a Systematic approach
– Aids in visualization of problems
– Facilitate data gathering
• Why is it important to identify the root-cause of a problem?
– If the root cause of a problem is not addressed, there is a very high probability that the problem will re-surface.
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Quality Management and Control
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• Why do we need to use these ‘new’ quality tools in problem solving? – Induces teams to think about alternative causes
of problems.
– Explores possible relationships between complex problems and their causes.
– Aid planning and implementation of solutions.
• Which tools would you use to plan and implement solutions? – Process Decision Programme Chart (PDPC)
– Arrow Diagram
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• What is the main Kaizen philosophy?
– Small continuous improvements which lead to Large
overall improvement of the company.
• Mention some main differences between Kaizen
and Innovation.
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• Use the following data in the table to plot an SPC chart by variable. The specification for the dimension is given as 29.5±0.5
– Is the Process in Statistical Control?
– Is the Process Capable?
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Grand or Process Mean
Mean Range Step 1: Establish Process Mean and Range
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Mean Chart:
A2 1.023
UCL 29.92
LCL 29.50
Range Chart:
D3 0
D4 2.574
LCL 0
UCL 0.532
Step 2:
Establish Control Limits
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UCL
LCL
Step 3:
Plot Variable Chart
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UCL
LCL
Step 4:
Plot Atribute Chart
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USL 30.00
LSL 29.00
Cp 1.363
𝜎 =𝑅
𝑑2
Step 5:
Check for
Process Capability Calculate σ
Calculate Cp
R 0.21
d2 1.693
σ 0.122
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Quality Management and Control
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© E.Francalanza MFE 3100 – Quality Management and Control