1 comparisons of capabilities of cas and spreadsheets via the statistical quality control mihály...
TRANSCRIPT
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Comparisons of capabilities of CAS and spreadsheets via the statistical quality
control
Mihály Klincsik
Csaba Sárvári
Department of Mathematics Pollack Mihály Faculty of Engineering
University of PécsHungary
Content 2
Content of the lecture
About the Statistical Quality Control course at PMMK
Teaching experiences with Excel through 2 examples
Capability of Maple 10 CAS enhanced by „ProcessControl” package through 2 examples
Special features of the statistical quality control
Comparisons the capabilities of using Excel and/or Maple
Our philosophy
Our philosophy/1 3
Our philosophy/1
Each mathematical entities can be described by a certain approximation with our tools. The tools are now the Maple, the Excel programs and the brain, the subject is the statistical quality control.
If we emphasize or focus to one feature of an entity than we push the others into the background. We can grasp only one particular segment of the mathematical things with our sense at the same time.
Our philosophy/2 4
Our philosophy/2When we recognize so many elements of this puzzle after than we have to put this pieces together into a whole unity. This concept is valid not only for learning situation but in research environment, too.
We can grasp with the Excel’s tool effectively some elements of this subject, however the other elements can be supported actively with the Maple’s tools.
We suggest that these tools are worthy to use together.
About the Statistical Quality Control course at PMMK/1
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Statistical Methods for Quality Control
Acceptance Sampling
Total Quality Management studies for Engineering students at PMMK
Statistical Process Control by charts
cou
rse
Topi
c 1 Topic 2
undergraduate students (cca 50 )
graduate students(cca 40 )
About the Statistical Quality Control course at PMMK/2
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Control charts for groups of data
Variable control charts
If we
can
mea
sure
Attributes control charts
Aim : monitoring the process characteristics over time
X- control charts for average
R- control charts for range
S- control charts for deviation
c- charts for counts of defectives
p- charts for percent defectivesT
yp
es
of
con
trol ch
art
s
If we can’t
measure
Control charts are statistical tools that monitor a process and alert us when the process has been disturbed so that it is now out of control. This is a signal to find and correct the cause of the disturbance.
About the Statistical Quality Control course at PMMK/3
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Acceptance sampling
Single sampling plan
Aim : monitoring the quality of manufactured items supplied by the manufacturer to consumers in batches by procedures
Double sampling plan
Sequential Sampling Plan
Types
of
sam
plin
g
pla
n
We want to decide whether the lot of products should be accepted or rejected on the basis of a sample randomly drawn from the batch.
Special features of the statistical quality control/1
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All of the concepts are in close connections with the practical life and the processes
Mathematical representations
Thinking in formulas, symbols and theorems
Fixing the concepts and schemes in mind throughout visual effects and experiences
ELE
MEN
TS
O
F TH
E
AB
STA
RC
T
AN
D C
ON
CEPTU
AL
TH
INK
ING
Special features of the statistical quality control
TR
AD
ITO
NA
L ELE
MEN
TS
SPEC
IAL
ELE
MEN
TS
Belief in the power of the numerical calculations
Our decisions have immediate effects on the estimated parameters of the real process
Practical representations
Special features of the statistical quality control/2
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Mathematical representations of the operating characteristic (OC) -curve
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0
50)2()( ppppppppdpd
dpd
pXPpOC
Numerical GraphicSymbolicDescriptive
The OC curve is the primary tool for displaying and investigating the properties of an acceptance sampling plan. This curve plots the probability of accepting the lot (Y-axis) versus the lot fraction or percent defectives (X-axis).
Binomial distribution
Special features of the statistical quality control/3
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Practical representations of the operating characteristic (OC) -curve
Practical interpretations
When p = 0 there are no defective items in the batch and so the batch is certain to be accepted, thus OC(0) = 1.
When p = 1 then all items are defective and so the batch is certain to be rejected, thus OC(1) = 0.
When the quality of the batch becomes worse and worse - i.e. p is increasing - then the probability of the acceptance of this batch is decreasing. So OC(p) curve is a monotone decreasing function on p[0,1].
Special features of the statistical quality control/4
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Using flow charts to visualize the schemes
Single sampling plan with rectifying scheme
Accept the
batch
producer ConsumerSelect n items =
sample d=Defectives ≤ c
Inspection of sample
Reject the
batch
Repla
ce a
ny
defe
ctiv
e ite
ms
wit
h g
ood o
nes
100% inspectionand rectification
Yes
No
Teaching experiences using Excel through 2 examples
12
Teaching experiences using Excel through 2 examples
Control Charts using Excel spreadsheet
Single Sampling Plan using Excel spreadsheet
Capability of Maple 10 CAS enhanced by "Process Control" package through 2 examples
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Capability of Maple 10 CAS enhanced by „ProcessControl” package through 2
examples
Control Charts using Maple Computer Algebra System
Single Sampling Plan using Maple Computer Algebra System
Comparison of teaching and learning attitudes using Excel and/or Maple CAS/1
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EXCEL MAPLE 10
License
Well-known?
Comparisons the capabilities of using Excel and/or Maple
Unlimited
Programmable
Manageability
Limited
ASPECTS
Can’t
Generally the students don’t know the Maple CAS
Easily Slightly difficult
Own language
The students know from the ICT lessons.
Comparison of teaching and learning attitudes using Excel and/or Maple CAS
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Comparisons the capabilities of using Excel and/or Maple
Numerical calculationswide range of functions Some extra features over the Excel facilities
Help supports
Symbolic capabilities
Graphics capabilities
Immediate and in Hungarian
Easily handle with many auxiliary settings
nothing Well equipped
Black-box, white-box
Not so comfortable as the E Excel
Context sensitive and in English
Mainly black-boxFunctions sometimes differ from the traditional
EXCEL MAPLE 10ASPECTS
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Thank you for your attention!