Poster presentation at the Use R! 2016 Conference (Stanford, CA, USA)

1. lM it i g N liMonitoring NonlineMonitoring NonlineMonitoring Nonlineg
lA A li ti tAn Application toAn Application toAn Application topp
E ili L C 1 2 * J i M M gEmilio L. Cano1,2, , Javier M. MoguEmilio L. Cano , Javier M. Mogu
1 Rey Juan Carlos University; 2 The Univesity of Castilla La Mancha; 31. Rey Juan Carlos University; 2. The Univesity of Castilla-La Mancha; 3
NSh h t C t l Ch t NShewhart Control Charts NShewhart Control Charts
Assignable causes of variation may beAssignable causes of variation may be
found and eliminated Sixfound and eliminated
l h h
SixWalter A Shewhart
SixWalter A. Shewhart
• Exte• Exte
library(qcc)
library(SixSigma)
Reguqcc(data = ss.data.density,
t " b ")
Regutype = "xbar.one")
g
str(ss data density)str(ss.data.density)
## num [1:24] 10.7 10.6 10.6 • Prof## num [1:24] 10.7 10.6 10.6
10.8 10.8 ...
• Prof10.8 10.8 ...
• ExplExpl
P1.smooth <
plotProfile
O f th 7 QC b i t l (I hik )• One of the 7 QC basic tools (Ishikawa)
• Phase I and II strategy• Phase I and II strategy
• Specification limits vs Statistical Control LimitsSpecification limits vs Statistical Control Limits
U d l i h th i t ti
Proto• Underlying hypothesis testing
Protoy g yp g
• qcr [1] and other packages• qcr [1] and other packages
I• In-coco
Q
N li fil
• Quan
Nonlinear profiles
Q
O t oNonlinear profiles • Out-oNonlinear profiles • Shew• Shew
• More complex quality characteristics• More complex quality characteristics wby.phase1
• Nonlinear relations wb.limits <
Nonlinear relations
l l
x = ss.
th
• Multiple measurements smoothp
smoothlMultiple measurements smoothl
wby.phase2
An example profile
wby.phase2
wb.out.phas
An example profile p
An example profile
l l b d d l fil
• Practical case: particle boards density plotProfile
Practical case: particle boards density
l t( d t b d t b [ "P1"] t "l")plot(ss.data.wbx, ss.data.wby[, "P1"], type = "l")
A fA profA prof
• AllowsAllows
ld b• Could bCould b
plotControl
I d t ti lIndustry practical caseIndustry practical casey p
str(ss data wbx)str(ss.data.wbx)
## num [1:500] 0 0 001 0 002 0 003 0 0## num [1:500] 0 0.001 0.002 0.003 0.0
0.007 0.008 0.009 ...
• Engineered woodboards
0.007 0.008 0.009 ...
str(ss.data.wby)
• Engineered woodboards ( y)
## num [1:500, 1:50] 58.4 58 58.2 58.4
• Data set of 50 boards
[ ]
## ‐ attr(*, "dimnames")=List of 2
• Data set of 50 boards ## ..$ : NULL
$ [ ]
• Sample of 5 boards per shift ## ..$ : chr [1:50] "P1" "P2" "P3" "P
d t b [1 10 1 5]Sample of 5 boards per shift ss.data.wby[1:10, 1:5]
## P1 P2 P3 ## P1 P2 P3
## [1 ] 58 38115 55 07859 58 92000 58## [1,] 58.38115 55.07859 58.92000 58.
## [2,] 57.99777 54.86589 58.70806 58.## [2,] 57.99777 54.86589 58.70806 58.
## [3,] 58.17090 53.98849 58.62810 57.[ ,]
## [4,] 58.35552 55.05162 58.42878 57.[ ]
## [5,] 57.92579 53.84910 58.22835 57.
• Quality characteristic: density ## [6,] 57.57768 53.94282 57.02633 57.
[ ]Quality characteristic: density
T l 500
## [7,] 56.92579 53.83517 57.90364 57.
## [8 ] 57 39193 53 18903 57 40367 56
• Total measurements: 500 ## [8,] 57.39193 53.18903 57.40367 56.
## [9 ] 57 66014 53 44279 57 23293 56Total measurements: 500
E 0 001 i l th b d
## [9,] 57.66014 53.44279 57.23293 56.
## [10 ] 57 35137 53 75801 57 16073 56
• Every 0.001 in along the board
## [10,] 57.35137 53.75801 57.16073 56.
... ... ...y g ... ... ...
... ... ...
REFERENCES
[1] Scrucca L : qcc: an r package for quality control charting and statistical process control R News 4/1 11–17 (2004)[1] Scrucca, L.: qcc: an r package for quality control charting and statistical process control. R News 4/1, 11–17 (2004)
[ ] C EL M JM d R d h k A ( ) Si Si ith R S i i l E i i f P I[2] Cano EL, Moguerza JM and Redchuk A (2012). Six Sigma with R. Statistical Engineering for Process Improvement,
[3] Moguerza, J.M., Muñoz, A.: Support vector machines with applications. Stat. Sci. 21(3), 322–336 (2006)g pp pp
[4] Cano EL Moguerza JM and Prieto M (2015) Quality Control with R An ISO Standards Approach series Use R! Sp[4] Cano EL, Moguerza JM and Prieto M (2015). Quality Control with R. An ISO Standards Approach, series Use R! Sp
ACKNOWLEDGEMENTS: Projects GROMA (MTM2015 63710 P) PPI (RTC 2015 3580 7) and UNIKO (RTC 2015 3ACKNOWLEDGEMENTS: Projects GROMA (MTM2015-63710-P), PPI (RTC-2015-3580-7), and UNIKO (RTC-2015-3
CREDITS: Images by Wikipedia users (top to bottom): Rotor DB, Swtpc6800 Michael Holley under CC license and publ
f l hP fil ith Rear Profiles with R:ear Profiles with R:ear Profiles with R:
l lQ lit C t lo Quality Controlo Quality Controlo Quality Controly
1 d M i P i t C b 3erza1 and Mariano Prieto Corcoba3erza and Mariano Prieto Corcoba
3 ENUSA Industrias Avanzadas; *Contact author: emilio@lcano com3. ENUSA Industrias Avanzadas; Contact author: emilio@lcano.com.
Nonlinear profiles with RNonlinear profiles with RNonlinear profiles with Rp
xSigma packagexSigma packagexSigma package
ends functions and data sets in Six Sigma with R [2]ends functions and data sets in Six Sigma with R [2]g
ularizing via Support Vector Machines (SVMs)ularizing via Support Vector Machines (SVMs)g pp
files Smoothing via SVMs [3]files Smoothing via SVMs [3]
licit or automatic fitting parameterslicit or automatic fitting parameters
<‐ smoothProfiles(profiles = ss.data.wby[, "P1"],(p y[, ],
x = ss.data.wbx)
es(profiles = cbind(P1.smooth,
ss.data.wby[, "P1"]),
d t b )x = ss.data.wbx)
otype profile and confidence bandsotype profile and confidence bandsyp p
t l fil d t t fil ( di ) ithi li itntrol process: profiles around a prototype profile (median) within some limitso p ocess: p o es a ou d a p o o ype p o e ( ed a ) w so e s
til b d fid b dtile-based confidence bands
of control process hen a gi en n mber of points are o t of the confidence bandsof-control process when a given number of points are out of the confidence bandsp g p
whart approach: Phase I and II etcwhart approach: Phase I and II, etc.
<‐ ss.data.wby[, 1:35]
<‐ climProfiles(profiles = wby.phase1,
d b.data.wbx,
f TRUEprof = TRUE,
lim = TRUE)lim = TRUE)
<‐ ss.data.wby[, 36:50] < ss.data.wby[, 36:50]
se2 <‐ outProfiles(profiles = wby.phase2,(p y p ,
x = ss.data.wbx,
cLimits = wb.limits,
tol = 0.8)
( b hes(wby.phase2,
d t bx = ss.data.wbx,
cLimits = wb limitscLimits = wb.limits,
outControl = wb out phase2$idOut)outControl = wb.out.phase2$idOut)
fil t l h tfiles control chartfiles control chart
to visualize the sequenceto visualize the sequence
b l h b f h h hbe also the base for a Shewhart p-chartbe also the base for a Shewhart p chart
lProfiles(wb.out.phase2$pOut, tol = 0.8)
M Q lit C t l ith R [4]More Quality Control with R [4]More Quality Control with R [4]
• An ISO Standards Approach004 0 005 0 006
• An ISO Standards Approach004 0.005 0.006
pp
• The 7 basic Quality Control Tools• The 7 basic Quality Control Tools4 57.9 ...
• Statistics probability and Sampling• Statistics, probability and Sampling
for Quality ControlP4" ...
for Quality Control
b l l
P4 P5
• Capability analysis
P4 P5
28303 56 60074 Capability analysis
A t S li
28303 56.60074
01612 56.00993
• Acceptance Sampling
01612 56.00993
65936 56.59959 Acceptance Sampling
C t l Ch t
10474 56.25226
• Control Charts49418 55.95592
N li P fil
06341 55.32283
• Nonlinear Profiles19756 55.59654
74017 55 2627174017 55.26271
21402 55 2163921402 55.21639
78578 55 38662
• Six Sigma with R [2]
78578 55.38662
• Six Sigma with R [2]
h // lit t l ithhttp://www.qualitycontrolwithr.comq y
i U R! S i N Y k, series Use R! Springer, New York
pringerpringer.
3521 7) funded by MINECO3521-7) funded by MINECO
lic domain respectivelly