monitoring nonlinear profiles with {r}: an application to quality control
TRANSCRIPT
lM it i g N liMonitoring NonlineMonitoring NonlineMonitoring Nonlineg l A 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. Mogu1 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 ChartsAssignable causes of variation may beAssignable causes of variation may befound and eliminated Sixfound and eliminated
l h hSix
Walter A ShewhartSix
Walter A. Shewhart• Exte• Exte
library(qcc)library(SixSigma) Reguqcc(data = ss.data.density,
t " b ")Regu
type = "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-cocoQ
N li fil• Quan
Nonlinear profilesQO t oNonlinear profiles • Out-oNonlinear profiles
• Shew• Shew• More complex quality characteristics• More complex quality characteristics wby.phase1
• Nonlinear relations wb.limits <Nonlinear relationsl l
x = ss.th• Multiple measurements smoothp
smoothlMultiple measurements smoothl
wby.phase2
An example profilewby.phase2 wb.out.phasAn example profile pAn example profile
l l b d d l fil• Practical case: particle boards density plotProfilePractical case: particle boards densityl 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 pstr(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 0.00.007 0.008 0.009 ...
• Engineered woodboards0.007 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 h P fil ith R ear Profiles with R: ear Profiles with R: ear Profiles with R: l l Q 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 Corcoba3 ENUSA Industrias Avanzadas; *Contact author: emilio@lcano com3. ENUSA Industrias Avanzadas; Contact author: [email protected].
Nonlinear profiles with RNonlinear profiles with RNonlinear profiles with Rp
xSigma packagexSigma packagexSigma packageends 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 ppfiles 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 pt 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 bandsof 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 chartto 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 Samplingfor Quality ControlP4" ... for Quality Control
b l l P4 P5 • Capability analysis P4 P528303 56 60074 Capability analysis
A t S li28303 56.6007401612 56.00993
• Acceptance Sampling01612 56.0099365936 56.59959 Acceptance Sampling
C t l Ch t10474 56.25226
• Control Charts49418 55.95592
N li P fil06341 55.32283
• Nonlinear Profiles19756 55.5965474017 55 2627174017 55.2627121402 55 2163921402 55.2163978578 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