Robert E. Gladd, James M. Littlefield
International
Technology Corporation, Oak Ridge Laboratory
alculationsof StatisticalProcessControl
(SPC)limits assumerepresentative
random samplingof processoutput for the
Wheredataaccruerapidly enoughfor the collection
of randomlysampledsubsetsto be practicable,random samplingis unquestionablythe method of
choicefor the computationof statisticalcontrol indices.In a manufacturingenvironmentwhere output
is measuredin hundredsor thousandsof units per
hour or day, randomly drawn quality control (QC)
datasetsare convenientlyobtainedand SPClimits
maybe derivedin a timely fashion.
In the counting room of the environmentalradioanalyticallaboratory,however,instrumentreliability QC processoutputsare typicallyobtainedby
the periodic placementof a radioactivestandardin
eachinstrument detectorchamberand countingthe
disintegrationsovera specifiedinterval.This
methodproducesa single"total counts"QC result
per detectorper data collectionperiod.Radioactive
disintegrationsbeing characteristically
stochastic
phenomena,one expectsa normally distributedvariability of sourcecountsovertime. The quality assuranceobjectiveis to insure that countinginstruments
exhibit an unbiased,random,expectedvariability
that maybe takeninto accountin the error term
computationsof analyticalresults,and that any
emergentdetectorperformancetrendsbecomereadily apparentso that correctiveadjustmentsmaybe
Reprint of "Prom the Counting Room", Vol. 1, No.4, 1990
appliedto the equipmentwhenwarrantedto assure
continuingaccuracyof output.
At a dataaccrualrate of one QC resultper detector per collectioninterval,the practicalimperatives
of countinginstrumentcontrol (i.e.,procedural,
regulatory,and contractual)precludethe useof traditional SPCrandom samplingtechniques.One simply cannotawaitthe amassingof severalmonths
worth of databeforesamplingthe databaseand generatingstatisticalcontrol limits, "flying blind" in the
interim. When an operatingdetectoris subjectedto
significantelectronicand/or mechanicaladjustment
or repair,the continueduseof prior parameterestimatesmaybe improper; new operatingconditions
properlymandatethe collectionof a new subsetof
datafor QC evaluationto assureeffectiveinstrument control.
Acceleratingthe data collectionprocessby performing multiple QC countsper detectorper dayis
impracticalgiventhe normal production scheduling
demandsof a laboratoryand,more importantly,
would be inappropriateowingto the inevitableresultant biasingof the databy transientenvironmental
variables.Clearly,a routine periodic QC source
countprocedurewith provisionsfor contingencyrecountingis the mostpracticalmethod of acquiring
the necessary
instrumentreliability QC data.
The Oak RidgeLaboratoryof International TechnologyCorporation (IT/ORL) operatesa variety of
alpha,beta,and gammacounters,and presently
Radioactivity & Radiochemistry
The Counting Room: SpecialEdition
Figure 1 GEl/Ol Bi-207 source control plot.
monitors the performanceof eightinstrumentscontaining a total of seventy-seven
detectors.In January
of 1989,an in-housedevelopedcomputerizedsystem of count QC data acquisitionand SPCanalysis
wasinstalledto assistin complyingwith the requirementsof instrument calibrationQC ("IQCDATX'
and "IQCSTATS").IT/ORL QC Procedurespecifies
the useof a minimum of twentydatapoints for the
derivationof SPCparameterestimatesand, of necessity,a sequentialsampleof the initial twentysource
countvaluesfor eachdetector"series"is usedto calculatethe meansand sigmasand constructupper
and lower control limits. Individual datapoints are
expressed
asnormalizeddeviates("NDEV") from
MEAN = 0 and SIGMA = 1,with warninglimits
LWL = -2 and UWL = +2, and control limits
LCL = -3 and UCL = +3 (sigmas).Betaand gamma
sourcecountsarecorrectedfor temporalsourcedecaybeforestatisticsaregenerated.Sourcebackground countsarealsoenteredand plotted asnormalizeddeviates.NDEV resultsarereturned by the
program in both tabularand high-resolutioncontrol
chart scatterplotformat. The usermayrequestof the
IQCSTATSmodule tables,scatterplots,or both, for
either an individual detectoror for all instruments.
Additionally,the programcontainsan option for a
daily "LastEntry" report which issuesa printout of
the input dataand statisticalindicesfor the mostrecententry in the systemfor eachdetector.
The recentlycompleted,fully integrated,interactive prototype of the IQCDATAmodule providesthe
28
analystwith immediateNDEV feedbackas datais enteredinto the system.Input dataare rapidly checked
for the most commonforms of keyboardinput errors, suchasinvalid dates,detectorIDs, unauthorized userIDs, exactinput duplication,and grossly
out-of-rangecount datastemmingfrom inadvertently mis-keyedor omitted digits.Statisticsarecomputed (for N ~ 2), and the count input dataareconvertedto NDEVsand returnedto the userin a
resultsscreenwindow within a fewseconds.ND EVs
falling outside:t3 sigmarequire recountingof the
source,and a secondconsecutive>ABS(3)sigma
outlier in the samedirectionmandatescorrectiveaction. NDEVvaluesfalling within the "warning"
zones[ABS(2s NDEV s 3)] aremonitored for evidenceof "runs" indicativeof detectortrend, or excessivesequentialswingsdenotinginordinatevolatility.
The initial sequentialsampleof N = 20accrues
overa period of approximatelyone month (source
checksare not performedon weekendsor holidays
whenthe instrumentsareidle). Tentativestatistical
control indicesarecalculatedduring this datacollection intervalwhere1 < N < 20to givethe analystan
ongoingindication of instrumentperformance
while awaitingthe requisitetwentydatavalueswith
which to generatethe "permanent"detectorseries
parameterestimates.With the addition of each
N < 20result,the tentativestatisticsarerecalculated
so that the indicesconvergetowardthe final N = 20
meansand sigmas.The final parameterestimatesare
written to disk from which theyarereferencedin
Reprint of "Prom the Counting Room", Vol. I, No.4, 1990
"RadioanalyticCounting-InstrumentReliability:An Interim Assessment
of a Computer-Assisted
StatisticalProcessControlApproachUnderDevelopment"
RobertE. Gladd,JamesM. Littlefield
Figure 2b
LB-5100(TA/OO2 alpha, renormalized control plot.
subsequentoperationsof the system.Thesepermanent statisticsmaybe clearedfrom the lookup file
upon userrequestto force recalculationin the event
that dataentry errorsarefound and correctedby a
password-authorized
editor.A "series"continues
from the datea detectoris placedin serviceuntil
suchtime as significantcorrectivemeasuresarerequired, at which point the adjustmentsand/or repairs undertakenaredocumentedand the nextseries
is assignedan ID for the processto beginanew.
At this writing, the IQC systemhasbeenin operation for sufficientdurationto haveacquireddetectorseriesdatasetsnumbering from approximately
fifty to overone hundredperiodic sourcecheckresultsper detector/series,
enoughdatato provide for
the assessment
of the robustnessof the IQCSTATS
sequential"convenience"sample-derivedcontrol statistics.Detectorswere chosenrandomlyfrom each
instrumentand, with the aid of a random number
table,N = 20 datasetswere drawn from the total
availablecountsfor eachchamberand compared
with the original sequentialsetsfor the respective
chamber.The datawereenteredinto a SAS-PCTM
(StatisticalAnalysisSystem)programwhich performed independentsampleT-testsand "Homogeneity of Variance"F-testson the original datasetsvs.
the randomly drawnresults.The nul hypothesisis
that the meansand variancesof the sequentialand
randomsubsetsdo not differ significantly(i.e.,that
theyare "statisticallyequivalent")and that by implication,the method of seriessequentialsamplingof
Reprint of "From the Counting Room", Vol. 1, No.4, 1990
Figure 3 LB-5100!TAjOO2
beta control plot.
detectordatais indeedserviceablefor the derivation
of instrumentSPCindices.
The results,summarizedin AppendixA, are at
oncereassuringand cautionary.Of the eightinstruments,si:xweresubjectedto statisticalre-examination. Oneproportional alpha/betacounteris a recent
acquisitionand lackssufficientoperatinghistory to
providea large enough"N" for meaningfulrandom
sampling.A 32 chamberalphacounteris monitored
by a pulsecount calibrationprocedurein which the
sigmais a fixed percentageof the seriesmean rather
than the usualsquareroot of the adjusted(N -1)
meansquareddeviation,renderinga conventional
T-testinapplicable.
Eightinitial T-testswereperformed on the si:xinstrumentsreviewed.Twocountersarealpha/beta
counters,and the T-testswereappliedto both alpha
and betasourcecounts(Figures2a,2b,and 3). Of
the eightT-tests,sevenreportedstatisticalequivalenceof parameterestimates(i.e., "nonsignificant
differencesat 0.05probabilitylevel"). Germanium
detectorGEl (Figure1),while nonsignificantat
p = 0.05,wasa bit closefor comfort, owingto three
extremesourcecountvaluesin the initial sequential
sample.The initial seriescount, whichwasthe most
extreme,wasbypassedduring the randomsampling.
The remainingtwo, both well belowthe mean,were
includedby the randomnumbertable,resultingin a
negativeshift in the meanand a contractionin the
sigmafrom sequentialto randomsample.The GEl
dataweresubjectedto anotherround of random
29
Radioactivity & Radiochemistry
The Counting Room: SpecialEdition
sampling,and a secondT-testyieldedsimilar marginally"nonsignificant"teststatistics.The GEl data
illustratesvividly the impactextremevalueshaveon
processcontrol statistics,particularlythe normalized
deviates.A few relativelylargesourcecountfluctuations in the initial twentyresultsdiminish the magnitudesof the NDEVs for the remainingcountvalues,
an important contextualpoint to keepin mind when
interpretingthe control charts.
One instrument,codedin the SASoutput summary (AppendixA) as"LB51X' ("LB5100/TNO02"
on the Alpha Count Control Chart-Figure 2a),
showedstatisticallysignificantsequential-to-random
samplealphasourcecount shift. This detectorseries
datasetwasrandomlysampleda secondtime and Ttestedagain.The repeatT-testresultsconfirmedthe
significantshift in the alphacount parameterestimates,raisinga pertinent question;arewe to conclude that the SPCparameterestimatesderivedfrom
the first twenty detectorseriesalphavaluesare in
this instanceinvalid?If we replacethe original mean
and sigmain the IQC systemlookup file with the second setof randomsample-derivedindicesand
renormalizethe daily alphacountsfor this seriesto
theserevisedstatistics,the revampedcontrol chart
(Figure2b) exhibitsanupward shift in the scatter.
This is with a barelyperceptibleexpansionof the
scatterowingto the slight contractionin the sigma.
The "Mean Deviation:' an index of overall detector
bias,risesfrom -0.78to -0.02,the newfigure indicating that the detectorevincesessentiallyno alpha
count reproducibilityvertical-axisbias whenviewed
in the contextof the random-samplestatistics,an
implicit reminderof the inherentmethodological
strengthof the randomsample.
Underthe revisedSPClimits, one earlyalpha
datapoint (fifth in the series,on 02/14/89,originally
atNDEV = +2.74) nowbecomes,post-hoc,an "outlier" at NDEV = +3.71.A comparisonof the original
vs.the revisedplot revealsa reduction,from sevento
two, in normalizeddeviationpoints lying between
the warningand control limits (i.e.,
ABS(2 < NDEV < 3), one of which is now our retroactiveoutlier). The "warning zone"points on the
original plot were,with the exceptionof the 02/14result, all <LWL. A decliningcount trend is visiblyevi-
30
dent on the alphaplot, one that merits testingfor significanceof slope.
Usingthe SASregressionprocedurePROCREG
(AppendixA), a testof the simplelinear regression
model, "y = (a)(X) + b:' for the LB51A/002dataset
yieldsa statisticallysignificantslopeof -4.453262
(Prob> ITI, 0.0001)with a modelAdjustedRSquaredof 0.2489.Formalstatisticalanalysisconfirms what is readilyapparentto the eye;a declining
alphasourcecounttrend is occurringfor this detector, one that merits closerscrutiny.Confirmation of
the statisticalsignificanceof the negativetrend is obtained by deletingthree earlyseriesresults(02/10,
02/14,02/15),all with disproportionatelyhigh
NDEVvalues,and testingthe remainingdatavia the
sameSASregressionmodel.The revisedmodel,
while diluted somewhatin strength,remainsstatisticallysignificantwith a slopeof -3.281061
(Prob> ITI, still 0.0001)and a modelAdjustedRSquaredof 0.1739.
AlthoughLB51A/002indisputablymanifestsa
negativetrend, a concernwith "statisticalsignificance"shouldbe temperedwith an awareness
of
"practicalsignificance:'The AdjustedR-Squarestatistic, a correlativemeasureof modelpredictive
strength,indicatesthat no more than 24.89%of the
alphasourcecount variability is accountedfor by the
relationshipbetweenthe sourcecountresultsand
their chronologicalpositions.Experimentalremoval
of the possiblyanomalousearlyextremevalueslowersthe predictivepowerof the lineartrend model to
17.39%.This "trend",while not to be casuallydismissed,is in fact ratherlooselycoupled.Leaningtoo
heavilyupon textbookstatisticaltrend-line analysis
hasits perils,as manya formerWall Streetbroker
would unhappilyattest.Continuedevidenceof detectortrend does,however,warrant inspectionof the
equipmentfor contaminationor damage,aswell as
inspectionof the sourcematerial.Severalof our germaniumdetectorsrecentlyexhibiteda declining
sourcecounttrend (Figure1); the causewasfound
to be a nearlyinvisible crackin the sourcecasing.
Effectiveradioanalyticcountinginstrumentcontrol is accomplishedthrougha blend of adaptive
SPCempirical methodologyand expertjudgement.
While traditional statisticalproceduresare useful
analyticaltools,a properperspectiveis essential.
Reprint of "From the Counting Room", Vol. 1, No.4, 1990
RobertE. Gladd,JamesM. Littlefield
Evenin the "worst" casefound in this study,that of
the LB5100alphaseries,the differencein the sequential vs.the random-samplemeans,while "significantlydifferent" in terms of a formal statisticalTtest,is on the order of 0.6percent.This relative
0.6%differencein the meansis far lessthan the customary 2.5to 5.0%"expectedlaboratoryprecision
parameters"specifiedfor analyticalresults.Whenwe
renormalizethe datato the random-sample-derived
meanand sigma,the scatteris shiftedupwardand all
but one of the individual points remainwithin the
controlbounds.Further,our revisionist"outlier"
mustbe viewedin the contextof a fundamental
characteristicof the normal distribution; 99.7%of
normally distributed data fall within :t3 standarddeviations of a meanvalue.Wewould thereforeexpect,
on average,
three out of 1000pointsto randomlyfall
outsideof 3 sigma.Only whena detectorexhibitsrepeatedextremedeviationsfrom the meanin the
samedirection maywe infer the presenceof a systematicproblem.With respectto the longer-term
trend indicatedby a predictivelyweakbut "statisticallysignificant"linear slope,similar interpretive
cautionis warranted.Justastransientenvironmental
variablesmay impacta singlecount, sotoo might
seasonalenvironmentalinfluencesbe substantivefactors in observeddetectordrift. Suchtrends,while
worthy of closerscrutiny,maytend to slowlyflatten
out and reversein responseto suchsubtlelong-term
backgroundinfluences.
The IQC developmentsystemnow a placeat the
IT Oak RidgeLaboratoryprovidesanalystsand managementwith timely and,asindicatedby this study,
generallyrobustSPCindicatorsof detectorperformance.Systemenhancements
installedsinceour initial
empirical inquiry provide the countingroom staff
with a comprehensivesetof statisticaltools for the
evaluationof instrumentreliability.The IQC control
chartroutine now fits a least-squares
trend line
through the scatterand reportsthe Regression
Correlation Coefficientand R-Squarevalueson the plot.
The regressioncoefficientis testedfor significance
usingthe standard0.01 ConfidenceLimit Critical
Values.Correlationindicesfalling outsidethe critical
valuesarenoted on the plot with a warningstatement. In a similar manner,the parameterestimates
are now continuallyreassessed
with the addition of
Reprint of "From the Counting Room", Vol. 1, No.4, 1990
eachnew setof sourceand backgroundcheckdata.
The "MeanNormalizedDeviation"and its standard
deviationarecalculatedfor the entire seriesdataset.
A T-Testis performedto revealwhetheror not the
overallseriesNormalizedMeandiffers significantly
from zero (zerobeing,you will recall,the normalizedmeancalculatedfrom the initial N = 20set).
Again,a 0.01 ConfidenceLevelis used,and the TTestis computedunderthe conservativeassumption
of "unequalvariances;'a method requiring the computation of "approximatedegreesof freedom"(ADF
on the plot). T-scoresfalling outsidethe critical valuesarenoted on the plot with a "T -TestFAILED"
warning.The MeanNormalizedDeviationis indicatedon the plot by a brokenline. Wherea detector
exhibitsneithertrend nor "Mean N_Dev" bias,the
leastsquarestrend line and the populationnormalized mean"biasline" collapseto the X-axis.
Finally,a "Coefficientof Variation' (C.V.)statistic is returnedto providean index of relativevariability. Sometimesreferredto asthe "Percentage
StandardDeviation;' this parameterestimateis simply the ratio of Sigmato Meanexpressed
asa percentage,enablingthe analystto quicklyassess
both
day-to-dayand overallfluctuationsof the detector
seriesdata.For example,whereC.V. = 0.8,the interval from the LCL(-3) to the UCL(+3), a rangeof
6 sigma,is equivalentto 4.8% of the mean.Useof
theC.v: permitsthe userto easilyascertainboththe
relativevolatilityof the seriesscatterandthe proportionalmagnitudesof individualsequentialfluctuations.
Our empirical reviewof the accruingIQC databaseand analyticalsystemfinds that the sequential
samplingmethodemployedby the softwareis indeeda conceptuallysoundone and a practicalprocedure yieldingSPCestimatesof a generallyrobustnature with which to monitor, analyze,and manage
instrumentperformance.The studyfurther demonstratesthat, evenundereventualitieswhereoriginal
detectorseriesparameterestimatesarefound to be
statisticallyunrepresentativeof the detectorseries
countpopulation,adverseimpact upon the accuracy
of analyticalresultsis highly unlikely.The IQC system providesthe IT/ORL counting room staffwith
up-to-dateand statisticallycomprehensivedecision
data for optimal equipmentmanagement.
31
Radioactivity 6- Radiochemistry
The Counting Room: SpecialEdition
SAS Output Summary
T -Test and Regression Model Results
ITAS Oak Ridge Laboratory: IQC System Sampling Test.
T -Test Sequential vs. Random Source Check Counts. SAS 12:28 Wednesday, May 31, 1989.
Table
Detector = C2A
Variable: Counts
Table
Detector
= C2B
Variable:
Counts
Table
Detector = GEl
Variable:Counts
T-Test
*1
Table
Detector = GEl
Variable:Counts
27554.75000000
27802.65000000
T-Test
#2
For HO: Variances are equal, F' = 2.18 with 19 and 19 DF
Table
Detector = L6
Variable: Counts
32
Reprint of "From the Counting Room", Vol. 1, No.4, 1990
"Radioanalytic Counting-Instrument
Reliability: An Interim Assessment of a Computer-Assisted Statistical Process Control Approach Under Development"
Robert E. Gladd, JamesM. Littlefield
SAS Output Summary
T -Test and Regression Model Results
ITAS Oak Ridge Laboratory: IQC System Sampling Test.
T -Test Sequential vs. Random Source Check Counts. SAS 12:28 Wednesday, May 31, 1989.
Table
Detector = LB51 A
Variable: Counts
T-Test*1
Table
Detector
= LB51 A
Variable:
Counts
T-Test *2
Table
Detector =LB51B
Variable:Counts
Table
Detector = LSCI
Variable: Counts
Table
Detector
= LSCI
Variable:
Counts
Reprint of "From the Counting Room", Vol. 1, No.4, 1990
33
Radioactivity & Radiochemistry
The Counting Room: SpecialEdition
SAS Output Summary, continued
T-Test and Regression Model Results
LB51 00!TAjO02: SAS Proc Reg Output, Linear Trend Regression Analyis
SAS 10:24 Tuesday, June 6, 1989.
c.v.
Parameter
Variable
Table
DF
Standard Error
T for HO:
Parameter = 0
39.57598903
623.464
1
24674
DAYS
1
-4.453262
Model: MODEL 1 Tria!
Estimates
Parameter
Estimate
INTERCEP
0.85953556
-5.181
24610
Model: MODEL 1 Trial 2
-4.098
Dep. Variable: SOURCE
Freund, R. J., Little, R C., SAS System For Linear Models, SAS Insti-
Goldin, Abraham 5., Internal Quality Control for Radioassay, USEPA
Office of Radiation Protection Programs, Washington, DC, (1983).
Kanipe, L. G., Handbook for Analytical Quality Control in RadioanaIytical Laboratories, TVNUSEPA Interagency Energy-Environment
Research & Development Program (EPA 600/7-77-088),
34
0.0001
654..856
References
ington, DC, (1977).
0.0001
Dep. Variable:SOURCE
-3.281061
Table
0.71119
Wash-
tute, Cary, NC, (1986).
Steel, R G. B., Torrie, J. H., Principles and Procedures of Statistics,
Second Edition, New York, McGraw-Hili Book Co., (1980).
Diem, K., Lentner, C., Ed., Scientific Tables, Seventh Edition, CibaGeigy, Ltd., Basle, Switzerland, (1970).
R&R
Reprint of "Prom the Counting Room", Vol. 1, No.4, 1990