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Sample Size Calculations

BYOB

(Bring your own Bias)

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MSB (Medtronic Spinal and

Biologics) Guidelines

• MSB uses two guidelines: GQ1!"is#ed Based $ot %cceptanceGuidelines and &' SamplingGuidance 'ocument *or 'esign+alidation and +eri,cation o*-mplants

• Bot. are used as re*erences *orteams to use in determining samplesizes *or testing or product

acceptance/ 0ut are not

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-* testing a particular *eature t.is isw.at - usually do

• Sometimes - can glue toget.er a strategy 0y com0iningot.er Medtronic guidelines 3 starting wit. t.e 4alidationpolicy2

• 5irst 3 determine t.e reuired con,dence and relia0ility

le4el

5rom S&26

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and t.en tapping intoinstructions (ne7t 8 slides)

pro4ided 0y a mem0er o* t.e

Medtronic corporate statisticsgroup t.at s.ows .ow to arri4eat a sample size t.roug. trial

and error using Mini9a0

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Sample Size For Normal-Distribution Tolerance Interval

Goal: 'etermine smallest sample size li#ely to result in a normaldistri0ution tolerance inter4al narrowenoug. to ,t wit.in t.e speci,cations

Typical Usage: &rocess +alidation %cti4ities (e2g2 OQ;&Q)

Approach: -terati4e approac. to arri4e at minimum sample size *or demonstrating a le4el o* processper*ormance at a speci,ed con,dence le4el using tolerance inter4als2 5or &Q sample size applies to eac. o* t.e8 runs separately2 9.e user must enter an initial guess *or sample size (start at 1 i* you donerent sample sizes until t.e tolerance 0ound is

 ?ust inside t.e de,ned speci,cation limit(s)2 9.is is t.e minimum sample size necessary2

 

Neee !e"ore Determining Sample Size:

• @usti,cation *or using normal distri0ution assumption (e2g2 pro0a0ility plot o* rele4ant .istorical data/ scienti,crationale *or distri0ution s.ape)

•Astimate *or mean and standard de4iation (e2g2 pull *rom .istorical data)

•'esired Con,dence $e4el (site reuirement typically D)

•&rocess &er*ormance you need to demonstrate (o*ten called "elia0ility $e4el)

•Speci,cation limits

#is$ o" %rong ans%er:  9oo small sample size causes unnecessary test *ailure2 9oo large sample size wastesresources2

!e conservative:  % larger sample size can protect you *rom *ailing unnecessarily2 Boost estimated standardde4iation estimate 0y 6D to D and mo4e t.e mean closer to t.e speci,cation to use as t.e input 4alues2

 9.is will lead to a larger sample size/ decreasing t.e widt. o* t.e computed tolerance inter4al2

&uestions:  Contact your local Su0?ect Matter A7pert or $e"oy Mattson

Rev 0, Oct 12,2011

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'(ample )one sie spec limit*:  E.at sample size (N) is needed to pro4e 95% confdence t.an at least90% within toleranceF &reliminary data s.owed data was normally distri0uted wit. sample mean (!ar) o" # and sample standard deviation (s) o" 1$52 &rocess .as a lower specifcation limit o" $

+initab , .ath%ay an Inputs: Stat/&uality Tools/ToleranceInterval

'(ample-nput 1 1 (-nitialGuess)

-nput 6 H-nput 8 12-nput D-nput D-nput ! lower speconly

Ans%er: +inimum Sample

Size 0

 9ry successi4ely smallersample size until tolerance0ound is ?ust I 82 (lowerspeci,cation)

-nitial Guess

result

+initab , 1utputs an User Decision on Sample Size

J is 0elow lower spec limit o* 8

J! greater t.an 8/ t.ere*ore/minimum sample size

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'(ample )t%o-sie spec limits*:  E.at sample size (N) is needed to pro4e 95% confdence t.an at least90% within toleranceF &reliminary data s.owed data was normally distri0uted wit. sample mean (!ar) o" 9 and sample standard deviation (s) o" 1$52 &rocess .as a lower specifcation limit o" and &pperspecifcation limit o" 1$ (note' mean is closer to * than **)

+initab , .ath%ay an Inputs: Stat/&uality Tools/ToleranceInterval

'(ample-nput 1 1 (-nitialGuess)

-nput 6 -nput 8 12-nput D-nput D-nput ! 9wosided

Ans%er: +inimum SampleSize 0 ,2

 9ry successi4ely larger samplesizes until tolerance 0ound isinside 0ot. spec limits($owerI8 and=pper K18)

-nitial Guess

result

+initab , 1utputs an User Decision on Sample Size

J16 is still a0o4e upper spec limit o* 18

J18 inside 0ot. spec limits/ t.ere*ore/minimum sample size

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 9.e main pro0lem wit. t.at

met.od is t.e pro0lem o*#nowing t.e standardde4iation *or items you

.a4en

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and you ?ust want to get an idea o*

o4erall per*ormance:

• Suppose you want t.e product to .a4e an a4erage li*e o* years(H mont.s)

• But t.e lower spec limit needs to 0e 1 year 0ecause you .a4e a no

*ault return warrantee *or 1 year (16 mont.s)• Eant a D con,dence t.at D will last at least a year

• %ssume a *airly generous standard de4iation o* 16 mont.s

=sing t.e Sample Size For Normal-Distribution Tolerance

Interval Mini9a0 met.od see t.e *ollowing e7ample2

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-nitial Settings

•  9ry it wit. 1 Samples

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"esult

• Jot so good Eit. t.at sample sizet.ere is D con,dence t.at t.elower 0ound will 0e 266 mont.s

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-ncrease sample size to

• Better2 Jow we .a4e a con,dencet.at t.e lower limit will 0e 182!mont.s

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Somew.ere 0etween 1 and ist.e minimum reuired sample size

• Continued trial and error re4eals t.eminimum sample size to 0e 8

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'iscussion o* Business needs w.ilewal#ing t.roug. Mini9a0 e7ample

• E.at i* you test to a sa*ety *actor2'o you still need t.at many samples2

 9ry reducing t.e standard de4iation and see

t.e e>ect on t.e lower 0ounds2