Test 3 spr 2010 KEY

7/23/2019 Test 3 spr 2010 KEY

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Test 3 – Name:_____________________________

NOTE: Each problem will be graded based on “proper English” and “proper content”

1. Speciic !otors "orp. has a new s#pplier or spar$ pl#gs and is concerned abo#t

the incoming %#alit&. The& p#rchase spar$ pl#gs in lots o 1'(''' at a time andwant to #se ) 1.* to determine an acceptance sampling plan. "orporate oicers

has agreed on an +,- al#e o 1./0 deecties and the #se o general inspection

leel .a. 2etermine the acceptance sampling plan &o# wo#ld recommend #sing ) 1.* as a

g#ideline.

Sample sie code letter: -

n 4 5''c 4 6

b. S$etch the operating characteristic c#re.

Operating Characteristic (OC) Curve

n=200, c=7

True percent defective

P r o b . o f a c c e p t a n c e

0 1 2 ! " # 7 $

0

0.2

0.!

0.#

0.$

1

c. 7hat is the al#e or the 8,- 9-, or -T2; or this sampling plan. 9ass#me < 4

'.1';8,- 4 /.=>0

d. the incoming %#alit& is act#all& 3./0 deectie( what is the probabilit& that&o#r acceptance sampling plan accepts the lot ?#se &o#r O" c#re in part b aboe

to answer@

+pproAimatel& '.B' ?B'0Ce. +ter a lot was accepted( man& Speciic !otors cars appeared to not r#n er&

good and it was determined that the ca#se was deectie spar$ pl#gs. +ter an

eAtensie st#d&( it was determined that the act#al percent deectie was in act

3./0 deectie 9m#ch larger that the +,- o 1./0 deectie;. n order to protect&o#rsel rom ta$ing the ris$ o accepting this leel o %#alit& in the #t#re( what

sampling plan wo#ld &o# s#ggest the& switch to and wh&@Drom spreadsheet containing most sampling plans in ) 1.*( or an +,- or 1./0( thesampling plan n 4 =''( c 4 51 has an 8,- o 3./50. This sampling plan its the criteria

aboe and wo#ld accept most ?>/0C lots i the percent deectie is less than 1./0

?+,-C and reFect most lots ?G>'0C i the percent deectie is greater than 3./50. n other words( i the %#alit& o a lot were 3./0 deectie( &o# hae approAimatel& a 1'0 chance

o accepting that lot. &o# want this ris$ to be less than 1'0( call me and we will tal$.

1

7/23/2019 Test 3 spr 2010 KEY


5. Dor a gien +,- o *0 deectie and general inspection leel ( eAplain the logic

associated with the contin#al increase in sample sie 9or sample sie code letter;

associated with larger batch sies. Show seeral O" c#res showing this eect.-ogicall&( as the lot sie increases( &o# sho#ld be able to aord to ta$e a larger sample in

order to minimie the probabilit& o accepting lots whose %#alit& is worse than the +,-(

b#t at the same time accept lots whose %#alit& is at or better than the +,-. Dor thisreason( the sampling plans were designed to proide more statistical power when the lot

sies were larger( altho#gh &o# ma& well re%#ire more statistical power een or smaller

lot sies. The O" c#res or three sampling plans with +,-s o *0 are shown below.+s &o# can see( the larger sample sie plan ?res#lted rom a larger lot sieC is #nli$el& to

accept a lot whose percent deectie is 1'0 whereas the smaller sample sie plan

?res#lted rom a smaller lot sieC has a B'0 chance o accepting that lot( b#t then again

this lot is smaller so ma&be it wonHt be too bad to commit this mista$e.

3. ) 1.* is an acceptance sampling scheme. EAplain the reasoning behind theswitching r#les associated with normal( tightened( and red#ced inspection. Ise

&o#r own words. 2o not cop& an& doc#mented eAplanations. JOI8 K8+2E

ON TLS 8OM-E! 7-- ME M+SE2 ON 8OE8 ENK-SL +N2

"ONTENT.The switching r#les were a nat#ral eol#tion o h#man behaior. That is( i most all o

&o#r lots were being accepted oer a period o time( it wo#ld be logical or someone toas$ “7h& are we wasting all this mone& on acceptance sampling@ 7e er& seldom reFectan& lots.” The sol#tion to this was to implement red#ced inspection where the sample

sie is smaller. This still aords some protection in the eent the %#alit& were to degrade(

b#t saes mone& as a res#lt o a smaller sample sie. n essence( we relaA the statistical power o the sampling plan. -i$ewise( i man& lots are being reFected( it wo#ld be logical

to state “Since we are reFecting so man& lots( the %#alit& m#st be a lot worse than the

+,- and we need to do something to orce an improement in the %#alit&.” This was

5

7/23/2019 Test 3 spr 2010 KEY


accomplished b& moing to tightened inspection where the probabilit& o accepting lots

wo#ld decrease rom the c#rrent normal inspection plan or all leels o %#alit&. n order

to hae a reasonable probabilit& o accepting a lot( the s#pplier wo#ld then hae toimproe their %#alit& to a leel een better than the +,-. The 3 O" c#res below depict

a normal( red#ced( and tightened inspection plan or a 10 +,- and sample sie code

letter !.

*. ) 1.* also incl#des( in additions to single sampling plans( do#ble and m#ltiple

sampling plans. EAplain the adantage o #sing do#ble or m#ltiple sampling

plans oer single sampling plans or a gien +,-. ncl#de in &o#r eAplanation a

pict#re o an operating characteristic c#re and an aerage sample sie c#re( i itis appropriate.

The basic adantage o #sing do#ble or m#ltiple sampling oer single sampling is that

the eApected sample sie will be less b#t the O" c#res or all three samplingschemes will be approAimatel& the same. Lence( or the same statistical power( &o#r

aerage sample sie or each lot will be smaller or do#ble sampling and een smaller

or m#ltiple sampling. The ollowing +SN c#re and O" c#re are or sample sie

code letter N and a 10 +,-.

3

7/23/2019 Test 3 spr 2010 KEY


*

7/23/2019 Test 3 spr 2010 KEY


/. the lot sie res#lted in a sample sie code letter L( an +,- o '.*0( and normal

inspection( #se Table + to determine the acceptance sampling plan.!#st moe #p to sampling plan with n 4 35( c 4 '

B. Jo# are loo$ing or an acceptance sampling plan that will accept most o the lots(i the percent deectie was *0( and reFect most o the lots( i the percent

deectie was 1'0 deectie. 7hat sampling plan rom )1.* wo#ld &o#

recommend( and wh&@Drom the matriA o sampling plans in the power point presentation on acceptance

sampling( &o# can ind two sampling plans which wo#ld appear to satis& the aboe

re%#irement.

lan 1: n 4 5''( c 4 1* with +,- 4 *0 and 8,- 4 1'.10lan 5: n 4 31/. c4 51 with +,- 4 *0 and 8,- 4 =.>/0

Moth o these plans will accept %#alit& leels less than or e%#al to *0 most o the time

and reFect %#alit& leels greater than or e%#al to 1'0 most o the time. Jo# m#st decide

i increased power associated with plan 5 is worth the increase in sample sie. The O"c#res or these two plans are shown below.

/

7/23/2019 Test 3 spr 2010 KEY


6. The acceptance sampling plans o#nd in ) 1.* are what we reer to as +,- drien

plans. n other words( i we speci& an +,- o 10 deecties and the tr#e 0deectie o o#r process is 10 or less( we want to accept. LO7EE8( the

sampling plans are also coded based on the “batchPlot sie”. +s the lot sie

increases( the sample sie code letter increases res#lting in a larger sample sie plan( b#t with the same +,-. EAplain wh& ) 1.* designed the sampling plans this

wa&. Deel ree to s$etch seeral O" c#res to help s#pport &o#r eAplanation.

See problem 5 or answer. Q#st wanted to see i &o# gae two dierent answers.

+ct#all&( F#st messed #p.

=. T he resident o the Iniersit& wants to $now what actors aect grades st#dentsma$e on tests. n order to st#d& this problem( a gro#p o ac#lt& and st#dents

identiies 5' potential actors the& elt might aect grades. + screening

eAperimental design was #sed to narrow these 5' actors down to the two 9n#mber

o ho#rs &o# st#d& and n#mber o ho#rs &o# sleep the night beore the test; thatappeared to hae the greatest eect on grades. t was decided to #se a two leel

complete actorial design to st#d& this problem. 1'' st#dents ol#nteered to participate in this st#d&. These 1'' st#dents were randoml& diided into * gro#ps

o 5/ each and as$ed to go home and sleep a speciied n#mber o ho#rs 9* or =;

and st#d& a speciied n#mber o ho#rs 9B or 15; or the test. The neAt da& theidentical test was gien to all 1'' st#dents res#lting in an “aerage” grade or

each gro#p o 5/ st#dents. The data is gien below.

a. Estimate the eect o Lo#rs St#died

Eect Lo#rs St#died 4 ?9=5R=';P5C ?9B=R6*;P5C 4 =1 – 61 4 1' b. Estimate the eect o Lo#rs Sleep

Eect Lo#rs Sleep 4 ?96*R=';P5C – ?9B=R=5;P5C 4 66 6/

B

7/23/2019 Test 3 spr 2010 KEY


>. Dor the ollowing meas#rement s&stem st#d&( ill in the missing 9blac$; cells.

lace &o#r answers in the “blan$” cells directl& to the right o the blac$ cells.

Note that n#mbers hae been changed within cells so donHt tr& to eri& how &o#calc#late &o#r answer b& chec$ing other cells.

+nswers rom top to bottom.

1. 15.333

5. '.1633. '.'''1*6

*. '.''''3*'*

/. negatie so answer is “'”B. '.''3/3

6. 3./P1.* 4 5./ ?5/'0C obio#sl& 3./ was s#ppose to be '.'3/

7o#ld &o# consider this a good meas#rement s&stem or this application@ EAplain &o#r

answer.

6

%&'PCTO 1 2 !

12.$00 11.*$7 12.002 12.01 12.200 11. *$ 11.*$2 11.**0 12.000 11.**# 12.01 11.*** 12.017 11.*$! 12.00" 12.00* 11.*$# 11.**2 11.*$" 11.**# 11.*7! 12.01! 11.*$7 11.** 12.007 12.00 11.**1 11.**$ 12.001 12.00$ 12.00* 11.**! 12.022 12.01! 12.01 12.001

%&'PCTO 'T+T%'T%C 1 2 ! -+ = 12.00000000 11.*$$$721" 11.***12* 12.000711$7

+%+&C(' 2 ) = 0.01000000 0.0000!"#1 0.0002#2"! 0.00012$$# -+ = 11.**2122* 11.**##2#7$ 11.**2!"$71 11.***#1*11

+%+&C(' 2 ) = 0.000!$1#" 0.000"#0 0.00012#$7 0.0000#$!2 -+ = 12.00**2#!2 12.00$#"!11 12.00!0$#*1 11.**7!"1#0

+%+&C(' 2 ) = 0.00012021 0.0000!222 0.0001!127 0.00001!0# 0.00"*" 0.0001102! 0.000 17#$* 0.000070!"

0.0000$!!! 0.0000**" 0.0000!0" 0.0000027"

0.00000000 0.0000#2#0 0.00000000 / 0.0000207 0.00"#*7!! 0.000172$!* 0.00017#$*! 0.000070!"

'T' 0."

1.! sti3ate for the std of 4eas. '5s. =

+ (4.'.) = ' 2 4 ' =

6idth of 'pec =

auge 8 =

C

epeatabi9it5 = +(' 2 ) = ' r 2 =

+%+&C O: -+s = ' 2 -+

eproducabi9it5 = ' 2 -+ / ('

r 2 ;n) = '

2=

NOTE : Each part is measured three times by each inspector

P+T &4-

+

-

P+T &4-

+

-

C

7/23/2019 Test 3 spr 2010 KEY


"ertainl& not(. The meas#rement s&stem itsel will ca#se the ariabilit& o &o#r data to

be 5./ times wider than the spec. Kage 88 sho#ld be( in general( 3'0 and preerabl&

1'0 ?not the 5/'0 calc#latedC

1'. 7rite a report &o# wo#ld send to management s#mmariing wh& meas#rement

s&stem st#dies are important when cond#cting eAperimental design and otherstatistical st#dies. ncl#de “a$e” n#mbers to aid in the eAplanation.

=

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Test 3 spr 2010 KEY