Chapter 3- Measure

8/20/2019 Chapter 3- Measure

1/75

Phase 2 - Measure


2/75

What is done?

Measurements related to problem area are taken

• What needs to be measured?

• How to measure it?

• What is customer requirement?• What is the variation between the customer

requirement and the current level of performance?

• Is there any additional measurement required to

precisely know the problem?• What measurements are required after the process

is improved?


3/75

ype of data to be collected

• !ontinuous

• "iscrete


4/75

#cales of measurement

• $ominal

• %rdinal

• Interval• &atio


5/75

"ata collection methods-#amplin'

• Why is samplin' required?

-- More economical

-- less handlin'

-- (ew errors

• %ther points to consider before startin'samplin'

)* Mar'in of error+ #maller the better2* #amplin' method and si,e+ ar'er the

better


6/75

#amplin' plans

)* #imple random sample

2* #trati.ed sample


7/75

#imple random sample

• ot should be homo'enous

• Properties+

)* /ach part in the sample has equal

opportunity of bein' selected2* /ach sample of the same si,e derived from

the population has an equal chance ofbein' selected

•. "i0erence between the sample statisticsand actual values in the correspondin'population is known as samplin' error


8/75

!ontd1*

• $ot suitable for chan'in' processes

• !ornerstone of si si'ma process


9/75

#trati.ed sample

• More re.ned than random samplin'

• #e're'ated from hetero'eneous lot on the basis ofsome criteria* (or eample+ percenta'e

• hree shifts 1takin' data for each shift to'ether

• &eason from strati.cation+

)* /nsure that particular 'roup is adequatelyrepresented

2* Improve e3ciency by 'ainin' 'reater control oversamplin'

•. /pensive

•. !omple to analy,e


10/75

Measurement #ystem4nalysis

Q: What is Measurement System Analysis (MSA)?

A: It’s a set of techniques that allow us to answer the question:

IF I USE THIS GAGE TO MEASURE, HOW MUCH CAN I TRUST

THE MEASUREMENTS I GET?

• MSA is ase! on Measurement "rror


11/75

5nderstandin' Measurement /rro ake a sin'le item6 and measure it multiple

times usin' the same 'a'e7sametechnique7same appraiser


12/75

#n!erstan!in$ Measurement "rror %ecor! the measurements an! !raw a histo$ram


13/75

#n!erstan!in$ Measurement "rror &he histo$ram re'resents a sam'le from a normal

!istriution with a Mean an! a Stan!ar! e*iation(!eri*e! from s'rea!)


14/75

#n!erstan!in$ Measurement "rror +onsi!er the 'osition of the mean , &his is how

we !etermine the bias of the systemImagine e ha! meas"#e! a #efe#en$e si%e & a stan!a#! & of a 'non

!imension( We $o")! $om*a#e the mean of o"# #es")ts to the a$t"a) si%e

of the stan!a#!(

The !iffe#en$e is +ias


15/75

-ias%eference alue / 0.100 , &his is a 2nown si3e

Mean of multi'le measurements / 0.141

&he $a$e is on a*era$e measurin$ aout 0.041 too i$.It has a 'ositi*e ias of 0.041


16/75

-ias-ut we ha*e only !ealt with -ias at one si3e at

one 'oint in time A 5a$e is use! o*er a ran$e of si3es an! o*er a

'erio! of time

-ias may chan$e !e'en!in$ on these factors:

inea#ity

+han$e in ias o*er the o'eratin$ ran$e of the

$a$e

Stabi)ity

+han$e in -ias o*er time


17/75

-ias

6inearity , +han$e in -ias o*er o'eratin$ ran$e


18/75

-ias

Staility , +han$e in -ias o*er time


19/75

%e'eataility 7 %e'ro!uciility

-ias is ase! on the location of the mean of the

!istriution

• We 2now that when one 'erson uses the $a$e we $et

*ariation , &his is the *ariation inherent in the 5a$e ,

RE-EATA+IIT.(

•If we ha*e more than one 'erson usin$ the $a$e this

may intro!uce more *ariation 8 RE-RO/UCI+IIT.


20/75

ariation

%e'eataility 7

%e'ro!uciility


21/75

Possible Sources of Process Variation

We will look at “repeatability” and “reproducibility” as primary contributors to

measurement error

We will look at “repeatability” and “reproducibility” as primary contributors to

measurement error

#tability inearity

on'-term

Process 8ariation

#hort-term

Process 8ariation

8ariation

w7i sample

4ctual Process 8ariation

&epeatability !alibration

8ariation due

to 'a'e

8ariation due

to operators

Measurement 8ariation

%bserved Process 8ariation

Systemt Measuremen2

ocessl Actua2

ocessObserved 2

-# -#

ity producibil y peatabilit Systemt Measuremen Re2

Re22 σ σ σ +=


22/75


23/75


24/75

ypes of 9au'e &:&

• !omparison with standards

• 9au'e &:& ;crossed<


25/75

!omparison with standards

• he followin' de.ned constants areused in the method+

)* n is the number of units with pre-inspected standard values available.

2* m is the number of appraisers thatcan be assigned to perform tests.

=* r is the current total number of runsat any given time in the method.


26/75

erminolo'y

• #tandard unit+ any of the n units withstandard values available

• 4bsolute error+ absolute value of themeasurement errors for a 'iven test run

• ///4/ + /stimates errors of the epectedabsolute errors

• Measurement system capability ;M#4< > @

//4/ ;/stimated epected absolute errors<• 9au'e capable+ If M#4 A"6 where user

speci.ed maimum tolerable di0erencefrom standard value* hus @ //4/ A "


27/75

/ample5se two )2*B-pound dumbbells to

determine whether the followin'measurement standard operatin'procedure ;#%P< is C'au'e capableD oftellin' apart di0erences of E*B pounds*

)* Put Caylor MetroD scale ;dial indicatormodel< on a Fat surface*

2* 4dGust dial to set readin' to ,ero*

=* Place items on scale and record thewei'ht6 roundin' to the nearest pound*


28/75


29/75

9 &:& ;! d


30/75

9au'e &:& ;!rossed


31/75


32/75


33/75


34/75


35/75

• 9au'e capable if &:& A "


36/75

=

Process !apability

4nalysis


37/75

=

Introduction

• &equired to analyse whether a product or service meets thespeci.cations 'iven by the customer by indicatin' themeasure of process performance

• Process capability analysis has to be conducted only whenthe process is in a state of statistical control

• #peci.cation limit , 9enerally used interchan'eably with tolerance limit , Cimits that de.ne the conformance boundaries for an

individual unit of a manufacturin' or service operationD;4$#I6 4)6 )JK<

, 4re used for cate'ori,in' materials6 product or services

in terms of their stated requirements , 4re determined by the needs of the customer , 4re placed on the product characteristic by en'ineers or

desi'ners to ensure proper functionin' of product , &epresents the desired bound on the variability for

individual items


38/75

=K

Introduction L !ontd**

• olerance limit , 4re subset of speci.cations , hey pertain to physical requirements ;len'th6 diameter6

thickness etc


39/75

=J

Process capability 4nalysis

• "etermination of process capability be'ins only afterthe process has been brou'ht to a state of statisticalcontrol

• Process capability , &epresents the performance of a process in a state of

statistical control , "etermined by the total variability that eists due to all

common causes present in the system , It can be viewed as the variation in the product quality

characteristic that remain after all special causes hasbeen removed

, It can also be a measure of uniformity of a qualitycharacteristic of interest , 4 common measure of process capability is 'iven by O

also called as process spread , "istance O encompasses virtually all values of the

output quality characteristic


40/75

NB

Process capability analysis

• Involves estimatin' the process mean andstandard deviation

• 4lso the form of the relative frequencydistribution of the characteristic of interest isestimated

• If speci.cation limits are known6 proportion of nonconformin' products can also be estimated

• o be precise6 a process capability study involvesobservin' a quality characteristic of the productand hence should be called product analysisstudy

• 4 true process capability study should involvecollectin' and analysin' data related to processparameters like feed6 depth of cut etc*

• %bGective of this study is to .nd the relationship

between process parameter and the product


41/75

N)

Process capability analysis L!ontd**• ene.ts

, !ontinuous estimation and monitorin' of theseparameters will ensure the best performance that theprocess is capable of achievin'

, 5sed to take decision re'ardin' buyin' of new machine

or about quality of raw materials etc6 based on theprocess avera'e and process spread , 5niformity of output+ helps to control the variability and

hence more uniform output is obtained , Maintained or improved quality , Product and process desi'n facilitated

• Information from process capability provides feedback todesi'n thereby makin' them aware of inherent variation and hence reduces lead time of product by desi'nin' for'iven tolerance

, Helpful in vendor selection and control , &eduction in total cost+ helps in monitorin' the

production of non conformin' items


42/75

N2

$atural olerance imits

• !alled as process capability limits6 whichare established or inFuenced by theprocess itself

• &epresents the inherent variation in the

quality characteristic of the individualitems produced by a process in control

• /stimated based on population or fromlar'e representative of samples

• 4ssumin' a normal distribution of qualitycharacteristic @ then $ > Q =O and5$ > Q - =O6where Q is process meanand O is process standard deviation


43/75

N=

#tatistical tolerance limits

• "e.ned by 4$#I 7 4#R! as the limits of aninterval that ;with a 'iven level ofcon.dence S< contains at least a specifiedproportion ;)-T< of the population

• imits are found from samplin'information

• /ample L evel of con.dence of B*JK6while sample si,e is )B and JEU of the

part len'th will be between =B and =Emm• imits are inFuenced by sample si,e• 4s sample si,e increase6 statistical

tolerance limit approach the values foundfrom population parameters


44/75

NN

#peci.cations and process capability

• echnically6 there mi'ht not be a mathematicalrelationship between the process capability limits;$< and the speci.cation limits

• $ is determined by the condition of the processand its inherent variability

• #peci.cation limits are inFuenced by customer• 4 desired relationship is that speci.cation limits

are preferably outside the natural tolerancelimits6 in which case6 most of the units produced

will be acceptable• !ase i+ Process spread less than speci.cationspread , Process is quite capable and a preferred situation

, #pread between speci.cation ;5#-#< V spread

between natural limits ;5$ L $


45/75


46/75

N

#peci.cations and process

capability L !ontd**

• !ase i L !ontd** , If the process mean Q at the tar'et value ;midway

between the speci.cation limits


47/75


48/75

NK

#peci.cations and process capabilityL !ontd**

• !ase iii+ Process spread 'reater thanspeci.cation spread , ;5# L #< V ;5$ L $< , 5ndesirable situation

, Inherent variability of the process eceeds thespeci.cation spread even thou'h the process isin control

, 4lways some proportion of items produced willnot meet speci.cation

, #hift in mean or increase in standard deviationresult in increasin' proportion of the productnot meetin' speci.cation

, #uch process is not capable


49/75

NJ


• !orrective measures , Possibility of increasin' the speci.cation limits

• !areful consideration must be 'iven to meet theneeds of the customer and hence speci.cation limitsshould be determined before

, &educe the process spread• Investin' in new equipment6 better raw material6 use

of eperienced operators etc*

, $ot economically feasible to reduce processvariability throu'h lar'e investment6 it is better

to shift the process avera'e to achieve adesirable balance in the proportion of scrap andrework

• !ost of scrap7unit is 'reater than cost of rework• Produce less scrap and more rework - a feasible short

term plan


50/75

EB


• !orrective measures L contd** , eave the process unchan'ed6 perform

)BBU inspection to eliminate the nonconformin' parts

• $ot an ideal solution6 as )BBU inspectionmay not 'et rid of all non conformin' items

• )BBU inspection is merely a sortin' activityand it does not 'et to the root causes

• It cannot be used to analyse the causes andto determine corrective measures

, est approach is to do thin's ri'ht the.rst time and reduce reliance oninspection


51/75

$s6 #s and !s

E)


52/75


53/75


54/75

Process capability


55/75

EE

Process capabilityinde• he ability of a process to meet speci.cation

limit should be estimated only6 when it is in stateof statistical control

• he process has no special causes and hence

variability is the reFection of what the processcan achieve

• (irst step is to analyse whether the process is incontrol before we 'o for process capabilityanalysis

• 4ssumptions , Process output ;distribution of quality characteristic< is

normal6 which helps to estimate the proportion of nonconformin'

, 4ssumption of normality can be validated by empirical

plots of histo'ram6 normal probability parts6 statisticaltest for oodness of .t like chi-s uare test Xlomo rov


56/75

E

Process capability inde L !ontd**

• 4bility to meet speci.cation is the criteria formeasurin' the attractiveness of the process

• !apability indices are non-dimensional6 makesthem more versatile and appealin' because theydo not depend on speci.c process parameter

units• It takes care of location and the variation of the

process• !p inde

, !ommon measure to describe the CpotentialD of a

process to meet speci.cation , &elates process spread ;di0erence between natural

tolerance limits< to speci.cation spread !p > 5# L# 7 O


57/75

E


• !p inde L contd** , When O is unknown6 it is replaced by its estimate L say

sample standard deviation ;&bar7d2 or sbar 7cN<

, 4 process centred between speci.cation limits willproduce a minimum proportions of items that fall

outside these limits , It is desirable to have !p V> )6 If !p > )6 the processspread equals speci.cation spread and process is saidto be barely capable

, If process is not centred6 it is possible that even forprocess with !p V )6 some proportion of the product will

be non-conformin' , If !p A )6 inherent variability in the process asmeasured by process spread O6 is 'reater than thespeci.cation limit

, !p is the ratio of allowable process spread and actualprocess spread

,It does not take to account the location of the processand is a measure of process potential and not process


58/75

EK


• 5pper and ower capability indices , 5sed when only one speci.cation limit

, Indices can be derived that measure shifts in the

process mean relative to the process spread

, (or a 'iven upper speci.cation limit6 upper capability

inde is 'iven by

, It is desirable to have !P5 'reater than )

σ

µ

3

−=USLCPU


59/75

EJ


• 5pper and ower capability indices L contd** , #imilarly if the lower speci.cation limit is 'iven6 the

lower capability inde ;!P< is 'iven by

, It is desirable to have !P 'reater than or equal to )

σ

µ

3

LSLCPL −=


60/75

B


• !pk Inde , It accounts for the location of the process mean and

used when it is not at the tar'et mean

, !pk is 'iven by

, "esirable values of !pk is 'reater than or equal to )

, It represents the actual capability of the process withthe eistin' parameter values* It measures processperformance

, (or the 'iven process !pk A )6 the value of !p V )

indicatin' process can potentially meet speci.cations;&efer .'ure<

−−

== σ µ

σ

µ

3,3min},min{

LSLUSL

CPLCPU C pk


61/75

)


• !pk Inde L contd**

, #olution is to move the process mean towards midpointYm

, 4 measure of this deviation of the process mean from

tar'et Ym is 'iven by scaled distance Yk

, Where m is sum of 5# and # divided by 2

, &elationship between !p and !pk is 'iven by

,If process mean is at the tar'et Ym6 k > B and hence !

p

> !pk and if process mean is at the 5# or # then !pk

> B

−

−=

2 LSLUSL

mk

µ

)1( k C C p pk −=


62/75

2


• !p , Measure of the process

potential

, "oes not chan'e as theprocess mean chan'es

• !pk , Incorporates both theprocess mean and thestandard deviation tomeasure actual process

performance , !han'es with theprocess mean6 if theprocess is centred6 !pk >

!p

!pk inde - contd** When the process mean is outside thespeci.cation6 cpk is ne'ative

!pk is always less than or equal to !p


63/75

Ruestion

• In an electrical circuit6 the capacitance of acomponent should be between 2E and NBpico farads* 4 sample of 2E components

yields a mean of =B p( and a standarddeviation of =p(* !alculate the processcapability inde !pk and comment on theprocess performance* If the process is not

capable6 what proportion of the product isnonconformin'6 assumin' a normaldistribution of the characteristic?


64/75


65/75

E


• !apability &atio , 4 measure of the ability of the process to produce item

within speci.cation limit is based on the speci.cationran'e ;5# L # )6 is desirable and processes that are centredand have a lar'e value of !p will obviously use muchless of the speci.cation ran'e

, It is a measure of process potential as it calculates U ofspeci.cation ran'e used under ideal circumstance of aprocess

LSLUSLCR

−= σ 6


66/75


• a'uchi !apability Inde !pm , ased on the reduction of variability around the tar'et

value

, !pm is 'iven by

, τis the standard deviation from the tar'et value and'iven by

, Hence !pm is 'iven by

, &epresents the deviation of the process mean from the

tar'et value in units of standard deviation

τ 6

LSLUSLC pm

−=

222 )(])[( T T X E −+=−= µ σ τ

σ

µ δ

δ µ σ

T where

C

T

LSLUSLC

p

pm

−=

+

=

−+

−=

22

1)(6 2


67/75

Ruestion

4 process in control has an estimatedstandard deviation of 2 mm* We havea product with speci.cation limits of)2BZKmm and a tar'et value of )2Bmm* !alculate the !p6 !P6 !P56 !pkand !pm for the process if the processmean shifts from ))K mm .rst to )22

mm and then to )2N mm but theprocess variability remains the same*


68/75


69/75


70/75


71/75

Ruestion

• 5# > 2mm[ # > =K mm[ > EB

• Mean > EB[ #" > N

• Mean > E[ #" > 2

• Mean > EJ[ #" > )


72/75


73/75


74/75


75/75

!ontinued

• If the natural tendency of process isto 'et deviated towards hi'her side ofmean and if it deviates ) mm per

week6 how many resettin' at tar'etvalue will be required in an year?4ssume that company can bear

maimum EU defectives on hi'herside of mean and it takes &s* )B6BBBfor each resettin' of process mean*Which process amon' 4 and !

Documents

Chapter 3- Measure