Lect 6 - Process Capability123

7/23/2019 Lect 6 - Process Capability123

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Control Chartsfor Attributes

p-chart: A chart used for controllingthe proportion of defective services orproducts generated by the process.

pp== pp(1 (1 pp)/)/nnWhere

n = sample size

p = central line on the chart, which can be either the historical

average population proportion defective or a target value.

z = normal deviate (number of standard deviations from the average)

ontrol limits are! "#p= p$zpp and ##p= p%zp


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&ometown 'an&ometown 'an*ample*ample

+he operations manager of the booing services department of &ometown 'anis concerned about the number of wrong customer account numbers recorded b

&ometown personnel.

ach wee a random sample of -, deposits is taen, and the number of

incorrect account numbers is recorded. +he results for the past 1- wees are

shown in the following table.

0s the booing process out of statistical control"se three2sigma control limits.


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3ample Wrong 4roportion

5umber 6ccount 7 8efective

1 1 .9

- 1- .:;

< 1 .>9 : - .;

1 .>9

9 : .19

> -: .9

; > .-; 1 .:

1 1> .9;

11 1 .9

1- < .1-

+otal 1:>

&ometown 'an&ometown 'an"sing a p2hart to monitor a process"sing a p2hart to monitor a process

n = -

p=1:>

1-(-)= .:

pp== pp(1 (1 pp)/)/nn

pp== .:.:(1 (1 .:.:)/)/--

pp= .1:= .1:

"#p = .: $


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&ometown 'an&ometown 'an"sing a p2hart to monitor a process"sing a p2hart to monitor a process

*ample


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In class Problem


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Control Charts

Two types of error are possible withcontrol charts

? A type I error occurs when a process

is thought to be out of control whenin fact it is not

? A type II error occurs when a processis thought to be in control when it is

actually out of statistical control

These errors can be controlled by thechoice of control limits


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Process Capability

? Process capabilityis the abilityof the process to meet the designspecications for a service orproduct.

? Nominal valueis a target fordesign specications.

? Toleranceis an allowance aboveor below the nominal value.


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-- --


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4rocess is not capable4rocess is not capable

-- --


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Process capability ratio, Cp, is the tolerance width divided by

standard deviations !process variability".

Process Capability #atio, Cp

pp=="pper specification 2 #ower specification"pper specification 2 #ower specification

99


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Cpk$ %inimum of&pper specication ' x

(

x' )ower specication

(,

= =

Process Capability Inde*, Cp+,is an inde* that measures

the potential for a process to generate defectiveoutputs relative to either upper or lower specications.

Process Capability Inde*, Cp+

e ta+e the minimum of the two ratios because it givesthe worst-case situation.


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Intensive Care )ab*ample

"pper specification =


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Cpk$ %inimum of&pper specication ' x

(

x' )ower specication

(,

= =

&pper specication $ (2minutes)ower specication $ /2minutes

Average service $ /./minutes$ 0.(1minutes

Intensive Care )abAssessing Process Capability

CCpkpk== @inimum of@inimum of-9.--9.- -. -.


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Cp$$&pper specication - )ower specication

pp==

(2 - /2

!0.(1"$ 0./( Process Capability #atio

'efore 4rocess @odification"pper specification =


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In Class Problem


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In Class Problem


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#ower#ower

specificationspecification

@ean@ean

"pper"pper

specificationspecification

5ominal value5ominal value

3i* sigma3i* sigma

Aour sigmaAour sigma

+wo sigma+wo sigma

4ects of #educing5ariability on Process Capability


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#ange Population in range*pected fre6uencyoutside range

Appro*. fre6uency fordaily event

7 8 09 2./;


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?i* ?igma

? (.< defects per million

? Cp+ $ /

? Impact of number of parts orproduction steps on yield:

sigma < sigma ( sigma

? 0 022@ ;;@ ;;@

? 1 022@ ;=@ =0@

? 02 022@ ;


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esigning in -sigma

? #educe the number of parts in a product

? #educe the number of steps in a process


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?i* ?igma

? Six Sigmais a comprehensive and Be*iblesystem for achieving, sustaining, andma*imiing business success by minimiingdefects and variability in processes.

? It relies heavily on the principles and tools ofTD%.

? It is driven by a close understanding of

customer needsE the disciplined use of facts,data, and statistical analysisE and diligentattention to managing, improving, andreinventing business processes.


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?i* ?igmaImprovement %odel

0. eneetermine the current processcharacteristics critical to customersatisfaction and identify any gaps.

/. %easureDuantify the wor+ theprocess does that a4ects the gap.(. Analye&se data on measures to

perform process analysis.


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?i* ?igmaImplementation

Top own Commitmentfrom corporateleaders.

%easurement ?ystems to Trac+

ProgressTough Goal ?ettingthrough

benchmar+ing best-in-class companies.

ducation: mployees must be trained

in the Hwhys and Hhow-tos of 6uality. Communication: ?uccesses are as

important to understanding as failures.

Customer Priorities: Jever lose sight ofthe customerKs priorities.


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?i* ?igma ducation

? Green Belt: An employee who achieved therst level of training in a ?i* ?igma program andspends part of his or her time teaching andhelping teams with their proFects.

? Black Belt: An employee who reached thehighest level of training in a ?i* ?igma programand spends all of his or her time teaching and

leading teams involved in ?i* ?igma proFects.

? Master Black Belt: Lull-time teachers andmentors to several blac+ belts.


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0nternational Bualit0nternational Bualit8ocumentation 3tandards8ocumentation 3tandards

03C03C

A set of standards governingdocumentation of a 6uality program.

03C03C

1:1:

ocumentation standards that re6uire

participating companies to +eep trac+ oftheir raw materials use and theirgeneration, treatment, and disposal ofhaardous wastes.


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0. Category 0 M )eadership 0/2 points/. Category / M ?trategic Planning 1 points

(. Category ( M Customer and %ar+et Locus 1 points

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Lect 6 - Process Capability123