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© Wiley 2010

Chapter 6 - Statistical Quality

Control

Operations Management

by

R. Dan Reid & Nada R. Sanders4th Edition © Wiley 2010

PowerPoint Presentation by R.B. Clough UNH

M. E. Henrie - UAA

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© Wiley 2010

Three SQC Categories Statistical quality control (SQC) is the term used to describe

the set of statistical tools used by quality professionals

SQC encompasses three broad categories of;

Descriptive statistics

e.g. the mean, standard deviation, and range

Statistical process control (SPC)

Involves inspecting the output from a process

Quality characteristics are measured and charted

Helpful in identifying in-process variations

Acceptance sampling used to randomly inspect a batch of goods to

determine acceptance/rejection

Does not help to catch in-process problems

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Sources of Variation Variation exists in all processes.

Variation can be categorized as either;

Common or Random causes of variation, or Random causes that we cannot identify

Unavoidable

e.g. slight differences in process variables like diameter, weight, service

time, temperature

Assignable causes of variation

Causes can be identified and eliminated

e.g. poor employee training, worn tool, machine needing repair

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Traditional Statistical Tools Descriptive Statistics

include The Mean- measure of central

tendency

The Range- differencebetween largest/smallest observations in a set of data

Standard Deviationmeasures the amount of datadispersion around mean

Distribution of Data shape Normal or bell shaped or Skewed

n

x

x

n

1i

i§!!

1n

Xx

n

1i

2

i

!

§!

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Distribution of Data Normal distributions Skewed distribution

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SPC Methods-Control Charts Control Charts show sample data plotted on a graph with CL,

UCL, and LCL

Control chart for variables are used to monitor characteristics

that can be measured, e.g. length, weight, diameter, time Control charts for attributes are used to monitor characteristics

that have discrete values and can be counted, e.g. % defective,number of flaws in a shirt, number of broken eggs in a box

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Setting Control Limits Percentage of values

under normal curve Control limits balance

risks like Type I error

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Control Charts for Variables Use x-bar and R-bar

charts together

Used to monitordifferent variables

X-bar & R-bar Chartsreveal different problems

In statistical control onone chart, out of controlon the other chart? OK?

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© Wiley 2010

Control Charts for Variables Use x-bar charts to monitor the

changes in the mean of a process

(central tendencies) Use R-bar charts to monitor the

dispersion or variability of the process

System can show acceptable central

tendencies but unacceptable variability or System can show acceptable variability

but unacceptable central tendencies

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© Wiley 2010

Constructing a X-bar Chart: A quality control inspector at the CocoaFizz soft drink company has taken three samples with four observationseach of the volume of bottles filled. If the standard deviation of thebottling operation is .2 ounces, use the below data to develop control

charts with limits of 3 standard deviations for the 16 oz. bottling operation.

Center line and control

limit formulas

xx

xx

n21

zxLCL

zxUCL

sample eachw/innsobservatioof #theis(n)andmeanssampleof #theis)(where

n

,

...xxxx x

!

!

!

!

k

k

observ 1 observ 2 observ 3 observ 4 mean range

samp 1 15.8 16 15.8 15.9 15.88 0.2

samp 2 16.1 16 15.8 15.9 15.95 0.3

samp 3 16 15.9 15.9 15.8 15.90 0.2

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© Wiley 2010

Solution and Control Chart (x-bar) Center line (x-double bar):

Control limits for±3 limits:

15.923

15.915.97515.875

!

!

15.624

.2315.92zLCL

16.22

4

.2315.92zUCL

!¹¹ º

¸©©ª

¨!!

!¹¹

º

¸©©

ª

¨!!

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© Wiley 2010

X-Bar Control Chart

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© Wiley 2010

Control Chart for Range (R) Center Line and Control Limit

formulas:

Factors for three sigma control limits

0.00.0(.233)R D

.532.28(.233)R D

.2333

0.20.30.2R

3

4

R

R

!!!

!!!

!

!

Facto fo x-Cha t

A2 D3 D4

2 1.88 0.00 3.27

3 1.02 0.00 2.57

4 0.73 0.00 2.28

5 0.58 0.00 2.11

6 0.48 0.00 2.00

7 0.42 0.08 1.92

8 0.37 0.14 1.86

9 0.34 0.18 1.82

10 0.31 0.22 1.78

11 0.29 0.26 1.74

12 0.27 0.28 1.72

13 0.25 0.31 1.69

14 0.24 0.33 1.67

15 0.22 0.35 1.65

Facto s fo R-Cha tSample Size

(n)

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R-Bar Control Chart

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Second Method for the X-bar Chart Using

R-bar and the A2 Factor (table 6-1)

Use this method when sigma for the processdistribution is not know

Control limits solution:

15.75.2330.7315.92AxLCL

16.09.2330.7315.92AxUCL

.2333

0.20.30.2

2x

2x

!!!

!!!

!

!

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© Wiley 2010

Control Charts for Attributes i.e. discrete events

Use a P-Chart for yes/no or good/baddecisions in which defective items are

clearly identified Use a C-Chart for more general counting

when there can be more than one defectper unit

Number of flaws or stains in a carpet sample cut from aproduction run

Number of complaints per customer at a hotel

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© Wiley 2010

P-Chart Example: A Production manager for a tire company hasinspected the number of defective tires in five random sampleswith 20 tires in each sample. The table below shows the number of defective tires in each sample of 20 tires. Calculate the control

limits.

Sample Numberof

DefectiveTires

Number of Tires ineach

Sample

ProportionDefective

1 3 20 .15

2 2 20 .10

3 1 20 .05

4 2 20 .10

5 1 20 .05

Total 9 100 .09

Solution:

0.1023(0.64).09z pLCL

.2823(0.64).09z pUCL

0.6420

(.09)(.91)

n

) p(1 p

.09100

9

InspectedTotal

Defectives# pCL

p p

p p

p

!!!!!!!

!!

!

!!!!

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P- Control Chart

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© Wiley 2010

C-Chart Example: The number of weekly customercomplaints are monitored in a large hotel using ac-chart. Develop three sigma control limits using the

data table below.

Week Number ofComplaints

1 3

2 2

3 3

4 1

5 3

6 37 2

8 1

9 3

10 1

Total 22

Solution:

02.252.232.2cc

6.652.232.2cc

2.210

22

sampleso#

complaints#c

c

c

!!!!

!!!

!!!!

z

z

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C- Control Chart

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© Wiley 2010

Out of control conditions indicated by:

Skewed distributionData Point out of limits

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© Wiley 2010

Process Capability Product Specifications

Preset product or service dimensions, tolerances

e.g. bottle fill might be 16 oz. ±.2 oz. (15.8oz.-16.2oz.)

Based on how product is to be used or what the customer expects

Process Capability Cp and Cpk

Assessing capability involves evaluating process variability relative to

preset product or service specifications

Cp assumes that the process is centered in the specification range

Cpk helps to address a possible lack of centering of the process6

LSLUSL

width process

widthionspecificatCp

!!

¹ º

¸

©ª

¨

! 3

LSL

,3

USL

minCpk

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© Wiley 2010

e a ons p e ween rocess Variability and Specification

Width Possible ranges for Cp

Cp < 1, as in Fig. (b), process notcapable of producing withinspecifications

Cp 1, as in Fig. (c), processexceeds minimal specifications

One shortcoming, Cp assumesthat the process is centered onthe specification range

Cp=Cpk when process is centered

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© Wiley 2010

Computing the Cp Value at Cocoa Fizz: three bottlingmachines are being evaluated for possible use at the Fizz plant.The machines must be capable of meeting the designspecification of 15.8-16.2 oz. with at least a process

capability index of 1.0 (Cp1)

The table below shows the informationgathered from production runs on eachmachine. Are they all acceptable?

Solution:

Machine A

Machine B

Machine C

Machine USL-LSL 6

A .05 .4 .3

B .1 .4 .6

C .2 .4 1.2

1.336(.05)

.46

LSLUSLCp !!

67.06(.1)

.4

6

SS p !!

0.336(.2)

.4

6

SS p !!

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© Wiley 2010

Computing the Cpk Value at Cocoa Fizz

Design specifications call for atarget value of 16.0 ±0.2 OZ.

(USL = 16.2 & LSL = 15.8)

Observed process output has nowshifted and has a µ of 15.9 and a

of 0.1 oz.

Cpk is less than 1, revealing that the process is not capable

.33.3

.1Cpk

3(.1)

15.815.9,

3(.1)

15.916.2minCpk

!!

¹¹

º

¸©©

ª

¨ !

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© Wiley 2010

±6 Sigma versus ± 3 Sigma Motorola coined six-sigma to

describe their higher qualityefforts back in 1980s

Ordinary quality standardrequiring mean±3 to be withintolerances implies that 99.74%of production is between LSLand USL

Six sigma is much stricter: mean±6 must be within tolerances

implying that 99.99966%production between LSL and USL

same proportions apply tocontrol limits in control charts

Six-sigma quality standard isnow a benchmark in many

industries

PPM Defective for ±3versus ±6 quality

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© Wiley 2010

Six SigmaSix Sigma Still Pays Off At Motorola

It may surprise those who have come to know Motorola (MOT ) for itscool cell phones, but the company's more lasting contribution to theworld is something decidedly more wonkish: the quality-improvementprocess called Six Sigma. In 1986 an engineer named Bill Smith, who hassince died, sold then-Chief Executive Robert Galvin on a plan to strive for

error-free products 99.9997% of the time. By Six Sigma's 20thanniversary, the exacting, metrics-driven process has become corporategospel, infiltrating functions from human resources to marketing, andindustries from manufacturing to financial services.

Others agree that Six Sigma and innovation don't have to be a culturalmismatch. At Nortel Networks (NT ), CEO Mike S. Zafirovski, a veteran ofboth Motorola and Six Sigma stalwart General Electric (GE ) Co., hasinstalled his own version of the program, one that marries concepts fromToyota Motor (TM )'s lean production system. The point, says JoelHackney, Nortel's Six Sigma guru, is to use Six Sigma thinking to takesuperfluous steps out of operations. Running a more efficient shop, heargues, will free up workers to innovate.

http://www.businessweek.com/magazine/content/06_49/b4012069.htm?chan=search

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© Wiley 2010

Acceptance Sampling Definition: the third branch of SQC refers to the

process of randomly inspecting a certain number ofitems from a lot or batch in order to decide whether to

accept or reject the entire batch Different from SPC because acceptance sampling is

performed either before or after the process ratherthan during

Sampling before typically is done to supplier material

Sampling after involves sampling finished items before shipment or finished components prior to assembly

Used where inspection is expensive, volume is high, orinspection is destructive

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Acceptance Sampling Plans Goal of Acceptance Sampling plans is to determine the criteria

for acceptance or rejection based on:

Size of the lot (N)

Size of the sample (n)

Number of defects above which a lot will be rejected (c)

Level of confidence we wish to attain

There are single, double, and multiple sampling plans

Which one to use is based on cost involved, time consumed, and cost of passing on a defective item

Can be used on either variable or attribute measures, but more

commonly used for attributes

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© Wiley 2010

Implications for Managers How much and how often to inspect?

Consider product cost and product volume

Consider process stability

Consider lot size

Where to inspect? Inbound materials

Finished products

Prior to costly processing

Which tools to use? Control charts are best used for in-process production

Acceptance sampling is best used for inbound/outbound

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© Wiley 2010

SQC in Services Service Organizations have lagged behind

manufacturers in the use of statistical quality control

Statistical measurements are required and it is more

difficult to measure the quality of a service Services produce more intangible products

Perceptions of quality are highly subjective

A way to deal with service quality is to devisequantifiable measurements of the service element

Check-in time at a hotel Number of complaints received per month at a restaurant

Number of telephone rings before a call is answered

Acceptable control limits can be developed and charted

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© Wiley 2010

Service at a bank: The Dollars Bank competes on customer service andis concerned about service time at their drive-by windows. They recentlyinstalled new system software which they hope will meet servicespecification limits of 5±2 minutes and have a Capability Index (Cpk) of

at least 1.2. They want to also design a control chart for bank teller use.

They have done some sampling recently (sample size of 4customers) and determined that the process mean hasshifted to 5.2 with a Sigma of 1.0 minutes.

Control Chart limits for ±3 sigma limits

1.21.5

1.8k

3(1/2)

5.27.0,

3(1/2)

3.05.2mik

!!

¹¹ º

¸©©ª

¨ !

1.33

4

1.06

3-76

LSLUSL !

¹¹ º

¸©©ª

¨!

mi utes6.51.55.04

135.0zXU L xx !!¹¹

º

¸©©ª

¨!!

mi utes3.51.55.04

135.0zXL L xx !!¹¹

º

¸©©ª

¨!!

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© Wiley 2010

SQC Across the Organization SQC requires input from other organizational

functions, influences their success, and are actuallyused in designing and evaluating their tasks Marketing provides information on current and future

quality standards

Finance responsible for placing financial values on SQCefforts

Human resources the role of workers change with SQC

implementation. Requires workers with right skills Information systems makes SQC information accessible for

all.

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© Wiley 2010

Theres $$ is SQC!

I also discovered that the work I had done forMotorola in my first year out of college had a name.

I was doing Operations Management, bymeasuring service quality for paging by usingstatistical process control methods.

-Michele Davies, Businessweek MBA Journals, May 2001http://www.businessweek.com/bschools/mbajournal/00davies/6.htm?chan=search

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© Wiley 2010

..and Long Life?http://www.businessweek.com/magazine/content/04_35/b3897017_mz072.htm?chan=searchhttp://www.businessweek.com/magazine/content/04_35/b3897017_mz072.htm?chan=search

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Chapter 6 Highlights SQC refers to statistical tools t hat can be sued by quality

professionals. SQC an be divided into three categories:traditional statistical tools, acceptance sampling, and

statistical process control (SPC). Descriptive statistics are sued to describe quality

characteristics, such as the mean, range, and variance. Acceptance sampling is the process of randomly inspectinga sample of goods and deciding whether to accept orreject the entire lot. Statistical process control involvesinspecting a random sample of output from a process anddeciding whether the process in producing products withcharacteristics that fall within preset specifications.

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Chapter 6 Highlights -

continued Two causes of variation in the quality of a product or process:

common causes and assignable causes. Common causes of variationare random causes that we cannot identify. Assignable causes of variation are those that can be identified and eliminated.

A control chart is a graph used in SPC that shows whether a sample of data falls within the normal range of variation. A control chart hasupper and lower control limits that separate common from assignablecauses of variation. Control charts for variables monitor characteristicsthat can be measured and have a continuum of values, such as height,

weight, or volume. Control charts fro attributes are used to monitorcharacteristics that have discrete values and can be counted.

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continued Control charts for variables include x-bar and R-charts. X-

bar charts monitor the mean or average value of a product characteristic. R-charts monitor the range or dispersion of

the values of a product characteristic. Control charts forattributes include p-charts and c-charts. P-charts are usedto monitor the proportion of defects in a sample, C-chartsare used to monitor the actual number of defects in asample.

Process capability is the ability of the production processto meet or exceed preset specifications. It is measured bythe process capability index Cp which is computed as theratio of the specification width to the width of the processvariable.

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continued The term Six Sigma indicates a level of quality in

which the number of defects is no more than 2.3parts per million.

The goal of acceptance sampling is to determinecriteria for the desired level of confidence.Operating characteristic curves are graphs that show the discriminating power of a sampling plan.

It is more difficult to measure quality in servicesthan in manufacturing. The key is to devisequantifiable measurements for important servicedimensions.

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© Wiley 2010

The End Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.

Reproduction or translation of this work beyond that permittedin Section 117 of the 1976 United State Copyright Act without the express written permission of the copyright owner isunlawful. Request for further information should be addressedto the Permissions Department, John Wiley & Sons, Inc. Thepurchaser may make back-up copies for his/her own use onlyand not for distribution or resale. The Publisher assumes noresponsibility for errors, omissions, or damages, caused by theuse of these programs or from the use of the informationcontained herein.

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