Biermann Ch. Handbook of Pulping and Papermaking

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404

19.

CARBOHYDRATE CHEMISTRY

CHO

—

-c

—

H — C - OH

H - 0 - OH

CH2OH

D—glucose

0-1 CHO

C-2 H - C - OH

C-3 HO-C-H

C-4

- C — OCH,

C-5 H - C — OH

C-6

COOH

4-O-methyl-D-glucuronic acid

Fig. 19-1. Some examples

hexoses.

HO-

H-

H -

CH«OH

1 •^

C = 0

•C-H

•C—OH

•C-OH

CH2OH

D—fructose

groups coming towards the viewer. Vertical lines

represent bonds going into the plane of the paper.

Although these models force the carbon backbone

to be curved,

it is

projected onto the plane

the

paper

flat. Carbon atoms

are

numbered con-

secutively from

the top

down. When

n is the

number

carbon atoms, aldoses have

minus

and ketoses have

minus

chiral (asymmetric)

substituted carbon atoms.

glucose these

are

carbon atoms

C-2, C-3, C-4, and C-5. The

stereochemistry

the chiral carbon farthest from

the anomeric carbon determines whether

not

monosaccharide

designated

as D or L; in the

case

glucose this

is the

C-5.

the hydroxyl

group on this carbon is on the right of the Fischer

projection, then

represents

D-series;

if the

hydroxyl group

is on

the left,

represents

L-

series. Most naturally occurring monosaccharides

are members

the D-series. Notable exceptions

CHO

H - C - OH

HO-C-H

- C - OH

H - C - OH

CH2OH

CHO

HO-C-H

- C - OH

HO-C-H

CH2OH

CHO

CH2OH

D-glucose

L-glucose

D-glucose

Fig. 19-2. Fischer projections

and

ball-and-

stick form

D-glucose.

are arabinose, fucose, rhamnose,

and

iduronic

acid. Since aldohexoses have four chiral carbons

there

are 2^ (or 16)

possible neutral mono-

saccharides, eight

the D-series and eight

the

L-series. With ketohexoses there

are 2^ (or 8)

possibilities.

In solution, monosaccharides

do not

remain

as aldehydes and ketones, but form hemiacetal and

hemiketal bonds, respectively,

shown

Fig.

19-3.

In the case

aldoses, one

the hydroxyl

groups will attack the carbon atom of the carbonyl

group

give

a C-0

bond

hemiacetal);

the

carbon oxygen double bond

the aldehyde

be-

comes

C-OH group. (The mechanism is proton-

ation

the oxygen

the carbonyl group; attack

of the carbonyl carbon atom by

hydroxyl group

which transfers the positive charge to the attacking

hydroxyl group; loss

of a

proton by the attacking

hydroxyl group leading

the cyclic form.)

Usually

five-member ring (sifuranose)

or a

six-member ring

pyranose)

formed, which

means that the hydroxyl group

the

C-4 or the

C-5,

respectively, will react with

the

aldehyde

group. The pyranose form

more common than

the furanose form, especially

polysaccharides.

With some monosaccharides, both pyranose

and

ftiranose forms exist

equilibrium.

Since stereochemistry

introduced

at the

aldehyde carbon atom (i.e.,

becomes asymmet-

ric),

there

are

two possible products, which

are

called anomers, for the pyranose or furanose.

The

carbon atom

the aldehyde

ketone

termed

the anomeric carbon atom.

The

equilibrium

FORMS OF MONOSACCHARTOES 405

between these possible forms depends on the

stereochemistry of the monosaccharide (i.e., glu-

cose is different from mannose, etc.), the compo-

sition of

the

solution and solvent, and the tempera-

ture of the solution.

The cyclic forms of carbohydrates are often

represented by Haworth projections. In fact,

pyranoses actually exist in a shape somewhat more

complicated than the Haworth projection indicates.

These shapes are chair conformations of which

there are two possibilities. The chair form with

the most bulky groups in the equatorial position is

greatly favored. The Haworth projection is a

convenient approximation of

the

chair form to use.

Fig. 19-3 shows the Fisher projections, the corre-

sponding Haworth projections, and the favored

chair conformations of the two anomers of gluco-

pyranose. a-Glucopyranoside is represented with

the anomeric OH group down in the Haworth

projection (trans to the terminal CH2OH), and B-

glucopyranoside is represented with the anomeric

OH group in the down position. Any group that

is on the right in the Fischer projection is project-

ed down in the Haworth projection.

The acid- or based-catalyzed conversion of

one anomer into its equilibrium mixture of

anomers is called

mutarotation

and is accompanied

by change in the optical rotation. (Carbohydrates,

like any compound containing asymmetric atoms,

cause plane polarized light to rotate when passed

through a solution of the carbohydrate; while this

phenomena provides an important tool to carbo-

hydrate chemists, it is not of particular signifi-

cance to the pulp and paper field.) The equilibri-

um mixture of glucose in dilute aqueous solution

at 20''C is about one-third in the a-glucopyranose,

two-thirds in the B-glucopyranose form, and much

less than

1 %

in the acyclic and furanose forms.

More complex carbohydrates occur in nature

when two or more simple sugars are linked to-

gether. In nature, the linkages are glycosidic

linkages, that is, acetal or ketal bonds involving

the anomeric carbon of at least one of the mono-

saccharides involved. These bonds are known as

glycosidic linkages and allow the formation of

dimers, trimers, tetramers, and so forth of mono-

saccharides termed disaccharides, trisaccharides,

tetrasaccharides, etc. In general, any compound

containing a glycosidic linkage may be termed a

H-

HO-

H-

H -

(

-C-

-OH

-H

-OH

-0

HO—C—H

C H

Fischer projections

HO OH.

- C - H

- C - OH

-C-0—

CH^OH

HO OH.

OH Howorth projections

CHoOH

1 ^^n^vjn Q

Chair confornnations

a-D-glucopyranose

/?-D-glucopyranose

Fig. 19-3. The Fischer and Haworth projec-

tions and conformations of the two gluco-

pyranoses.

glycoside. Each glycosidic linkage is formed with

removal of a water molecule between the two

monosaccharides; this makes polysaccharides

condensation

polymers.

Glycosidic linkages of compounds in aqueous

solutions are subject to hydrolysis in the presence

of acid at reflux temperatures. Hydrolysis is the

breaking of a bond by the addition of a water

molecule across it. For example, hydrolysis of a

disaccharide would yield the original

monosaccharides. Carbohydrates with a degree of

polymerization (DP, number of monosaccharide

units) of more than eight units are considered

polysaccharides. Sucrose (table sugar) and malt-

ose are examples of disaccharides; cellulose and

starch are examples of polysaccharides.

A glycosidic linkage involving the anomeric

OH of an aldose is called an acetal linkage; if the

anomeric OH of a ketose is involved, the bond is

406 1^- CARBOHYDRATE CHEMISTRY

CH,

CH.

OCH.

4-0-(a-D-glucopyranosyl)--D-glucose

(maltose)

Fig. 19-4. Two examples

glycosidic linkages.

-0-methyl-/8-D-glucopyranoside

a ketal.

The

anomeric OH group may also react

with an ROH group in general. The reaction with

methanol produces

methyl glycoside,

the

reac-

tion with phenol produces

phenyl glycoside,

and

so forth. Once

glycosidic linkage

formed

it is

usually fairly stable; however, glycosidic linkages

of glycosides

aqueous solutions

may

often

cleaved quantitatively by acid-catalyzed hydrolysis

at reflux temperatures

or by the use of

specific

enzymes known as glycosidases.

Fig.

19-4 shows

some examples

glycosidic linkages.

19.4 SELECTED REACTIONS OF

CARBOHYDRATES

Acid-catalyzed hydrolysis

was

discussed

Section 19.3. Anthraquinone (Section 3.6) causes

oxidation

cellulose reducing

end

groups

and

thereby protects

against

the

alkaline peeling

reaction.

Acid hydrolysis

Acid hydrolysis becomes important

in the

pulp

and

paper industry whenever

process

wood fibers below pH

2 or so at

elevated temper-

atures.

Let us

consider some examples

acid

hydrolysis.

one treats cellulose (which has been

swelled

in 72 % w/w

sulfiiric acid

room tem-

perature) with

6 % w/w

aqueous sulfiiric acid

under reflux, glucose is obtained in high yield with

little secondary decomposition (Fig. 19-5).

If polysaccharides are treated with strong acid

such

20% sulfiiric acid

high temperatures,

they

are

first hydrolyzed

to the

component

monosaccharides.

The

monosaccharides then

undergo decomposition reactions. Under these

conditions, fiirfiiral can

produced near-quanti-

tatively from pentoses or pentosans (polymers

pentoses such

xylan,

polymer

xylose)

if it

is distilled from the solution as

it is

formed.

(The

fiirfiiral can

measured colorimetrically with

addition

suitable reagents,

and

this

was an

important method

for

determination

pentoses

and pentosans

in the

older literature.)

The

reac-

tion

hexoses,

polymers

hexoses such

cellulose, starch, and glucomannans, produces

(hydroxymethyl)-2-fiirfiiral that

not volatile and

undergoes decomposition

levulinic acid

and

numerous other compounds. These reactions

are

summarized

Fig.

19-6.

6% H2SO4

reflux,

4 h

D-glucose

CH,

\jf>jnoO

D-glucose

(ra98%)

6% H2SO4

reflux,

4 h

cellulose

D-glucose

(0^5%)

Fig. 19-5. Dilute acid hydrolysis

glycosidic

linkages.

SELECTED REACTIONS OF CARBOHYDRATES 407

CHO

H - C -

- H

H — C

—

CH2OH

D-xylose

(or xylons)

CHO

- C - OH

 C  H

 C  OH

CH2OH

25%

H2SO4

reflux

(co98%)

2-furaldehyde

25%

H2SO4

reflux

HOCH^

/ .r

(<^^0%)

5-(hydroxymethyl)-

2-furaldehyde

D-glucose

(or cellulose)

Fig. 19-6. Decomposition of carbohydrates by

strong acids.

Reduction

One can reduce the reducing end of mono- or

polysaccharides by using sodium borohydride

(NaBH4) under alkaline conditions at room temper-

ature. NaBH4 must be used under alkaline condi-

tions as it decomposes by reacting with protons.

This reaction is important because it stops the

alkaline peeling reaction of cellulose. While

NaBH4 is too expensive to use commercially, it is

has been an important tool to investigate the

CHO

H ~

HO-

C-H

H - 0 -

CH2OH

D-glucose

(R=H)

Cellulose (R=polyglucose)

NaBH.

OK"

CH^OH

- C -

HO-C-H

- C -

CH2OH

D—glucitol

Protected end group

Fig. 19-7. Reduction of the reducing end of a

carbohydrate.

alkaline peeling reaction. The reduction of glu-

cose and cellulose is shown in Fig. 19-7.

Reactions with alkali

Under conditions of

dilute

alkali (perhaps 0.1

M NaOH at 100°C) monosaccharides (and the

reducing group of polysaccharides) will slowly

undergo a reaction that causes C-2 epimerization

(a change in configuration of the second carbon

atom) as shown in Fig. 19-8. The reaction is not

of any significance to the pulp and paper industry.

Under conditions of fairly concentrated alkali

(«1 M NaOH above «80°C), polysaccharides

undergo several important degradation reactions.

These reactions are important during kraft pulping,

alkaline sulfite pulping, alkali extraction during

bleaching, and other pulping and bleaching opera-

tions conducted at elevated temperatures and pH

because they degrade cellulose and hemicelluloses.

CHO

H - C - OH

HO-C-H

H - C - OH

CH2OH

dilute 0H~

CHO

H - C - OH

HO-C-H

H - C - OH

CH2OH

D-glucose

CHO

HO-C-H

H-C-OH

H - C - OH

CH2OH

D-mannose

<Sc

CH9OH

C^O

HO-C-H

H - C - OH

CH2OH

D-fructose

Fig. 19-8. C-2 epimerization of glucose with dilute alkali.

408 19. CARBOHYDRATE CHEMISTRY

The first reaction is random cleavage where some

glycosidic linkages anywhere along the chain are

broken. Alkali cleavage is not nearly as effective

as acid hydrolysis at reducing the chain length;

however, a relatively few breaks in the cellulose

chain greatly decreases its average degree of poly-

merization. This, in turn, greatly diminishes fiber

strength. Oxygen increases this reaction so air

should be excluded from the digester; however,

magnesium ion helps protect cellulose during

oxygen bleaching.

The second reaction is the alkaline peeling

reaction. The reaction is summarized in Fig. 19-9

and the mechanism is given in Fig. 19-10. The

peeling reaction will typically cleave 50 to 100

glucose units from the reducing end of cellulose

until another reaction occurs, the stopping reac-

tion,

which leaves the reducing end of cellulose as

a carboxylic acid not subject to the alkaline peel-

ing reaction.

Each time a RO" acts as a leaving group it

quickly abstracts a proton from solution to give

ROH, another reducing end which is capable of

undergoing the peeling reaction. When the stop-

ping reaction occurs, that particular reducing end

is protected from further cleavage of glucose units;

however, random alkali cleavage does expose new

reducing end groups.

The peeling reaction decreases the yield of

fiber from kraft cooks but does not affect the

cellulose viscosity to an appreciable extent. Imag-

ine a cellulose chain containing at least 1000

glucose molecules. If 50 of these are removed as

isosaccharinic acid, the DP has gone from 1000 to

950,

a relatively small change for chain length.

However, the yield will decrease by 50/1000 or

5%,

which is 50 tons per day for a mill that pro-

duces 1000 tons per day; this corresponds to

something on the order of $25,000 a day or $9

million per year. Also, the carboxylic acids that

are formed deplete the alkali in the pulping liquor

increasing the amount of alkali required and put a

higher load on the recovery system.

Anthraquinone (described at the end of

Section 3.6) is used to decrease the peeling reac-

H — C — OH

HO —

C — H

- C -

H — 0 — OH

CH2OH

cone OH

Various

organic

acids

D—glucose (R = H) or

Cellulose (R = glucose chain)

Fig. 19-9. Conversion of D-glucose (R = H) or

cellulose (R = glucose chain) to organic acids

with strong alkali.

tion by oxidation of the reducing group of

cellulose. Polysulfide pulping (page 90) can be

used to oxidize the reducing end of cellulose too.

Both of these methods increase the pulp yield from

1 to

3%;

for example, from 50% to

51-53%

yield.

Summary of reactions of carbohydrates

Table 19-1 is a summary of acid and base

degradation reactions of

carbohydrates.

It includes

the reaction of NaBH4 that protects against the

alkaline peeling reaction.

Holocellulose isolation

Holocellulose from wood or high yield pulps

is isolated from lignin in the laboratory by the

reaction of chlorine dioxide. Chlorine dioxide is

produced directly in the pulp slurry by the follow-

ing reaction:

NaClOs + HAc -^ CIO2

This procedure allows the viscosity of cellu-

lose in high yield pulps to be measured where

lignin would otherwise interfere. It is also an

effective tool for isolating holocellulose for further

studies since the holocellulose is not degraded

appreciably during the isolation procedure.

o o

g O O X

^T"

II II 1

o—o—o—o-

s §

' X

-o ~o

o -

tt: X -

3- X O O §

1 j 1 <N

X ' ' ' X

-o—o—o—o~o

II 11

3-^ II

o ~o —o =o-

1 1

1 i

O X

o^l r\^l

o —o =o —o-

1 1 1

X O X

-o -

- o

o II

—

X O

I I

X X

o —o =o.

o —o

—

I I

^ X

LxJ

LiJ

LxJ

«J

1 1 *

T- Ql

§ O X O

^^ II /-I 1

o ~o —o ~o-

1 i

1 1

O X

^x a:

(O X O

V ^' 1 1

o—o—o—o-

i ' ' '

-*- X o X

-o

o =o o

•

o—o

^':>

^11

410 19- CARBOHYDRATE CHEMISTRY

Table 19-1. Summary of products when model carbohydrate compounds are treated under various

conditions.

sugar

xylose

glucose

maltose

phenyl-D-

glucoside

strong OH"

acids

no reaction

weak OH'

C-2 epimers

C-2 epimers on

reducing end

no reaction

weakH"^

no reaction

glucose

glucose,

phenol

strong

H"^

furfural

HMF, etc.

phenol,

HMF, etc.

NaBH4

xylitol

glucitol

4-0-gluco-

glucitol

no reaction

EXERCISES

Explain how sodium borohydride stabilizes

cellulose and hemicelluloses. (From what

does it stabilize these polysaccharides?)

What is a hexose? What is a pentose?

What is the difference in structure between

cellulose and the backbone of starch? How

does this affect their physical properties?

If you are given a polysaccharide and want to

isolate its monosaccharide constituents for

subsequent analysis, what sort of treatment

will you subject it to?

Does one usually measure the viscosity of

cellulose in mechanical pulps? Why or why

not?

How does anthraquinone increase pulp yield

during alkaline pulping methods?

TOTAL QUALITY MANAGEMENT

20.1 INTRODUCTION TO TQM AND SPC

Introduction

When speaking about quality control it is

important to know the background of the key

people behind developments in this field. Three

people from Bell Telephone Laboratories, W. A.

Shewhart, H. F. Dodge, and H. G. Roming, con-

tributed much to statistical quality control (SQC)

during its early years in the 1920s.

Dr. W. Edwards Deming is considered to be

the originator of

total

quality management (TQM),

which includes management philosophy and style

along with statistical process control. By the end

of the 1930s Deming (1938) had written a book,

helped edit one (Shewhart, 1939) about statistical

analysis in regard to quality control, and began

working for the U.S. Census Office. During

World War II quality control rose to prominence

and with it, the work of

Deming.

In the 1950s his

ideas on how companies should manage their

people and processes were not widely accepted by

American management. He took his ideas to

Japan, where he started by assisting with their

census, and is credited with helping that country

become highly successful in industry. TQM has

two important elements to it: a management

philosophy (the human aspect) and methods of

process control (the process aspect).

Philip B. Crosby has contributed much to the

terminology and economic analysis of investments

in quality improvement. Dr. Joseph M. Juran

contributed to the organization methodology to

implement and support project improvement.

Juran

(1951,

1962) believed that inspection of the

final product is not an efficient or successful

method of making high quality products. Instead,

inspection of materials and methods should be

made throughout the process. Quality should not

be stamped on the product as the last step but

should be incorporated throughout the process.

One can discuss quality at length without

defining it, but trying to achieve quality control

means specific goals must be kept in mind.

Quality has many facets. One of the most obvious

in paper products is product variation. It is

always desirable to make one*s product in a

rehable and consistent manner. It is said that the

color of your paper is not as important as making

it the same color all the time. Quality is also the

suitability of a product for its intended purpose.

Another aspect is the cost. One can always make

a quality product if money is no object; however,

a quality product that few can afford does very

little good unless you are contracting for the

government.

Total quality

management,

TQM

Total quality management involves more than

just statistical process control, which is not a

management style, only a tool. This aspect of

TQM is considered separately.

GOAL/QPC, an organization of proponents

and practitioners of TQM in the U.S., defines

TQM as "a structured system for creating organi-

zation-wide participation in the planning and

implementation of a continuous improvement

process that exceeds the needs of the customer.

Deming (1982) has 14 points of management

covering aspects of purpose, quality in products,

eliminating waste, error and inefficiency, improv-

ing methods, removing fear in the workers, com-

munication between departments, and implement-

ing education and self-improvement programs.

Deming points out that you pay for mistakes

twice: once to make them and once to correct

them. If you have 10% of your workers rework-

ing products, that means 20% of your workforce

is making and correcting mistakes. Deming also

has a list of 66 questions in Chapter 5 to help

managers understand their responsibilities.

Managers should allow workers to work

together in teams throughout this process. An

important aspect of

this

is two way communication

between all parties with a sincere desire to work

together, not just hand down orders.

TQM assumes that, given the chance, work-

ers (or suppliers) will perform best when they

know and understand the company or process

goals.

Productivity should not be enforced by

411

412 20. TOTAL QUALITY MANAGEMENT

rules,

regulations, monitoring, performance stan-

dards,

and other degrading methods. Arbitrary

standards, personnel evaluations, and other humili-

ating tools should not be used to increase produc-

tion and efficiency from workers. One might

summarize these aspects of TQM as "you catch

more flies with honey that with vinegar.

With paper, there are intrinsic tradeoffs in

quality. Choices are made about which properties

must be decreased in order to improve others.

For example, for any type of paper, there is

always a choice between tensile and tear strengths.

Improving one means decreasing the other.

However, once a choice is made, the tools of

TQM and SPC can be used to maintain the pro-

cess,

reduce variation, and improve efficiency.

Deming

's 14

points for

management

Deming (1982) presents 14 points for man-

agement in his classic work. They are presented

here in concisely with examples relating to the

pulp and paper industry, but Deming's work must

be used to get the full meaning of them.

Constancy of purpose to improve. The

purpose of a paper company is to make high

quality paper in an efficient manner with little

waste. Teams of employees should always be on

the lookout to make the process better, especially

with communication between and among all levels.

New philosophies. The pulp and paper

world is a much different place than it was in the

past. Management must now compete interna-

tionally and use present circumstances.

Cease inspection as the means to quality.

Quality should not be stamped on the product at

the end, but built into the entire system so that

quality is insured, not just a matter of chance.

4. Do not consider the lowest price as the

ultimate bargain. For example, "Sawmill A" may

sell wood chips at $85 per bone dry unit while

"Sawmill B" sells wood chips at $90 per ton.

"Mill A", however, has 1% more bark, 2% more

fines,

and 6% more pin chips and actually costs

$10 per ton extra to process. Develop long-term

relationships of loyalty and trust with suppliers

rather than jumping around from supplier to

supplier to try to save a dollar.

When selecting a supplier for a part that is

part of a larger assembly, it is wise to let the

supplier help in the design

process,

rather than just

making specifications that later need to be altered

at great expense.

Always be looking for methods of improv-

ing the process. Process improvement does not

necessarily mean buying new equipment. Often

the present equipment can be improved or used

more efficiently. The relative amounts of varia-

tion by each component of a system must be

identified to determine if an improvement (such as

new equipment) will actually mean a benefit. For

example, it may be useful to work with chip

suppliers to decrease the amount of overthick chips

rather than purchase an additional chip slicer.

It should be clear that putting out fires should

be only a minor component of the process

engineer's time. In the pulp and paper industry,

however, it tends to be a major portion of the

engineer's time. If more time were spent on

improving the process, then little time would be

spent on fighting fires. Unfortunately, the argu-

ment is that there is no time to work on the pro-

cess because of all the fires to fight. This is only

short-term thinking and, in the long run, will lead

to ruin.

6. Use on the job training. On the job

training is very successful since the tools being

taught are immediately put to use. Deming says

"the greatest waste in America is failure to use the

abilities of people.

Leadership. The goal of leadership

should be to help people and machinery do a

better job. To merely demand increased produc-

tivity without improving the process will lead

nowhere. If management spends its time supervis-

ing workers, then there are two people doing the

same job.

8. Drive out fear. Setting production goals,

other quotas, and demands of zero-defect strongly

imply "punishment" if they are not met. If one

shows people how to do a good job, or improves

the process so a good job can be done, quality and

production will automatically improve. Manage-

ment should not assume the worker is failing, the

failure may be attributable to the manager.

INTRODUCTION TO TQM AND SPC 413

Break down

barriers

between departments

internally,

and

customers and suppliers

externally.

Chip suppliers must know what a pulp mill is

looking for in wood chips and why it is important

to the pulping process. Management must also

promote internal teamwork.

10, Do not use slogans, work targets, and

exhortations

to try to

increase quality

and produc-

tion.

These techniques lead to fear by implied

consequences as described in (8) above. Further-

more, if the system was capable of higher produc-

tivity as is, why isn't that level of productivity

already being achieved?

11.

Do not manage by objectives, but by

leadership. As in (10), to demand more produc-

tivity is not as useful as showing people how the

process or testing methods can be modified to

achieve higher productivity.

12,

Remove

barriers that rob people of pride

in workmanship. One barrier is the annual merit

rating. Often the letter of the "law" is followed

without the spirit of the "law" so that compliance

may appear to be occurring, but in fact is not.

Workers must not feel that they are only following

orders, but that they are in control of the situation

and responsible for the final product.

13,

Make

education

and

self-improvement

goal. People who are challenged and see growth

in themselves will enjoy their jobs more and

perform better in the long run.

14. Everyone is involved in the

transforma-

tion of the company. Accomplishments are the

result of team effort. This reduces duplication of

effort and allows different departments to interact

more successfully.

20.2 STATISTICAL PROCESS (QUALITY)

CONTROL, SPC, SQC

Introduction

Statistical process control (SPC) or statistical

quality control (SQC) involves data collection and

analysis, modeling of systems, problem solving,

and design of experiments. I like to summarize

SPC as the application of elementary statistical

analysis to control a process. It is the scientific

method applied to manufacturing. Shewhart

(1939) made the following comparison:

Mass

Production

Specification

Production

Inspection

Scientific Method

Hypothesis

Experiment

Test of Hypothesis

Statistical analysis

Statistical analysis of the process is a key part

of SPC since it is crucial to determine what is

random variation and what is nonrandom variation

that can be controlled. Anyone who wants to

implement SPC must understand elementary

statistics, experimental design, and sampling tech-

niques. There are many good books on statistical

analysis so there is little point including all this

information here, but some basic statistical equa-

tions are included later. When using statistical

analysis, the underlining assumption is that all of

the variation is random. SPC tools must be devel-

oped when the process is in control and there are

no trends in the data. (This does not mean all of

the product will be satisfactory, only that the

operator is doing the best that he/she can with the

equipment.) This is not always easily done since

an apparent trend in the short run could be due to

statistical fluctuation. Steps can be taken to de-

crease the random variation so that "actual"

changes can be observed more easily.

Most aspects of statistical analysis

common

use assume that statistical deviation follows the

normal

distribution,

which is symmetrical and has

a bell-shaped curve as shown in Fig. 20-1. Many

statistical equations are only applicable to this

distribution. Most measurements have variations

that follow the normal distribution. Some, howev-

er, such as the time between failures, follow other

distributions. These other distributions can be

predicted, but require tools generally found in

advanced simulation or statistical analysis text-

books.

EXAMPLE 1. What is the probability that a

sample from a normal distribution will be 1 or

more standard deviations less than the mean?