tabulation · 2019-09-09 · wedel, gregory supplier - equipment affirmative wells, philip...

TABULATION STANDARD-SPECIFIC INTEREST GROUP BALLOT OFFICIAL TEST METHOD OR STANDARD PRACTICE DATE: 9/4/19 Please return report to: Standards Department TAPPI TO: Ian A. Journeaux DUE DATE: N/A 15 Technology Parkway South

Working Group Chairman Peachtree Corners, GA 30092 [email protected] RE: T 545, WI 150404.01, Draft 2 SARG FAX: (770) 446-6947 The results of the SSIG ballot of the subject document are as follows: AFFIRMATIVE 10 NEGATIVE 0 ABSTENTION 0

10 ballots returned = 77% / 100% affirmative; Standard may proceed to SARG after resolution of comments and negatives

No comments received. Standard is being balloted for the SARG. X Copies of comments from the SSIG ballots are attached.

Please review and return this form with recommendations and dispositions of comments and negatives, along with your MARKED UP COPY for preparation of the next ballot. DO NOT RE-TYPE.

Please indicate whether the method is to be: re-balloted to the SSIG,

_____or balloted for the SARG.

RECOMMENDATIONS AND DISPOSITIONS OF COMMENTS AND NEGATIVES: (MUST be in BLACK or RED ink for reproduction)

Minor editorial corrections incorporated into Draft 2. Standard ready for SARG

❐ Continuation on attached sheet(s)-PLEASE DO NOT WRITE ON REVERSE

Your completion of this form constitutes the working group chairman's report. Please send copies of your resolution of comments to those SSIG members who made comments. This form and attachments should be returned to the Standards Department. WORKING GROUP CHAIRMAN

Signature Date

Option # VotesAffirmative 10Negative 0Abstention 0

TOTAL VOTES RECEIVED 10

Total Members of SSIG 13Percent return 77%Votes received 10Total votes minus abstentions 10Percent affirmative 100%

Voter Name Interest Category VoteCrawshaw, Dennis Producer AffirmativeEisert, Eric Producer AffirmativeFigiel, Kerry Producer AffirmativeFrank, Benjamin Producer AffirmativeJourneaux, Ian Producer AffirmativeMcDevitt, Neal Producer AffirmativeReese, Richard Consultant AffirmativeTrotter, Janice General Interest AffirmativeWedel, Gregory Supplier - equipment AffirmativeWells, Philip Consultant AffirmativeChen, Shih-Chin Supplier - equipment Did not voteLin, Lang-Dong Educator Did not voteSutman, Frank Supplier - chemicals/raw materials Did not vote

T 545 - Draft 2, due Sunday, January 20, 2019

Voting Summary by Option

Voting Statistics

Voting Details

Name Subject Comment

Neal McDevitt

Typo

My memory of the sigma notation uses an equal mark under the Sigma, like on the two found in the Residual row. I’m not sure if the “k-1” and “i-1” usages that I’m not aware of, or if they are typo’s. (In the old photocopied version of the standard, there was an “=”, not a “-“ but the copy is fuzzy.)


Voter Comments Collected During Ballot Voting

One editorial comment received for this ballot

Comments were addressed by WGC and incorporated into the

Draft.

Interest Category Affirmative Negative Abstention Not ReturnedQt. %

Consultant 2 0 0 0 2 15.4%Educator 0 0 0 1 1 7.7%General Interest 1 0 0 0 1 7.7%Producer 6 0 0 0 6 46.2%Supplier - chemicals/raw materials 0 0 0 1 1 7.7%Supplier - equipment 1 0 0 1 2 15.4%Total 10 0 0 3 13 100.0%

Total


Voting Summary by Voter Interest Category

NOTICE: This is a DRAFT of a TAPPI Standard in ballot. Although available for public viewing, it is still under TAPPI’s copyright and may not be reproduced or distributed without permission of TAPPI. This draft is NOT a currently published TAPPI Standard. WI 150404.01

T 545

DRAFT NO. 02

DATE December 6, 2018 WORKING GROUP CHAIRMAN Ian Journeaux SUBJECT CATEGORY Water Removal RELATED

METHODS See “Additional Information”

Approved by the Standard Specific Interest Group for this Test Method TAPPI

CAUTION: This Test Method may include safety precautions which are believed to be appropriate at the time of publication of the method. The intent of these is to alert the user of the method to safety issues related to such use. The user is responsible for determining that the safety precautions are complete and are appropriate to their use of the method, and for ensuring that suitable safety practices have not changed since publication of the method. This method may require the use, disposal, or both, of chemicals which may present serious health hazards to humans. Procedures for the handling of such substances are set forth on Material Safety Data Sheets which must be developed by all manufacturers and importers of potentially hazardous chemicals and maintained by all distributors of potentially hazardous chemicals. Prior to the use of this method, the user must determine whether any of the chemicals to be used or disposed of are potentially hazardous and, if so, must follow strictly the procedures specified by both the manufacturer, as well as local, state, and federal authorities for safe use and disposal of these chemicals.

Cross-machine grammage profile measurement

(gravimetric method) (Five-year review of T 545 om-11)

(Draft 2 contains revisions made in Draft 1. This version of Draft 2 shows all the changes made.)

1. Scope

1.1 This method describes a procedure which can be applied to determine the variation in mass per unit

area in the cross-machine direction, commonly referred to as the grammage (or basis weight) profile. This method is

appropriate for the acceptance testing of both the papermaking process and the product.

1.2 This method is laborious, but it is reliable and accurate. It requires simple, well-defined operations:

cutting out samples, weighing samples, and data evaluation.

Formatted Table

T 545 om-11 Cross-machine grammage profile / 2 measurement (gravimetric method)

1.3 The general procedures outlined in TAPPI T 410 “Grammage of Paper and Paperboard (Weight Per

Unit Area)” and in TAPPI T 402 “Standard Conditioning and Testing Atmospheres for Paper, Board, Pulp Handsheets,

and Related Products” are used as basic references for this method.

2. Summary

The cross-machine grammage (basis weight) profile is determined by sampling 20 consecutive cross-machine layers

from the outer layers of a parent reel, preconditioning the samples, cutting the layers into a series of rectangular sheets

200 mm CD × 300 mm MD, discarding those sheets with obvious defects, conditioning the samples, and weighing the

samples. The sample weights are then analyzed using analysis of variance to determine the MD, CD, residual, and

total standard deviations.

3. Significance

The evaluation of grammage variation from measurements on cross-machine direction strips is a useful way to analyze

the performance of a paper machine. This method provides sufficient accuracy and repeatability to be used for

acceptance testing of the papermaking equipment and for product specification.

4. Definitions

4.1 Grammage, mass per unit area, expressed as grams per square meter (g/m2). The customary English

term is basis weight, expressed in pounds per ream, which must be defined, e.g., as 1000, 3000 or other appropriate

square footage.

4.2 Cross-machine direction, direction perpendicular to the running direction of the paper machine (CD).

4.3 Layer, single cross-machine direction strip of paper cut for grammage profile measurement.

4.4 Machine direction, direction parallel to the running direction of the paper machine (MD).

4.5 Mean, arithmetic average.

5. Apparatus

5.1 The apparatus required for this method is detailed in T 410:

5.1.1 Weighing device, readable and accurate to within 0.1% of the applied load.

5.1.2 Cutting device, having an attachment for ensuring parallelism of the opposite edges.

5.1.3 Scale, such as a finely graduated steel ruler reading in 0.5 mm, capable of measuring the dimensions

of the test specimen to an accuracy of 0.2%.

3 / Cross-machine grammage profile T 545 om-11 measurement (gravimetric method)


Fig. 1. Sampling of paper.

6. Sampling

6.1 Obtain the requisite samples in accordance with the guidelines of TAPPI T 400 “Sampling and

Accepting a Single Lot of Paper, Paperboard, Containerboard, or Related Product.”

6.2 Obtain 20 consecutive CD layers nominally 400 mm wide (MD) from the outer 100 layers of a parent

reel with a diameter of at least 1 m, as shown in Fig. 1.

6.3 These layers must be free from creases, wrinkles, folds, and tears.

6.4 Mark the corner of the front edge (tending side) “FS” (front side). Note the date, time, reel number,

and machine number. Mark the wire side of the sheet with “WS” (wire side).

6.5 Number each CD layer, in order, starting with a 1 at the outermost layer.

6.6 Carefully transfer the samples to a climate-controlled conditioning room. Avoid putting creases,

wrinkles, or corrugations in the sheets.

6.7 Depending on the purpose of the testing, it may be useful to obtain a copy of the grammage profile

which was displayed by the on-machine profile scanner just before the reel was completed.


6.8 Depending on the purpose of the testing, it may be useful to note any abnormal operating conditions

which occurred while this sample was being taken.

7. Test specimens

7.1 Precondition the test samples on the dry side in atmospheres in accordance with TAPPI T 402

“Standard Conditioning and Testing Atmospheres for Paper, Board, Pulp Handsheets, and Related Products.” Initial

drying can be accelerated using an oven.

7.2 Unroll the layers on a long, flat surface.

7.3 Carefully align the layers.

7.4 Calculate the number of samples to cut per layer and the amount to discard from each edge. Samples

will be adjacent and 250 mm wide. Discard 100 mm plus one-half of any remainder from each edge of the layer, as

shown in Fig. 2.


Fig. 2. Cutting test specimens from sample layers.

7.4.1 For example, a sheet width of 4600 mm would be divided as follows: The minimum discard would be

100 mm from each end, so the maximum test width would be 4400 mm. When divided into 250-mm widths, there

would be 17 full tablets and a 150-mm remainder. The 150-mm remainder should be divided so that both edge discards

are approximately the same width (175 mm). The difference in the width of the discard from one end should be less

than 50 mm of the width of the discard from the other end.

7.5 Cut the layers against a template into a series of tablets of 250 mm CD width x 400 mm MD length,

as determined above.

7.6 Label each sample with a pair of numbers. The first number shall designate the layer as numbered

from the outside and the second number shall designate the CD position as numbered from the front side.

7.7 Trim each tablet to a rectangle of 200 mm (CD) by 300 mm (MD) using a suitable knife, guillotine,

or paper cutter. The dimensions of the sampled sheets shall lie within ± 0.25% of the mean dimension, per T 410.

7.8 Examine each sample. Reject any sample which contains clearly visible lumps of slime, pitch, filler,

or similar defects within a total area greater than 1 cm2.

7.9 Reject any sheet that has holes in it with an area exceeding 1 cm2, as well as any sheets which have

been damaged such that the dimensions cannot be established within the prescribed degree of accuracy.


7.10 The grammage of any rejected sheet should be replaced by the average of its two most immediate

neighbors in the machine direction. Use the average grammage of the preceding two MD sheets if the sheet was

rejected from the top or the bottom of a tablet.

7.11 Abandon any test in which the total number of rejected sheets exceeds 3% of the total number of

sheets.

7.12 Separate the sheets into stacks no greater than 5 mm thick and allow the samples to be conditioned for

at least 24 hours as outlined in TAPPI T 402.

8. Procedure

8.1 Weigh each test specimen to within 0.1% in a climate-controlled atmosphere in accordance with T

402 and T 410.

8.2 Record the results in tabular form, using the format given in Table 1 as a guide. The results of each

layer are entered in order on successive lines.

9. Calculations

9.1 Use the common two-factor analysis of variance to evaluate the CD profile. A mathematical

description of this method can be found in most textbooks on statistics. A basic review can be found in some of the

references (1-6).

9.2 Equations describing the items in the variance analysis are given in Table 2.

9.3 Follow the equations listed in Table 2 and compute the sum of squares, the degrees of freedom, the

mean square, the F ratio, the systematic variance, and the standard deviation for the CD, MD, residual, and total

variations.

10. Report

10.1 List the grammage for each sample G(i,k) in Table 1 in g/m2 to three significant figures.

10.2 List the MD, CD, residual, and total standard deviations and the mean grammage of all points in g/m2

to three significant figures.

10.3 If desired, the results may also be reported in pounds for customary trade sizes.

10.4 List the MD and CD F ratios and the MD, CD, and residual degrees of freedom.

10.5 List in Table 1 the mean grammage of all MD samples at each CD position (G•k) in g/m2 to three

significant figures.


10.6 Note in Table 1 the maximum and minimum grammage at each CD position in g/m2 to three significant

figures.

10.7 Include a composite profile report displaying the mean grammage at each CD position (G•k) as a

function of the cross-machine position as shown in Fig. 3. The abscissa (or x axis) should be the cross-machine position

in mm with the front side located on the left. The ordinate (or y axis) can be in expressed as a deviation from the mean

grammage defined as:

Grammage deviation = (Gk - G)

or, as a percent deviation from the mean defined as:

Percent deviation = 100 × [(G.k - G) / G)]

10.8 Include on the composite profile report a plot of the minimum and maximum grammages, expressed

in grammage or percent deviation from the mean, as a function of the cross-machine position, as shown in Fig. 3.

10.9 List the MD, CD, residual, and total standard deviations and the coefficients of variation (CV)

100×=GsCV

100×=GsCV

and expressed in percentage with three significant figures.

Field Code Changed


Table 1. Measured grammage record table

Sample CD sample position

layer Front Back

number k = 1 2 3 4 n

i=1 G(1,1) G(1,2) G(1,3) G(1,4) .... G(1,n)

2 G(2,1) G(2,2) G(2,3) G(2,4) .... G(2,n)

3 G(3,1) G(3,2) G(3,3) G(3,4) .... G(3,n)

4 G(4,1) G(4,2) G(4,3) G(4,4) .... G(4,n)

5 G(5,1) G(5,2) G(5,3) G(5,4) .... G(5,n)

.... .... .... .... .... .... ....

.... .... .... .... .... .... ....

.... .... .... .... .... .... ....

.... .... .... .... .... .... ....

m G(m,1) G(m,2) G(m,3) G(m,4) .... G(m,n)

Mean G(•,1) G(•,2) G(•,3) G(•,4) .... G(•, n)

Minimum G(i,1) G(i,2) G(i,3) G(i,4) .... G(i, n)

Maximum G(i,1) G(i,2) G(i,3) G(i,4) .... G(i,n)

Note: m = 20 for this test method; n is dependent on the machine width.

NOTE 1: The (i, k) indices on the grammage G correspond to the sample layer number and the CD position number, respectively. For

example, G (3,5) represents the grammage of the sample taken from the third layer and located in the fifth position from the

front of the machine.

11. Precision

11.1 Repeatability of grammage test results within a laboratory = 0.94%, per T 410.

11.2 Reproducibility of grammage test results within a laboratory = 2.84%, per T 410.

11.3 The above values of precision are averages calculated from 18 reports of the TAPPI/NBS

Collaborative Reference Program for Paper. Each test result is an average for approximately 5000 cm2 of paper or

paperboard.

11.4 For the precision noted above, the repeatability of the standard deviations within a laboratory =

11.86%.

11.5 For the precision noted above, the reproducibility of the standard deviations between laboratories =

12.38%.


11.6 The values in items 11.4 and 11.5 are determined in accordance with the definitions of these terms in

TAPPI T 1200 “Interlaboratory Evaluation of Test Methods to Determine TAPPI Repeatability and Reproducibility.”

The results were obtained from round robin testing among seven laboratories. Three paper grades (Fine paper,

Corrugating medium and Newsprint) were tested in all seven laboratories.

12. Keywords

Basis weight, Variations, Cross direction, Profiles

13. Additional information

13.1 Effective date of issue: to be assigned.

13.2 The two-factor analysis of variance used in this test method assumes that there is no significant

MD−CD interaction. The F ratios and degrees of freedom listed in Table 2 can be used with standard statistics tables

to determine the level of confidence. Table 3 is typical, containing values of F for which the confidence level is 95%.

For example, if 26 CD samples are taken from each of the 20 sample layers, then the CD degrees of freedom would

be (26 - 1) (20 - 1) = 475. If the CD F ratio is greater than about 1.51, then there is greater than a 95% probability that

the CD variance is significant with respect to the residual (3).

0 1000 2000 3000 4000

-8

-6

-4

-2

0

2

4

6

Gra

mm

age

Varia

tion,

%

Front CD Position Back

Maximum Average Minimum


0 1000 2000 3000 4000

-8

-6

-4

-2

0

2

4

6G

ram

mag

e Va

riatio

n, %



Fig. 3. Composite profile report.

13.3 There are several additional statistical tools which can be used to analyze the profile data. These

methods can be used to identify and quantify stable ridges in the profile, rate the profile stability, and identify the

source of profile non-uniformities. These methods are discussed in the listed references (1-7).

13.4 In order to ensure the sheet samples are fully conditioned within 24 hours, the stacks of sheets in 7.12

should be no more than 5 mm thick.

13.5 ThisThe 2011 version was revised to correct an error in the calculation of the total variance.

13.6 The F-ratio referred to in Table 2 provides a way to test the significance of the MD and CD variability.

The F-ratio is a ratio of 2 different measure of variance for the data. If the null hypothesis (F-ratio > Fcrit from Table

2 is true then the CD or MD term contributes significantly to the overall variability. The reader is referred to rreferences

(1,3,7) provide for additional details.

Field Code Changed


Table 2. Equations for two-factor analysis of variance for cross-machine grammage variations

Direction Sum of Squares Degrees of Freedom Mean Sum of

Squares F-Ratio Systematic Variance

Standard

Deviation

CD

( )∑ −=•

n

1-kk

2CD GGmSS

( )∑ −=•

n

1-kk

2CD GGmSS

1-nDFCD = 1-nDFCD = CD

CDCD DF

SSMSS =

CD

CDCD DF

SSMSS =

MSS

MSS

RES

CD

MSS

MSS

RES

CD

mMSS-MSS

VRESCD

CD=

mMSS-MSS

VRESCD

CD=

CDCD V=σ

CDCD V=σ

MD

( )∑ −=•

m

1-ii

2MD GGnSS

( )∑ −=•

m

1-ii

2MD GGnSS

1-mDFMD =

1-mDFMD =

MDDFSS

MSS MDMD =

MDDFSS

MSS MDMD =

MSS

MSS

RES

MD

MSS

MSS

RES

MD

nMSS-MSS

V RESMDMD =

nMSS-MSS

V RESMDMD =

MDMD V=σ

MDMD V=σ

Residual

( )∑∑= =

•• +−=m

1i

n

1kki-ik

2RES GGGGSS

( )∑∑= =

•• +−=m

1i

n

1kki-ik

2RES GGGGSS

1)-1)(m-(nDFRES =

1)-1)(m-(nDFRES =

RES

RESRES DF

SSMSS =

RES

RESRES DF

SSMSS =

RESRES MSSV =

RESRES MSSV =

RES RES V=σ

RES RES V=σ

Total

( )∑∑= =

=m

1i

n

1kik

2TOT G-GSS

( )∑∑= =

=m

1i

n

1kik

2TOT G-GSS

1-nmDFTOT =

1-nmDFTOT =

TOT

TOTTOT DF

SSMSS =

TOT

TOTTOT DF

SSMSS =

TOTTOT MSSV =

RESMDCDTOT VVV V ++≅

TOTTOT MSSV =

RESMDCDTOT VVV V ++≅

TOTTOT V=σ

TOTTOT V=σ

CDCD MSSV m 100 systematic is that variationCD ofPercent = CDCD MSSV m 100 systematic is that variationCD ofPercent =

Formatted Table

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MDMD MSSVn 100 systematic is that variationMD ofPercent = MDMD MSSVn 100 systematic is that variationMD ofPercent =

k)(i, sample of GrammageG :where ik = k)(i, sample of GrammageG :where ik =

=•kG =•kG

∑=

=m

1iik )Position(k CDat Samples MD all ofMean G

m1

∑=

=m


m1

=•iG =•iG

∑=

=n

1kik )Position(i MDat Samples CD all ofMean G

n1

∑=

=n


n1

=G =G

∑∑= =

=m

1i

n

1kik samples all of grammageMean G

mn1

∑∑= =

=m

1i

n


mn1

=n =n Number of CD samples in an MD strip

=m =m Number of MD strips

Field Code Changed

Field Code Changed

Field Code Changed

Field Code Changed

Field Code Changed

Field Code Changed

Field Code Changed

Field Code Changed

Field Code Changed

Field Code Changed


Table 3. F-distribution, 95% confidence type.

\ 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ 1 161 200 216 225 230 234 237 239 241 242 244 246 248 249 250 251 252 253 2542 18.5 19.0 19.2 19.3 19.3 19.3 19.4 19.4 19.4 19.4 19.4 19.4 19.5 19.5 19.5 19.5 19.5 19.5 19.53 10.1 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.74 8.70 8.66 8.64 8.62 8.59 8.57 8.55 8.534 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.635 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.62 4.56 4.53 4.50 4.46 4.43 4.40 4.36

6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.00 3.94 3.87 3.84 3.81 3.77 3.74 3.70 3.677 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.57 3.51 3.44 3.41 3.38 3.34 3.30 3.27 3.238 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.28 3.22 3.15 3.12 3.08 3.04 3.01 2.97 2.939 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.07 3.01 2.94 2.90 2.86 2.83 2.79 2.75 2.7110 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.91 2.85 2.77 2.74 2.70 2.66 2.62 2.58 2.54

11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.4012 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.3013 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.60 2.53 2.46 2.42 2.38 2.34 2.30 2.25 2.2114 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.53 2.46 2.39 2.35 2.31 2.27 2.22 2.18 2.1315 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.48 2.40 2.33 2.29 2.25 2.20 2.16 2.11 2.07

16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.42 2.35 2.28 2.24 2.19 2.15 2.11 2.06 2.0117 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.38 2.31 2.23 2.19 2.15 2.10 2.06 2.01 1.9618 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.34 2.27 2.19 2.15 2.11 2.06 2.02 1.97 1.9219 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.8820 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.28 2.20 2.12 2.08 2.04 1.99 1.95 1.90 1.84

21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.25 2.18 2.10 2.05 2.01 1.96 1.92 1.87 1.8122 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.23 2.15 2.07 2.03 1.98 1.94 1.89 1.84 1.7823 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.20 2.13 2.05 2.01 1.96 1.91 1.86 1.81 1.7624 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.18 2.11 2.03 1.98 1.94 1.89 1.84 1.79 1.7325 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.16 2.09 2.01 1.96 1.92 1.87 1.82 1.77 1.71

30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.09 2.01 1.93 1.89 1.84 1.79 1.74 1.68 1.6240 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2.00 1.92 1.84 1.79 1.74 1.69 1.64 1.58 1.5160 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.92 1.84 1.75 1.70 1.65 1.59 1.53 1.47 1.39

120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91 1.83 1.75 1.66 1.10 1.55 1.50 1.43 1.35 1.25∞ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1.00

Degrees of freedom for the numerator (MD or CD)

Deg

rees

of f

reed

om fo

r den

omin

ator

(Res

idua

l)



\ 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ 1 161 200 216 225 230 234 237 239 241 242 244 246 248 249 250 251 252 253 2542 18.5 19.0 19.2 19.3 19.3 19.3 19.4 19.4 19.4 19.4 19.4 19.4 19.5 19.5 19.5 19.5 19.5 19.5 19.53 10.1 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.74 8.70 8.66 8.64 8.62 8.59 8.57 8.55 8.534 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.635 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.62 4.56 4.53 4.50 4.46 4.43 4.40 4.36

6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.00 3.94 3.87 3.84 3.81 3.77 3.74 3.70 3.677 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.57 3.51 3.44 3.41 3.38 3.34 3.30 3.27 3.238 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.28 3.22 3.15 3.12 3.08 3.04 3.01 2.97 2.939 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.07 3.01 2.94 2.90 2.86 2.83 2.79 2.75 2.7110 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.91 2.85 2.77 2.74 2.70 2.66 2.62 2.58 2.54

11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.4012 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.3013 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.60 2.53 2.46 2.42 2.38 2.34 2.30 2.25 2.2114 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.53 2.46 2.39 2.35 2.31 2.27 2.22 2.18 2.1315 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.48 2.40 2.33 2.29 2.25 2.20 2.16 2.11 2.07

16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.42 2.35 2.28 2.24 2.19 2.15 2.11 2.06 2.0117 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.38 2.31 2.23 2.19 2.15 2.10 2.06 2.01 1.9618 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.34 2.27 2.19 2.15 2.11 2.06 2.02 1.97 1.9219 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.8820 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.28 2.20 2.12 2.08 2.04 1.99 1.95 1.90 1.84

21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.25 2.18 2.10 2.05 2.01 1.96 1.92 1.87 1.8122 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.23 2.15 2.07 2.03 1.98 1.94 1.89 1.84 1.7823 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.20 2.13 2.05 2.01 1.96 1.91 1.86 1.81 1.7624 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.18 2.11 2.03 1.98 1.94 1.89 1.84 1.79 1.7325 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.16 2.09 2.01 1.96 1.92 1.87 1.82 1.77 1.71

30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.09 2.01 1.93 1.89 1.84 1.79 1.74 1.68 1.6240 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2.00 1.92 1.84 1.79 1.74 1.69 1.64 1.58 1.5160 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.92 1.84 1.75 1.70 1.65 1.59 1.53 1.47 1.39

120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91 1.83 1.75 1.66 1.10 1.55 1.50 1.43 1.35 1.25∞ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1.00

Degrees of freedom for the numerator (MD or CD)

Deg

rees

of f

reed

om fo

r den

omin

ator

(Res

idua

l)

Field Code Changed


Literature cited

1. Wonnacott, T., “Introductory Statistics,” Wiley, 1972, p. 222.

2. Burkhard, G., and Wrist, P.E., “The Evaluation of Paper Machine Stock Systems by Basis Weight Analysis,”

Pulp Paper Mag. Can. 55 (13): 188 (1954).

3. Burns, J. W., “The Use of Analysis of Variance to Characterize Paper Web Nonuniformities,” Tappi 57 (12):

143 (1974).

4. Wasserstrass, J.D., “Machine Evaluation by Analysis of Basis Weight Variation,” Tappi 59 (10): 65 (1976).

5. Mardon, J., et al., “Analysis of Paper Machine Stability and Performance by Means of Basis Weight

Investigation,” PAPTAC Technical Section Monograph, May 1973.

6. Haglund, L., Lindstrom, R., and Wahren, D., “Off-Machine Basis Weight Analysis and Acceptance Testing of

Headboxes,” STFI, SCAN Forsk Report No. 53, Stockholm, 1973.

7. Smith, N., “An Analysis of Basis Weight Variation,” Tappi 69 (3): 101 (1979).

References Deodhar, S., “Statistical Analysis of Cross Machine Variations in Basis Weight”, Tappi Journal, 71 (10): 223 (1988).

Cutshall, K. A., Ilott, G.E., and Rogers, J. R., “Grammage Variation - Measurement and Analysis,” PAPTAC

Monograph (1988).

Your comments and suggestions on this procedure are earnestly requested and should be sent to the TAPPI Standards

Department.

NOTICE: This is a DRAFT of a TAPPI Standard in ballot. Although available for public viewing, it is still under TAPPI’s copyright and may not be reproduced or distributed without permission of TAPPI. This draft is NOT a currently published TAPPI Standard. WI 150404.01

T 545

DRAFT NO. 02

DATE December 6, 2018 WORKING GROUP CHAIRMAN Ian Journeaux SUBJECT CATEGORY Water Removal RELATED

METHODS See “Additional Information”

Approved by the Standard Specific Interest Group for this Test Method

TAPPI

CAUTION: This Test Method may include safety precautions which are believed to be appropriate at the time of publication of the method. The intent of these is to alert the user of the method to safety issues related to such use. The user is responsible for determining that the safety precautions are complete and are appropriate to their use of the method, and for ensuring that suitable safety practices have not changed since publication of the method. This method may require the use, disposal, or both, of chemicals which may present serious health hazards to humans. Procedures for the handling of such substances are set forth on Material Safety Data Sheets which must be developed by all manufacturers and importers of potentially hazardous chemicals and maintained by all distributors of potentially hazardous chemicals. Prior to the use of this method, the user must determine whether any of the chemicals to be used or disposed of are potentially hazardous and, if so, must follow strictly the procedures specified by both the manufacturer, as well as local, state, and federal authorities for safe use and disposal of these chemicals.

Cross-machine grammage profile measurement

(gravimetric method) (Five-year review of T 545 om-11)

(Draft 2 contains revisions made in Draft 1. This version of Draft 2 has all the changes

incorporated.)

1. Scope

1.1 This method describes a procedure which can be applied to determine the variation in mass per unit

area in the cross-machine direction, commonly referred to as the grammage (or basis weight) profile. This method is

appropriate for the acceptance testing of both the papermaking process and the product.


1.2 This method is laborious, but it is reliable and accurate. It requires simple, well-defined operations:

cutting out samples, weighing samples, and data evaluation.

1.3 The general procedures outlined in TAPPI T 410 “Grammage of Paper and Paperboard (Weight Per

Unit Area)” and in TAPPI T 402 “Standard Conditioning and Testing Atmospheres for Paper, Board, Pulp Handsheets,

and Related Products” are used as basic references for this method.

2. Summary

The cross-machine grammage (basis weight) profile is determined by sampling 20 consecutive cross-machine layers

from the outer layers of a parent reel, preconditioning the samples, cutting the layers into a series of rectangular sheets

200 mm CD × 300 mm MD, discarding those sheets with obvious defects, conditioning the samples, and weighing the

samples. The sample weights are then analyzed using analysis of variance to determine the MD, CD, residual, and

total standard deviations.

3. Significance

The evaluation of grammage variation from measurements on cross-machine direction strips is a useful way to analyze

the performance of a paper machine. This method provides sufficient accuracy and repeatability to be used for

acceptance testing of the papermaking equipment and for product specification.

4. Definitions

4.1 Grammage, mass per unit area, expressed as grams per square meter (g/m2). The customary English

term is basis weight, expressed in pounds per ream, which must be defined, e.g., as 1000, 3000 or other appropriate

square footage.

4.2 Cross-machine direction, direction perpendicular to the running direction of the paper machine (CD).

4.3 Layer, single cross-machine direction strip of paper cut for grammage profile measurement.

4.4 Machine direction, direction parallel to the running direction of the paper machine (MD).

4.5 Mean, arithmetic average.

5. Apparatus

5.1 The apparatus required for this method is detailed in T 410:

5.1.1 Weighing device, readable and accurate to within 0.1% of the applied load.

5.1.2 Cutting device, having an attachment for ensuring parallelism of the opposite edges.

5.1.3 Scale, such as a finely graduated steel ruler reading in 0.5 mm, capable of measuring the dimensions

of the test specimen to an accuracy of 0.2%.


Fig. 1. Sampling of paper.

6. Sampling

6.1 Obtain the requisite samples in accordance with the guidelines of TAPPI T 400 “Sampling and

Accepting a Single Lot of Paper, Paperboard, Containerboard, or Related Product.”

6.2 Obtain 20 consecutive CD layers nominally 400 mm wide (MD) from the outer 100 layers of a parent

reel with a diameter of at least 1 m, as shown in Fig. 1.

6.3 These layers must be free from creases, wrinkles, folds, and tears.

6.4 Mark the corner of the front edge (tending side) “FS” (front side). Note the date, time, reel number,

and machine number. Mark the wire side of the sheet with “WS” (wire side).

6.5 Number each CD layer, in order, starting with a 1 at the outermost layer.

6.6 Carefully transfer the samples to a climate-controlled conditioning room. Avoid putting creases,

wrinkles, or corrugations in the sheets.

6.7 Depending on the purpose of the testing, it may be useful to obtain a copy of the grammage profile

which was displayed by the on-machine profile scanner just before the reel was completed.


6.8 Depending on the purpose of the testing, it may be useful to note any abnormal operating conditions

which occurred while this sample was being taken.

7. Test specimens

7.1 Precondition the test samples on the dry side in atmospheres in accordance with TAPPI T 402

“Standard Conditioning and Testing Atmospheres for Paper, Board, Pulp Handsheets, and Related Products.” Initial

drying can be accelerated using an oven.

7.2 Unroll the layers on a long, flat surface.

7.3 Carefully align the layers.

7.4 Calculate the number of samples to cut per layer and the amount to discard from each edge. Samples

will be adjacent and 250 mm wide. Discard 100 mm plus one-half of any remainder from each edge of the layer, as

shown in Fig. 2.

Fig. 2. Cutting test specimens from sample layers.

7.4.1 For example, a sheet width of 4600 mm would be divided as follows: The minimum discard would be

100 mm from each end, so the maximum test width would be 4400 mm. When divided into 250-mm widths, there

would be 17 full tablets and a 150-mm remainder. The 150-mm remainder should be divided so that both edge discards


are approximately the same width (175 mm). The difference in the width of the discard from one end should be less

than 50 mm of the width of the discard from the other end.

7.5 Cut the layers against a template into a series of tablets of 250 mm CD width x 400 mm MD length,

as determined above.

7.6 Label each sample with a pair of numbers. The first number shall designate the layer as numbered

from the outside and the second number shall designate the CD position as numbered from the front side.

7.7 Trim each tablet to a rectangle of 200 mm (CD) by 300 mm (MD) using a suitable knife, guillotine,

or paper cutter. The dimensions of the sampled sheets shall lie within ± 0.25% of the mean dimension, per T 410.

7.8 Examine each sample. Reject any sample which contains clearly visible lumps of slime, pitch, filler,

or similar defects within a total area greater than 1 cm2.

7.9 Reject any sheet that has holes in it with an area exceeding 1 cm2, as well as any sheets which have

been damaged such that the dimensions cannot be established within the prescribed degree of accuracy.

7.10 The grammage of any rejected sheet should be replaced by the average of its two most immediate

neighbors in the machine direction. Use the average grammage of the preceding two MD sheets if the sheet was

rejected from the top or the bottom of a tablet.

7.11 Abandon any test in which the total number of rejected sheets exceeds 3% of the total number of

sheets.

7.12 Separate the sheets into stacks no greater than 5 mm thick and allow the samples to be conditioned for

at least 24 hours as outlined in TAPPI T 402.

8. Procedure

8.1 Weigh each test specimen to within 0.1% in a climate-controlled atmosphere in accordance with T

402 and T 410.

8.2 Record the results in tabular form, using the format given in Table 1 as a guide. The results of each

layer are entered in order on successive lines.

9. Calculations

9.1 Use the common two-factor analysis of variance to evaluate the CD profile. A mathematical

description of this method can be found in most textbooks on statistics. A basic review can be found in some of the

references (1-6).

9.2 Equations describing the items in the variance analysis are given in Table 2.


9.3 Follow the equations listed in Table 2 and compute the sum of squares, the degrees of freedom, the

mean square, the F ratio, the systematic variance, and the standard deviation for the CD, MD, residual, and total

variations.

10. Report

10.1 List the grammage for each sample G(i,k) in Table 1 in g/m2 to three significant figures.

10.2 List the MD, CD, residual, and total standard deviations and the mean grammage of all points in g/m2

to three significant figures.

10.3 If desired, the results may also be reported in pounds for customary trade sizes.

10.4 List the MD and CD F ratios and the MD, CD, and residual degrees of freedom.

10.5 List in Table 1 the mean grammage of all MD samples at each CD position (G•k) in g/m2 to three

significant figures.

10.6 Note in Table 1 the maximum and minimum grammage at each CD position in g/m2 to three significant

figures.

10.7 Include a composite profile report displaying the mean grammage at each CD position (G•k) as a

function of the cross-machine position as shown in Fig. 3. The abscissa (or x axis) should be the cross-machine position

in mm with the front side located on the left. The ordinate (or y axis) can be in expressed as a deviation from the mean

grammage defined as:

Grammage deviation = (Gk - G)

or, as a percent deviation from the mean defined as:

Percent deviation = 100 × [(G.k - G) / G)]

10.8 Include on the composite profile report a plot of the minimum and maximum grammages, expressed

in grammage or percent deviation from the mean, as a function of the cross-machine position, as shown in Fig. 3.

10.9 List the MD, CD, residual, and total standard deviations and the coefficients of variation (CV)

100×=GsCV

and expressed in percentage with three significant figures.


Table 1. Measured grammage record table

Sample CD sample position

layer Front Back

number k = 1 2 3 4 n

i=1 G(1,1) G(1,2) G(1,3) G(1,4) .... G(1,n)

2 G(2,1) G(2,2) G(2,3) G(2,4) .... G(2,n)

3 G(3,1) G(3,2) G(3,3) G(3,4) .... G(3,n)

4 G(4,1) G(4,2) G(4,3) G(4,4) .... G(4,n)

5 G(5,1) G(5,2) G(5,3) G(5,4) .... G(5,n)

.... .... .... .... .... .... ....

.... .... .... .... .... .... ....

.... .... .... .... .... .... ....

.... .... .... .... .... .... ....

m G(m,1) G(m,2) G(m,3) G(m,4) .... G(m,n)

Mean G(•,1) G(•,2) G(•,3) G(•,4) .... G(•, n)

Minimum G(i,1) G(i,2) G(i,3) G(i,4) .... G(i, n)

Maximum G(i,1) G(i,2) G(i,3) G(i,4) .... G(i,n)

Note: m = 20 for this test method; n is dependent on the machine width.

NOTE 1: The (i, k) indices on the grammage G correspond to the sample layer number and the CD position number, respectively. For

example, G (3,5) represents the grammage of the sample taken from the third layer and located in the fifth position from the

front of the machine.

11. Precision

11.1 Repeatability of grammage test results within a laboratory = 0.94%, per T 410.

11.2 Reproducibility of grammage test results within a laboratory = 2.84%, per T 410.

11.3 The above values of precision are averages calculated from 18 reports of the TAPPI/NBS

Collaborative Reference Program for Paper. Each test result is an average for approximately 5000 cm2 of paper or

paperboard.

11.4 For the precision noted above, the repeatability of the standard deviations within a laboratory =

11.86%.

11.5 For the precision noted above, the reproducibility of the standard deviations between laboratories =

12.38%.


11.6 The values in items 11.4 and 11.5 are determined in accordance with the definitions of these terms in

TAPPI T 1200 “Interlaboratory Evaluation of Test Methods to Determine TAPPI Repeatability and Reproducibility.”

The results were obtained from round robin testing among seven laboratories. Three paper grades (Fine paper,

Corrugating medium and Newsprint) were tested in all seven laboratories.

12. Keywords

Basis weight, Variations, Cross direction, Profiles

13. Additional information

13.1 Effective date of issue: to be assigned.

13.2 The two-factor analysis of variance used in this test method assumes that there is no significant

MD−CD interaction. The F ratios and degrees of freedom listed in Table 2 can be used with standard statistics tables

to determine the level of confidence. Table 3 is typical, containing values of F for which the confidence level is 95%.

For example, if 26 CD samples are taken from each of the 20 sample layers, then the CD degrees of freedom would

be (26 - 1) (20 - 1) = 475. If the CD F ratio is greater than about 1.51, then there is greater than a 95% probability that

the CD variance is significant with respect to the residual (3).

0 1000 2000 3000 4000

-8

-6

-4

-2

0

2

4

6

Gra

mm

age

Varia

tion,

%



Fig. 3. Composite profile report.


13.3 There are several additional statistical tools which can be used to analyze the profile data. These

methods can be used to identify and quantify stable ridges in the profile, rate the profile stability, and identify the

source of profile non-uniformities. These methods are discussed in the listed references (1-7).

13.4 In order to ensure the sheet samples are fully conditioned within 24 hours, the stacks of sheets in 7.12

should be no more than 5 mm thick.

13.5 The 2011 version was revised to correct an error in the calculation of the total variance.

13.6 The F-ratio referred to in Table 2 provides a way to test the significance of the MD and CD variability.

The F-ratio is a ratio of 2 different measure of variance for the data. If the null hypothesis (F-ratio > Fcrit from Table

2 is true then the CD or MD term contributes significantly to the overall variability. The references (1,3,7) provide

additional details.


Table 2. Equations for two-factor analysis of variance for cross-machine grammage variations

Direction Sum of Squares Degrees of Freedom Mean Sum of

Squares F-Ratio Systematic Variance

Standard

Deviation

CD ( )∑ −=•

n

1-kk

2CD GGmSS 1-nDFCD =

CD

CDCD DF

SSMSS =

MSS

MSS

RES

CD m

MSS-MSSV

RESCDCD

= CDCD V=σ

MD ( )∑ −=•

m

1-ii

2MD GGnSS 1-mDFMD =

MDDFSS

MSS MDMD =

MSS

MSS

RES

MD n

MSS-MSSV RESMD

MD = MDMD V=σ

Residual ( )∑∑= =

•• +−=m

1i

n

1kki-ik

2RES GGGGSS 1)-1)(m-(nDFRES =

RES

RESRES DF

SSMSS = RESRES MSSV = RES RES V=σ

Total ( )∑∑= =

=m

1i

n

1kik

2TOT G-GSS 1-nmDFTOT =

TOT

TOTTOT DF

SSMSS = TOTTOT MSSV =

RESMDCDTOT VVV V ++≅ TOTTOT V=σ

CDCD MSSV m 100 systematic is that variationCD ofPercent =

MDMD MSSVn 100 systematic is that variationMD ofPercent =

k)(i, sample of GrammageG :where ik =

=•kG ∑=

=m


m1

=•iG ∑=

=n


n1

=G ∑∑= =

=m

1i

n


mn1

=n Number of CD samples in an MD strip

=m Number of MD strips



\ 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ 1 161 200 216 225 230 234 237 239 241 242 244 246 248 249 250 251 252 253 2542 18.5 19.0 19.2 19.3 19.3 19.3 19.4 19.4 19.4 19.4 19.4 19.4 19.5 19.5 19.5 19.5 19.5 19.5 19.53 10.1 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.74 8.70 8.66 8.64 8.62 8.59 8.57 8.55 8.534 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.635 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.62 4.56 4.53 4.50 4.46 4.43 4.40 4.36

6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.00 3.94 3.87 3.84 3.81 3.77 3.74 3.70 3.677 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.57 3.51 3.44 3.41 3.38 3.34 3.30 3.27 3.238 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.28 3.22 3.15 3.12 3.08 3.04 3.01 2.97 2.939 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.07 3.01 2.94 2.90 2.86 2.83 2.79 2.75 2.7110 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.91 2.85 2.77 2.74 2.70 2.66 2.62 2.58 2.54

11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.4012 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.3013 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.60 2.53 2.46 2.42 2.38 2.34 2.30 2.25 2.2114 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.53 2.46 2.39 2.35 2.31 2.27 2.22 2.18 2.1315 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.48 2.40 2.33 2.29 2.25 2.20 2.16 2.11 2.07

16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.42 2.35 2.28 2.24 2.19 2.15 2.11 2.06 2.0117 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.38 2.31 2.23 2.19 2.15 2.10 2.06 2.01 1.9618 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.34 2.27 2.19 2.15 2.11 2.06 2.02 1.97 1.9219 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.8820 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.28 2.20 2.12 2.08 2.04 1.99 1.95 1.90 1.84

21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.25 2.18 2.10 2.05 2.01 1.96 1.92 1.87 1.8122 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.23 2.15 2.07 2.03 1.98 1.94 1.89 1.84 1.7823 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.20 2.13 2.05 2.01 1.96 1.91 1.86 1.81 1.7624 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.18 2.11 2.03 1.98 1.94 1.89 1.84 1.79 1.7325 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.16 2.09 2.01 1.96 1.92 1.87 1.82 1.77 1.71

30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.09 2.01 1.93 1.89 1.84 1.79 1.74 1.68 1.6240 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2.00 1.92 1.84 1.79 1.74 1.69 1.64 1.58 1.5160 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.92 1.84 1.75 1.70 1.65 1.59 1.53 1.47 1.39

120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91 1.83 1.75 1.66 1.10 1.55 1.50 1.43 1.35 1.25∞ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1.00

Degrees of freedom for the numerator (MD or CD)D

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es o

f fre

edom

for d

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or (R

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Literature cited

1. Wonnacott, T., “Introductory Statistics,” Wiley, 1972, p. 222.

2. Burkhard, G., and Wrist, P.E., “The Evaluation of Paper Machine Stock Systems by Basis Weight Analysis,”

Pulp Paper Mag. Can. 55 (13): 188 (1954).

3. Burns, J. W., “The Use of Analysis of Variance to Characterize Paper Web Nonuniformities,” Tappi 57 (12):

143 (1974).

4. Wasserstrass, J.D., “Machine Evaluation by Analysis of Basis Weight Variation,” Tappi 59 (10): 65 (1976).

5. Mardon, J., et al., “Analysis of Paper Machine Stability and Performance by Means of Basis Weight

Investigation,” PAPTAC Technical Section Monograph, May 1973.

6. Haglund, L., Lindstrom, R., and Wahren, D., “Off-Machine Basis Weight Analysis and Acceptance Testing of

Headboxes,” STFI, SCAN Forsk Report No. 53, Stockholm, 1973.

7. Smith, N., “An Analysis of Basis Weight Variation,” Tappi 69 (3): 101 (1979).

References Deodhar, S., “Statistical Analysis of Cross Machine Variations in Basis Weight”, Tappi Journal, 71 (10): 223 (1988).

Cutshall, K. A., Ilott, G.E., and Rogers, J. R., “Grammage Variation - Measurement and Analysis,” PAPTAC

Monograph (1988).

Your comments and suggestions on this procedure are earnestly requested and should be sent to the TAPPI Standards

Department.

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