United States

Department of

Agriculture

Forest Service

Forest

Products

Laboratory

Research

Paper

FPLRP576

Monitoring of

Visually Graded

Structural Lumber

David E. Kretschmann

James W. Evans

Linda Brown
Abstract

To satisfy the increased demand for forest products, much of

the future timber supply is expected to be derived from improved trees grown on managed plantations. This fast-grown

resource will tend to be harvested in short-age rotations and

will contain higher proportions of juvenile wood compared

with wood in current harvests. As a result, current allowable

properties may need to be reduced in the future. This report

explores four options for monitoring the properties of fastgrown wood and briefly discusses the advantages and disadvantages of these approaches. The recommended multiplestage sampling approach is illustrated in detail using simulated results based on the North American In-Grade test

results for Southern Pine. Finally, the report presents details

of a “real world” example of monitoring lumber properties

currently being conducted by the Southern Pine Inspection

Bureau.

Keywords: monitoring, visually graded structural lumber,

Southern Pine

July 1999

Kretschmann, David E.; Evans, James W.; Brown, Linda. 1999. Monitoring

of visually graded structural lumber. Res. Pap. FPL–RP–576. Madison, WI:

U.S. Department of Agriculture, Forest Service, Forest Products Laboratory.

18 p.

A limited number of free copies of this publication are available to the

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Research Highlights

Previous research has helped draw attention to a potential

problem associated with fast-grown plantation material: the

higher percentage of juvenile wood. The lower mechanical

properties of juvenile wood, compared with mature wood,

account for the inferior properties of aggressively grown

plantation wood harvested on short rotations compared with

the properties of longer rotation, naturally suppressed timber.

Independent grading agencies have a strong interest in determining whether a significant change (particularly a decrease in material properties) in the lumber resource has

occurred. The work reported here explores four options for

monitoring lumber properties and briefly discusses the advantages and disadvantages of these options. The recommended multiple-stage approach is discussed in detail using

simulated results based on the North American In-Grade test

data for Southern Pine.

Some possible choices for monitoring the lumber resource

are the use of control charts, Bayesian statistics, repetition of

an In-Grade program, and multiple-stage sampling. Of these

choices, a multiple-stage sampling approach has been

deemed the most practical for visually graded lumber. Simulations demonstrate the relative sensitivity of this method to

sample size, juvenile wood content, and selected “trigger

levels.” The term trigger level is used to describe the property value level associated with a targeted shift in property.

The Southern Pine Inspection Bureau has been monitoring

modulus of elasticity since 1994. The results of this program

are presented here.

Contents

Page

Introduction ...........................................................................1

Background—Approaches to Monitoring ............................2

Control Charts ...................................................................2

Bayesian Statistical Approach ...........................................2

Full In-Grade Program.......................................................2

Multiple-Stage Sampling ...................................................2

Questions for Multiple-Stage Approach ............................3

Simulations............................................................................5

Data ...................................................................................5

Methods.............................................................................5

Results ...................................................................................5

Regressions........................................................................5

Sample Size .......................................................................6

Juvenile Wood...................................................................7

Example Simulations.........................................................9

Implications of Simulations.............................................14

SPIB Resource Monitoring Program...................................14

Method of Sampling ........................................................14

Results to Date.................................................................16

Discussion ...........................................................................16

Conclusions .........................................................................17

References ...........................................................................17
Monitoring of Visually Graded

Structural Lumber

David E. Kretschmann, Research General Engineer

James W. Evans, Supervisory Mathematical Statistician

Forest Products Laboratory, Madison, Wisconsin

Linda Brown, Engineer

Southern Pine Inspection Bureau, Pensacola, Florida

Introduction

Early research drew attention to the potential for lower mechanical properties in plantation material. The study involved

an 8-year-old plantation of Caribbean pine (Pinus caribaea

Morelet) from Puerto Rico (Boone and Chudnoff 1972).

Specific gravity, bending stiffness, and strength of this plantation-grown wood were 50% lower than that of published

values for virgin lumber of the same species. In actuality,

Boone and Chudnoff compared juvenile wood to mature

wood rather than plantation wood to virgin lumber. In this

study, differences between juvenile and mature wood were

probably accentuated because the trees were very young.

Thus, the study evaluated early-formed juvenile wood,

which has significantly lower properties than later-formed

juvenile wood.

Research conducted at North Carolina State University and

the Forest Products Laboratory (FPL) on clear wood of

loblolly pine demonstrated that the problem of lower properties was the result of juvenile wood, not plantation wood per

se (Pearson and Gilmore 1971, Bendtsen and Senft 1986).

This research demonstrated that juvenile wood is substantially lower in mechanical properties than is mature wood

and generally accounts for the inferior properties of plantation wood compared to that of virgin timber. Later studies

further investigated the effect of juvenile wood on full-size

structural lumber properties for various species. In New

Zealand, in-grade testing was completed on radiata pine lumber cut from 40- to 60-year-old stands (Walford 1982) and 28-

year-old stands (Bier and Collins 1984). In Canada, work by

Barrett and Kellogg (1989) and Smith and others (1991)

looked at plantation Douglas-fir and red pine. In the United

States, several studies were conducted on the bending and

tension parallel-to-grain properties of Douglas Fir and Southern Pine dimension lumber cut from plantations (Bendtsen and

others 1988, Biblis 1990, Clark and Saucier 1989, Kretschmann and Bendtsen 1992, MacPeak and others 1990, Pearson

1984, Ying and others 1994).

Independent grading agencies have a strong interest in determining whether a significant change in the resource has

occurred, resulting in a decrease in strength properties. Section 13, “Reassessment and Affirmation,” was included in

American Society for Testing and Materials (ASTM) Standard D1990 to ensure that a procedure was developed to

detect significant changes in allowable properties as a result

of change in the raw material resource or product mix

(ASTM 1997). Satisfying Section 13 requires a method for

detecting a significant change in the resource. In 1994, the

Southern Pine Inspection Bureau (SPIB), with the assistance

of the FPL, initiated a resource monitoring program to track

possible changes that may occur in modulus of elasticity of

No. 2 dimensional (24) lumber (SPIB 1994) with time.

(Note: 24 denotes nominal 2- by 4-in. (standard 38- by

89-mm) lumber.)

As part of the background for this program, the FPL initiated

a study to investigate options for monitoring properties of

structural lumber. The objective of this study was to answer a

series of questions, which will help grading agencies make

informed decisions on a monitoring program. These questions included the following:

• Is one property, such as modulus of elasticity (MOE), a

better predictor of true changes or shifts in the resource

than are other properties, such as modulus of rupture

(MOR), or the presence of pith?

• What are the relationships between shifts in MOE and

MOR?

• How much of a shift in MOE can occur before there is a

significant shift in MOR?

• How much of a shift in MOR can occur before there is a

significant shift in MOE?

• If monitoring MOE, how does the probability of correctly

detecting no shift in MOE increase with each additional

sampling for MOE?

• What sample size is required: 50, 100, 200, 400, or

1,000?
2

The FPL conducted simulations that provide information to

assist in understanding the meaning of shifts in MOE of

structural lumber over time.

Background—Approaches

to Monitoring

Of the many possible choices for monitoring structural lumber properties, this report discusses four approaches: control

charts, Bayesian statistics, full In-Grade testing, and multiple

sampling.

Control Charts

Control charts have the advantage of being a well-recognized

method of quality control with a well-established procedure

for tracking changes in properties. Control charts are graphical displays of summary statistics of a process plotted over

time. Trends in the data are examined to see if the process is

“in control” or “out of control.” Through the use of control

chart theory, it is possible to set up control limits (boundaries

on performance properties) that the results of routine production must meet (Montgomery 1997). If the sampled properties are outside the control limits or there is a persistent

pattern of the monitored properties to be consistently above

or below the production mean, the operation is deemed out of

control. To apply the method correctly requires very intensive repeated sampling at specific mills, which, depending on

selection of mills, might ultimately be insensitive to changes

in the overall resource. If the method is used incorrectly,

there is a high risk that it will mistakenly indicate that allowable properties should be reassessed even when this is not

needed.

Bayesian Statistical Approach

The Bayesian statistical method of sampling has been pursued by FPL researchers David W. Green and James W.

Evans and University of Wisconsin–Madison statistician

Richard Johnson (Johnson and others, 1995, 1999). In this

approach, the distributional data of an initial sample is used

to weight subsequent samples to obtain global properties.

The benefit of the Bayesian method is that it uses existing

information to provide guidance on sampling. This can potentially result in a smaller required sample size. The Bayesian approach could be used for a single sample or in a threestage approach similar to that outlined for multiple-stage

sampling. However, because the Bayesian approach is less

traditional than other approaches, it would require additional

sensitivity studies to confirm its applicability. In addition,

adoption by a consensus organization might be difficult

to obtain.

Full In-Grade Program

Another sampling option is to repeat the full In-Grade program periodically (Green and others 1989), an approach that

has the advantage of being an accepted procedure. However,

this program would merely indicate whether a change in

design values had occurred. The long time-frame needed for

in-grade testing also reduces the usefulness of the sequential

nature of data collection. Decades would be needed to acquire an indication of trends. Furthermore, since the original

In-Grade program was very expensive, any further full-scale

testing program is likely to be even more costly. Finally, this

approach does not indicate whether repeated testing is necessary until all testing has been completed. Thus, if no change

in properties had indeed occurred, the expense of conducting

a full In-Grade program would have been unnecessary.

Multiple-Stage Sampling

The method selected by SPIB is a multiple-stage sample

across the growth region. With this method, the detection of

a change in resource is approached in stages. The advantages

of multiple-stage sampling are that it requires smaller sampling in the initial stages, it can be adjusted for cost and risk,

and it focuses resources on the grade–size combination expected to be most sensitive to changes. The disadvantages of

this method are that considerable time is required for sampling, consensus must be reached on an acceptable boundary

for significant changes and number of stages, and multiple

stages are needed to confirm significant changes in the

resource.

Figure 1 shows an example of a potential system for the

multiple-stage approach. In Stage I, a nondestructive test

program is conducted on what is anticipated to be the most

sensitive grade and size combination. This stage may have

multiple steps to further decrease sample size. Steps are

defined as repeated sampling on a regular or periodic basis.

Stage II is reached if the most sensitive grade–size combination indicated that a change in properties had occurred.

Change is defined as a targeted shift of x amount in a property. The term trigger level describes the property value level

associated with the targeted shift. The trigger level is defined

as the original property value of the sample minus the

targeted shift amount.

In Stage II, additional tests (destructive or nondestructive)

are conducted on one or more sizes and grades to confirm

that the trigger level has been reached. If the targeted shift is

not confirmed, the original periodic testing of Stage I is

reinitiated. If the targeted shift is confirmed in Stage II, a

further stage of destructive testing in the full range of grade–

size combinations may be initiated.
3

Questions for Multiple-Stage Approach

In a multiple-stage approach, three initial questions must be

answered:

1. Which material is most sensitive to changes in the resource; that is, what grade–size combination would be

first to reflect a change in the resource?

2. How much of a change in that sensitive material is

significant?

3. What are the economic impacts of reaching Stage II

and beyond?

Choosing the most sensitive grade(s) and size(s) reduces the

amount of material that must be tested. It is also assumed to

be the most efficient way of detecting a change in the resource. Which grade(s) and size(s) are most sensitive to

changes in the resource is judged by agency personnel on the

basis of past experience and available test data.

The determination of a significant change is preferably made

by consensus, but it can also be made by individual agencies.

Pertinent questions to consider include the following:

• Is the agency most concerned with detecting a shift that

will affect a rounding rule or with detecting a shift of a

particular absolute value?

• How much confidence is needed that a change has really

occurred and therefore how powerful does the test of

change have to be? (Power is defined as the probability

that if there is a difference between two distribution

means, it will be detected.)

• How does the selection of power affect the sample

size tested?

• How many samples is it practical to test?

The economic impact of progressing beyond Stage I is considerable. Progressing to Stage II and beyond will require

testing a large number of pieces. Consequently, it is critical

to determine that a change in the resource has occurred with

a considerable degree of certainty.

Basic statistical procedures may be used to help answer these

questions. Assuming normality, a quick estimate for the

sample size required to detect differences in two means of

two normal distribution means can be calculated. The agency

must know its acceptable “comfort level” for detecting a

difference in means when there is none (α) and for not detecting a difference in means when there is one (β). Alpha

(α) is the probability that a difference will be detected between the two means when none exists. Ideally, α should be

minimized. For the probability that a difference between the

two means will not be detected even though one exists, the

power is 1−β. Ideally, this power should be maximized, so β

should be small. Equation (1) rearranges the definition of

standard variate at the chosen α level in terms of the mean of

the sample tested. Equation (2) rearranges the definition of

the standard variate at the chosen β level in terms of the

mean for the sample tested. Equating Equations (1) and (2)

and solving for n results in a quick estimate of sample size n

(Eq. (3)) required to detect differences in two means of two

populations, where the α and β levels and the standard

deviation s for the population are known.

Z x Z s n s n

x = α => = μ + α

− μ

0

0 (1)

Z x Z s n s n

x = − β => = μ + β

− μ

1

1 (2)

where

Zα is standard normal variate at chosen α level,

Zβ standard normal variate for chosen β level

for second sample,

Stage I

Stage II

Stage III

Yes

No

Yes

Yes

Yes

Publish new value

Publish new

conservative

value

Detect

a

shift

Stage IV

Willing

to redo

in-grade

test

Shift in

destructive

tested

cell

No

No

Yes

Shift in

characteristic

MOE

Detect

a

shift

No

Figure 1—Potential flowchart for monitoring program.
4

n sample size,

s common standard deviation of two populations,

μ0 average value of original population,

μ1 average value of new sample to be detected

(trigger level),

x value of sample average above which no

difference is declared, and

μ0 − μ1 magnitude of change to be observed

(targeted shift).

Setting Equation (1) = Equation (2) gives sample size n:

( )

( )

2

















μ − μ

− + =

0 1

β Z Z s n α (3)

Figure 2 illustrates the effect of selecting different α and β

levels. For example, if the agency is monitoring MOE, it may

want to limit the chance of falsely detecting a change in

MOE to 5% (α = 0.05, Zα = −1.645) and to set the probability of proceeding to Stage II to 50% if there is a change in

MOE (β = 0.5, Zβ = 0) (Fig. 2a). This is quite different

from setting criteria so that there is 90% probability of detecting that MOE has shifted (Fig. 2b). Parts (c) and (d) of

Figure 2 provide examples of 95% and 99% assurance,

respectively, that MOE has shifted.

There are further complications, however, to choosing a

particular α or β level on MOE for monitoring structural

properties. The true concern is not only whether MOE has

changed, but also how this change affects other mechanical

properties. Existing information can be used to make assumptions about the relationship between other properties

and MOE. However, it is preferable to run a number of

simulations, making use of real strength and stiffness data, to

provide a clearer understanding of the potential variability

and sensitivity of a multiple-stage monitoring program. The

rest of this report provides simulated results based on the

North American In-Grade test data for Southern Pine and the

specific example of the monitoring program initiated by

SPIB. The simulated results are dependent on the MOE–

MOR relationship observed during the In-Grade test

program. If this relationship itself is altered, the simulation

results may not be valid.

H0: μ1 = μ0

H1: μ1 < μ0 Frequency

(a)

Estimated MOE

α β

Power

50%

x

Frequency

(c)

α β

Power

95%

0 μ1 μ0

0 Estimated MOE

μ1 μ0

x

Zα = 1.645

Zβ = 0

Zα = 1.645

Zβ = 1.645

Frequency

(b)

Estimated MOE

α β

Power

90%

x

Frequency

(d)

α β

Power

99%

0 μ1 μ0

0 Estimated MOE

μ1 μ0

x

Zα = 1.645

Zβ = 1.28

Zα = 1.645

Zβ = 2.33

1β = Power

Figure 2—Differences in selection of α and β levels.
5

Simulations

Data

The data used in the simulations were the SPIB In-Grade test

results (Green and Evans 1987). The test data were adjusted

using the procedures outlined in ASTM D1990 that are

currently used to calculate the allowable properties listed in

the American Forest & Paper Association (AF&PA) National

Design Specification (NDS) for Wood Construction

(AF&PA 1997).

Methods

Simulations were conducted in two phases. In Phase 1, we

examined the impact of different sample sizes on the ability

to predict changes in properties. In Phase 2, we investigated

the sensitivity of MOE as a monitoring parameter by simulating potential scenarios of future resource changes.

Phase 1

Phase 1 investigated the likelihood of falsely predicting

targeted shifts in properties when no change had occurred in

the data set for a range of sample sizes. A program was

developed to randomly select monitoring samples from the

existing In-Grade data sets for bending with no changes. The

properties considered were MOE and MOR. All trials looked

at data randomly selected from either the entire data set or

within each geographic region, weighting by production

percentages. The use of closed-form solutions was also investigated.

Phase 2

Phase 2 addressed the sensitivity of the monitoring technique

to detect predetermined changes in strength properties

(trigger levels) with one to three steps. Targeted shifts in

MOE were investigated. A targeted shift is a change of a

specific amount x in MOE. The corresponding values of

MOR were adjusted in accordance with MOE–MOR regression equations determined from the original In-Grade Southern Pine data.

In a number of simulations, regression equations were used

to evaluate possible shifts of concern. Required sample sizes

to detect a given change in MOE were investigated. Also,

possible shifts in MOE caused by increases in juvenile wood

were simulated.

Results

Regressions

Data from several sizes of No. 2 lumber and several grades

of 24 lumber were regressed to establish the relationship

between MOR and MOE. Regression relationships are shown

in Table 1. These relationships were used to establish the

anticipated required change in MOE (∆MOE = x1 − x2) associated with change of a certain amount in MOR. For example, for a change of one rounding rule in MOR

(50 lb/in2

 (344 kPa) as defined in ASTM D1990), the numeric value of the change in MOR (∆MOR = y1 − y2) would

equal the safety-load duration factor (2.1) multiplied by the

rounding rule or 2.1⋅50 lb/in2

 =105 lb/in2 (724 kPa).

Using MOR = b ⋅ MOE + a

and ) ( ) ( 1 2 1 2 y − y = b x − x

the corresponding 02 ∆MOE ≈ 0.  106

 lb/in2 (0.14 GPa).

Table 1—Regression relationships for various grade–size combinationsa

One rounding rule

in MOR is ∆ MOE Lumber

sizeb Grade

Samples

with

pith (no.)

Samples

without

pith (no.)

Intercept

(a)

Slope

(b) (×106

 lb/in2 (GPa))

24 No. 1 15 91 0.306 5.422 0.019 (0.13)

No. 2 91 320 −0.864 5.767 0.018 (0.12)

Select Structural 49 360 −1.329 5.294 0.020 (0.14)

Stud 62 117 −0.521 5.229 0.020 (0.14)

2×8 No. 2 166 592 −0.151 4.016 0.026 (0.18)

2×4 No. 2 juvenilec 48 — 0.559 4.457 0.024 (0.17)

2×4 No. 2 juveniled 106 — 0.711 4.706 0.022 (0.15)

a

MOE and MOR values adjusted to 15% moisture content were used for calculations (Green and Evans 1987).

b

Note: 28 denotes nominal 2- by 8-in. (standard 38- by 184-mm) lumber. c

Juvenile defined as presence of pith and less than 8 rings/inch (approximately 3 rings/cm). d

Juvenile defined as presence of pith or less than 4 rings/inch (approximately 1.5 rings/cm).
6

There is considerable variability about the MOE–MOR

regression relationships for lumber but a well-established

correlation (Green and Kretschmann 1991). For the sizes and

grades considered, one rounding rule in MOR corresponds

to, on average, a change in MOE of approximately 0.02 

106

 lb/in2 (0.14 GPa). Using defined juvenile wood data sets,

one rounding rule in MOR corresponds to a change in MOE

of 0.025  106

 lb/in2 (0.17 GPa). These changes in MOE

are much smaller than the rounding rule change of

0.1  106

 lb/in2 (0.69 GPa) in ASTM D1990.

Sample Size

The effect of sample size on the percentage of false positive

readings, for one rounding rule in MOE and MOR (Table 2)

and three targeted shifts in MOE (0.1, 0.025, and 0.02, Tables 3 to 5, respectively), was investigated using 100,000

simulated samples for each case. For each sample, a failure

was considered to have occurred when the average MOE or

the 5th percentile MOR for the sample was below the respective trigger level for the property. The MOE trigger level was

the original mean MOE minus the targeted shift of one

rounding rule of 0.1  106

 lb/in2 (0.69 GPa). For a sample

size of 50 and a change in MOE of 0.1  106

 lb/in2

(0.69 GPa), when two successive sample failures are required

there is a 0.033% chance of falsely declaring a shift in MOE

(Table 2). The MOR trigger level was the original MOR 5th

percentile minus 50 lb/in2 (344 kPa). For the same example,

there is a 23% chance of a false indication of a shift in MOR.

In Table 2, a step represents one complete sample of material. In the example just described, one step represents the

survey of data from 1 year. Step 2 represents sampling from

the next year and so on. For the MOE and MOR data in

columns 3 and 4, “overall” designates samples selected

randomly, with replacement, from all of the original 413 24

Select Structural (SS) pieces until the test sample was obtained. The number of No. 2 24 pieces tested in the InGrade program was 413. The second run (columns 5 and 6)

was a repeat of the original overall simulation. “Regional

selection” designates material sampled randomly from within

a given region, proportional to production in that region,

until the 413-piece sample was reached.

The results shown in Table 2 suggested that the false positive

rates for the two overall simulations were not substantially

different than those for the regional selection. Therefore, the

rest of the tests were run using random selection from the

overall database.

Tables 3 to 5 compare the effect of sample size on the

chances of falsely detecting a change in MOE for three levels

of change in MOE (0.1, 0.025, and 0.020  106

 lb/in2

(0.69 GPa, 0.17 GPa, 0.14 GPa), respectively). If multiple

steps are used, these results suggest little difference between

sample sizes of 1000, 413, or 200. If the sample size is below

200, there is a significant increase in the chance of false

positive readings.

The results of these simulations demonstrate the importance

of sampling method in regard to the sample size required. If

an agency were dependent on the information gathered over

only 1 year (that is, one step), then the sample size required

to reduce the chance of detecting false positive below 1% for

a change in MOE of 0.025 would usually be well over 1,000

specimens (Table 4). This same level of confidence can be

reached with slightly more than 200 specimens after three

steps have been taken. For a random sample size, repeated

sampling (multiple-stage approach) helps to ensure that a

detected shift is not a result of the natural variability of the

random sample by reducing the chances of falsely detecting a

property shift. The original In-Grade grade–size sample of

413 pieces is very unlikely to give a false positive indication

of a shift for MOE in a multiple-step process. The sample

size simulation results in Tables 2 to 5 also suggest that

detection with three steps and a sample size of 200 is roughly

equivalent to a two-step procedure with a sample size of 413.

Table 2—Probability of falsely detecting change of one rounding rulea when no change had occurred

Probability (%)

Overall Second run of overall Regional selection

Sample size Step MOE MOR MOE MOE MOR MOR

50 1 1.76 48.0 1.75 47.8 1.31 47.7

2 0.033 23.0 0.41 22.9 0.016 22.8

200 1 0 34.4 0.001 34.3 0.001 31.9

2 0 11.9 0 11.8 0 10.2

413 1 0 27.1 0 26.9 0 26.9

2 0 7.3 0 7.2 0 7.3

1,000 1 0 17.5 0 17.6 0 14.5

2 0 3.1 0 3.1 0 2.1

a

Rounding rule defined as 0.1 × 106 lb/in2 (0.69 GPa) in MOE or 50 lb/in2 (344 kPa) in MOR.
7

Therefore, a smaller sample size could be used with more

steps to detect a targeted shift in MOE. A sample size of at

least 360 should be considered to obtain good representation

of all geographic regions. Also, if a shift in MOE of one

rounding rule is observed, a shift of several rounding rules

may have occurred for MOR.

Juvenile Wood

Increases in the percentage of juvenile wood in a piece were

simulated in three ways. In each simulation, the criteria for

defining the presence of juvenile wood were presence or

absence of pith and number of rings per unit length, with

4 rings/inch equal to approximately 1.5 rings/cm.

Simulation 1 Presence of pith

Simulation 2 Presence of pith and <4 rings/inch

Absence of pith or ≥4 rings/inch

Simulation 3 Presence of pith or <4 rings/inch

Absence of pith and ≥4 rings/inch

The effects of these three sets of sorting criteria on MOE and

MOR are illustrated in Tables 6, 7, and 8, respectively. Information on the presence or absence of pith was not available for all of the original In-Grade samples. Therefore, the

total number of pieces listed by presence or absence of pith

may not equal the actual number of pieces tested. 

Table 3—Probability of falsely detecting 0.1  106 lb/in2

(0.69 GPa) change in MOE when no change had

occurred

Probability (%)

Sample

 size Step

2x4

No. 2

2x4

SSa 2x4Stud

2x8

No. 2

50 1 2.964 1.665 3.223 4.377

2 0.092 0.019 0.088 0.193

3 0.005 0 0.004 0.009

100 1 0.381 0.120 0.411 0.746

2 0.004 0 0.001 0.010

30 0 0 0

200 1 0.009 0.001 0.015 0.036

20 0 0 0

30 0 0 0

413 1 0 0 0 0.001

20 0 0 0

30 0 0 0

1000 1 0 0 0 0

20 0 0 0

30 0 0 0

a

SS is Select Structural.

Table 4— Probability of falsely detecting

0.025  106 lb/in2 (0.17 GPa) change in MOE when no

change had occurred for various sizes and grades (%)

Probability (%)

Sample

 size Step

2x4

No. 2

2x4

SS

2x4

Stud

2x8

No. 2

50 1 33.571 29.481 32.690 34.155

2 11.235 8.811 10.725 11.679

3 3.754 2.722 3.517 4.032

100 1 27.369 22.267 26.122 27.877

2 7.411 4.875 6.893 7.839

3 2.028 1.095 1.797 2.182

200 1 19.788 13.972 18.173 20.234

2 3.932 1.911 3.271 4.033

3 0.776 0.286 0.604 0.785

413 1 11.087 5.990 9.420 11.359

2 1.189 0.344 0.877 1.319

3 0.142 0.016 0.086 0.154

1000 1 2.832 0.741 2.130 3.009

2 0.051 0.007 0.054 0.088

3 0 0 0.002 0.003

Table 5—Probability of falsely detecting 0.02  106 lb/in2

(0.14 GPa) change in MOE when no change had

occurred

Probability (%)

Sample

 size Step

2x4

 No. 2

2x4

SS

2x4

Stud

2x8

No. 2

50 1 37.137 33.283 36.123 37.329

2 13.729 11.256 13.056 13.965

3 5.028 3.832 4.727 5.291

100 1 32.108 27.065 30.663 32.014

2 10.176 7.269 9.470 10.310

3 3.286 1.988 2.928 3.304

200 1 25.476 19.257 23.335 25.458

2 6.498 3.666 5.448 6.349

3 1.641 0.704 1.286 1.576

413 1 17.204 10.545 14.689 16.819

2 2.891 1.082 2.106 2.776

3 0.480 0.111 0.332 0.435

1000 1 7.148 2.582 5.193 6.630

2 0.458 0.060 0.293 0.425

3 0.033 0 0.017 0.020
8

For Simulation 1, MOR values for No. 2 lumber were not

very sensitive to the presence of pith (Table 6). This was

probably caused by the exclusion of some pieces with larger

knots from the pith group when pieces were selected on the

basis of pith alone. However, for all grades, MOE was sensitive to changes in the presence of pith. We concluded that

defining juvenile wood on the basis of presence of pith and

the number of rings per unit length resulted in too few pieces

for a proper simulation. Therefore, for the remaining simulations, presence of pith was used as the criterion for juvenile

wood.

Changes in properties were simulated using random sampling

with discarding. Increases in the percentage of pieces with

juvenile wood were simulated by discarding pieces that did

not meet the criteria defining juvenile wood. Thus, for a 20%

discard rate, if a piece were drawn that did not meet the

juvenile wood definition (that is, a piece without pith), it

would be discarded from the sample 20% of the time. Note

that this is different from requiring certain percentages of

pieces with juvenile wood in the sample. The 20%, 40%,

60%, and 80% discard rate sample sets were established by

discarding, with that probability, pieces without pith and

replacing those pieces by resampling the original 413-piece

sample. The resampled pieces did or did not have pith.

Table 9 lists the random sampling results for SS 24 lumber

for various properties when the discard rate was increased.

An example is given for each property simulated to demonstrate how the boundaries were established for various comparisons of the 100,000 simulation samples.

Table 6—Effect of Simulation 1 sorting criteria on MOE and MOR

Mean MOE 5th

Lumber percentile MOR

size Grade Sorting criteria Samplesize (x106 lb/in2 (GPa)) (x103 lb/in2 (MPa))

24 SS All 409 1.823 (12.6) 6.987 (48.2)

With pith 49 1.660 (11.4) 4.996 (34.4)

Without pith 360 1.845 (12.7) 7.121 (49.1)

24 No. 2 All 411 1.534 (10.6) 3.842 (26.5)

With pith 91 1.334 (9.2) 3.835 (26.4)

Without pith 320 1.591 (11.0) 3.821 (26.3)

24 Stud All 179 1.487 (10.3) 3.246 (22.4)

With pith 62 1.356 (9.3) 2.908 (20.1)

Without pith 117 1.556 (10.7) 3.798 (26.2)

28 No. 2 All 758 1.543 (10.6) 2.584 (17.8)

With pith 166 1.464 (10.1) 2.473 (17.1)

Without pith 592 1.566 (10.8) 2.588 (17.0)

Table 7—Effect of Simulation 2 sorting criteria on MOE and MOR

Mean MOE 5th

Lumber percentile MOR

 size Grade Sorting criteriaa Samplesize (x106 lb/in2 (GPa)) (x103 lb/in2 (MPa))

24 SS All 409 1.823 (12.6) 6.987 (48.2)

With pith and <4 rpi 1 1.490 (10.3) — (—)

Without pith or >4 rpi 408 1.824 (12.6) 6.983 (48.1)

No. 2 All 411 1.534 (10.6) 3.842 (26.5)

With pith and <4 rpi 5 0.971 (6.7) 3.575 (24.6)

Without pith or >4 rpi 406 1.541 (10.6) 3.863 (26.6)

24 Stud All 179 1.487 (10.3) 3.246 (22.4)

With pith and <4 rpi 9 0.967 (6.7) 2.901 (20.0)

Without pith or >4 rpi 170 1.515 (10.4) 3.405 (23.5)

28 No. 2 All 758b 1.543 (10.6) 2.584 (17.8)

With pith and <4 rpi 36 1.153 (7.9) 2.473 (17.1)

Without pith or >4 rpi 721 2.584 (17.8) 2.588 (17.8)

a

rpi is rings per inch; 4 rpi is approximately 1.5 rings/cm.

b

One piece was eliminated from study as result of lack of information on both pith and rings

 per unit length.
9

Example Simulations

MOE Simulation

In Table 10, the boundary for MOE is the average MOE

(1.823  106

 lb/in2 (12.6 GPa), Table 6) of the original InGrade SS 24 sample minus 0.025  106

 lb/in2 (0.17 GPa) or

1.798  106

 lb/in2 (12.4 GPa). For step 1 (the first 413-piece

sample), the average MOE was determined and compared

against 1.798  106

 lb/in2 (12.4 GPa). A failure was considered to have occurred if this average value was less than the

boundary MOE; 5,990 of 100,000 samples had averages

below the boundary (Table 10). Step 2 represents the number

of times that two failures occurred in a row. Thus, if a failure

had already occurred and the average MOE of the next sample of 413 pieces fell below the boundary, one piece was

added to the total of failures for step 2. If the average MOE

of the subsequent sample was above 1.798  106

 lb/in2

(12.4 GPa), no step 2 failure had occurred and the comparison was conducted the next time when the average MOE of

a 413-piece sample fell below the boundary.

For the 99,999 samples checked, there were 344 occurrences

when two samples in a row had an average MOE below the

boundary by chance with no discard. The same process was

used for three samples in a row. For SS 24, there were only

16 occurrences when three samples in a row had an average

MOE < 0.025  106

 lb/in2 (<0.17 GPa) less than the average

MOE of the original sample when no change in population

had occurred (that is, no pieces had been discarded). As the

discard rate increased (that is, increase in percentage of

pieces with juvenile wood), the percentage of failures

detected with repeated samplings (steps 1 to 3) increased

dramatically.

MOR Simulation

In Table 10, the boundary used for MOR was the safety-load

duration factor of 2.1 times one rounding rule (2.1 50 = 105

lb/in2

 (723 kPa)) subtracted from the 5th percentile (6.987 

103

 lb/in2 (48.2 MPa)). The actual value of the SS 24 MOR

boundary was 6.882  103

 lb/in2 (47.5 MPa). For each 413-

piece sample, the 5th percentile MOR was determined and

compared to this boundary. The regression relationship in

Table 1 was used to determine what an equivalent change in

MOE would be with a rounding rule change in MOR.

Table 8—Effect of Simulation 3 sorting criteria on MOE and MOR

 Mean MOE 5th percentile MOR

Lumber

size Grade Sorting criteria Samplesize (x106 lb/in2 (GPa)) (x103 lb/in2 (MPa))

24 SS All 409 1.823 (12.6) 6.987 (48.2)

With pith or <4 rpi 53 1.654 (11.4) 4.662 (32.1)

Without pith and >4 rpi 356 1.848 (12.7) 7.230 (49.9)

24 No. 2 All 411 1.514 (10.4) 3.842 (26.5)

With pith or <4 rpi 106 1.314 (9.1) 3.879 (26.7)

Without pith and >4 rpi 305 1.541 (10.6) 3.835 (26.4)

24 Stud All 179 1.487 (10.3) 3.246 (22.4)

With pith or <4 rpi 78 1.303 (9.0) 2.893 (19.9)

Without pith and >4 rpi 101 1.629 (11.2) 3.835 (26.4)

28 No. 2 All 758 1.543 (10.6) 2.584 (17.8)

With pith or <4 rpi 274 1.416 (9.8) 2.391 (16.5)

Without pith and >4 rpi 484 1.616 (11.1) 2.630 (18.1)

Table 9—Effect of discard rate on properties and pitha

Property No discard 20% discard 40% discard 60% discard 80% discard

Pith range 25–78 32–95 42–113 68–147 126–218

Pith mean 49 59 76 104 166

MOE mean (x106 lb/in2 (GPa)) 1.824 (12.6) 1.819 (12.5) 1.812 (12.5) 1.799 (12.4) 1.771 (12.2)

MOR 5% (x103 lb/in2 (MPa)) 6.939 (47.8) 6.873 (47.4) 6.769 (46.7) 6.589 (45.4) 6.290 (45.4)

a

Data from 24 SS sample. Sample size = 413. Target MOE = 0.025  106 lb/in2 (0.17 GPa).
10

From Table 10, of 100,000 samples, there were 35,830 occurrences when the calculated MOR 5th percentile was below

the boundary. For the 99,999 samples checked in step 2,

there were 12,847 occurrences when two samples in a row

had a calculated MOR 5th percentile below the boundary.

Finally, for the 99,998 samples checked in step 3, there were

4,564 occurrences when three samples in a row had a calculated MOR 5th percentile below the boundary.

Pith Simulation

A binomial distribution was used to determine a one-sided

upper 95% confidence interval for the expected number of

specimens discarded, based on the lack of pith in a 413-piece

sample. Equation (4) was used to calculate the bounds of the

95% confidence interval,

































± + n n

pq n p 21 1 (4) .645

where p is the probability a specimen has pith, q is 1 − p, and

n is sample size.

The continuity correction factor (1/2n) was ignored because

the large sample sizes made it negligible. The upper boundary for the confidence interval was used for both pith and

proof-load simulations. Using the upper boundary ensured

a high level of confidence that the shift had in fact occurred

and was not merely observed as a result of chance. We were

interested in the side of the interval where there would be too

many, rather than too few, pieces with pith or proof-load

failures.

In the original In-Grade SS 24 sample, 49 of 413 pieces

contained pith:

0.119 (1 ) 0.881 413

413

49

p = = q = − p = n = (5)

Equation (5) can be written in terms of pieces containing

pith:

49 10.81 59.81

413

364

413

49 1.645 413

413

49 413 + ⋅ ⋅ = + = (6)

Therefore, the boundary for pith that should be used is

49 60. In this case, a “failure” was said to + (0.026 ⋅ 413) ≅

occur if 60 pieces in the 413-piece sample contained pith.

From Table 10, 5,837 of 100,000 samples had 60 pieces

with pith. However, in only 371 of 99,999 occurrences did

two sample sets in a row have 60 pieces with pith, and in

only 19 of 99,998 occurrences did three sample sets in a row

have 60 pieces with pith.

Table 10—Percentage of failures in average MOE, MOR, pith, or proof load observed

at different steps for various discard ratesa

Failures (%)

Property Step No discard 20% discard 40% discard 60% discard 80% discard

MOEb 1 5.990 10.337 20.788 48.501 94.892

2 0.344 1.060 4.290 23.451 90.029

3 0.016 0.110 0.899 11.385 85.449

MORc 1 35.830 46.116 51.586 82.899 98.664

2 12.847 21.188 37.864 68.706 97.347

3 4.564 9.645 23.259 56.932 96.047

Pithd 1 5.837 49.221 98.278 100 100

2 0.371 24.115 96.583 100 100

3 0.019 11.833 94.915 100 100

Proof loade 1 4.800 8.146 15.931 36.270 82.205

2 0.232 0.676 2.533 13.088 67.489

3 0.012 0.060 0.434 4.688 55.372

a

Simulation based on 24 SS sample. Sample size = 413. b

Target MOE = 1.798  106 lb/in2 (12.4 GPa). c

Target MOR = 6.882 lb/in2  103 lb/in2 (47.4 MPa). d

Target number of pieces with pith >60.

e

Target order statistic >27th order.
11

Proof-Loading Simulation

Proof loading is a process of loading a member to a selected

level to obtain “proof” that the member will perform at that

load level. For wood, proof loading is usually used to determine which samples pass a 5th percentile criterion for a

strength property. To simulate the effect of proof loading, the

comparison boundary was determined again by using a binomial function. Using the 5th percentile definition and

Equation (4), the upper 95% confidence limit boundary was

determined to be anything greater than the 27th order statistic

of the MOR of the original 413-piece SS 24 sample. Therefore, a “failure” was considered to have occurred if the MOR

of 28 of 413 pieces was less than that of the targeted proofload:

 20 .65 7.286 27 .9

413 0.05 1.645 413 0.05 0.95

= + =

⋅ + ⋅ ⋅ (7)

Tables 11 to 13 present results similar to those presented in

Tables 8 to 10 for different grades and sizes and a sample

size of 413. The results suggest that proof-load testing for

MOR is not a meaningful monitoring scheme when a shift in

MOR is linked to a shift in MOE because monitoring for

MOE is more powerful. Also, using the presence of pith to

detect a change in resource may be overly sensitive to shifts

in MOE but may have potential as an early detection mechanism for property shifts. However, pith sensitivity varies

from cell to cell.

The results of these simulations show that several steps are

needed to limit the probability of detecting a shift in MOE

when one does not truly exist. In Tables 6 and 9 and the

upper part of Table 11, results on the effect of discard rate on

properties and presence of pith show that for a given change

in MOE, there may be several rounding rule changes in MOR

for higher grade lumber and few changes for low-grade

material. If MOR is chosen as the monitoring property, the

simulations suggest that shifts in MOR can be detected easily. Monitoring of MOR may also be grade dependent. MOE,

on the other hand, seems to be quite grade-independent and

does not give as high a rate of false declarations of a change.

Therefore, MOE is a better monitoring property than is

MOR.

MOE Trigger Levels

The MOE trigger is the amount of a shift in MOE that is

acceptable prior to initiating Stage II testing. To determine

how the discard rate affected the percentage of samples

resulting in a MOE shift of a particular magnitude, we considered MOE shifts of 0.02, 0.04, 0.05, and 0.1  106

 lb/in2

(0.14, 0.28, 0.34, and 0.69 GPa, respectively). The results

are listed in Tables 14 and 15.

Table 11—Effect of discard rate on properties and presence of pith and percentage of failures

in No. 2 2×4 sample for various discard ratesa

Effect of discard rate

Pith or property Step No discard 20% discard 40% discard 60% discard 80% discard

Pith range — 56–125 72–150 95–174 131–220 200–286

Pith mean — 91 108 132 171 242

MOE mean (x106 lb/in2

 (GPa)) — 1.530 (10.5) 1.520 (10.5) 1.505 (10.4) 1.482 (10.2) 1.438 (9.9)

MOR 5% (x103 lb/in2

 (MPa)) — 3.845 (26.5) 3.845 (26.5) 3.846 (26.5) 3.848 (26.5) 3.851 (26.6)

Failures (%)

MOE 1 11.087 25.775 57.339 93.604 99.997

2 1.189 6.662 32.978 87.616 99.993

3 0.142 1.674 18.857 82.024 99.989

MOR 1 12.730 12.180 11.100 9.743 7.597

2 1.640 1.541 1.265 0.926 0.564

3 0.191 0.207 0.151 0.079 0.038

Pith 1 5.759 64.222 99.859 100 100

2 0.341 41.371 99.717 100 100

3 0.015 26.652 99.576 100 100

Proof load 1 4.850 4.682 4.203 3.772 3.142

2 0.233 0.231 0.193 0.118 0.093

3 0.011 0.008 0.008 0.003 0.003

a

Target MOE = 0.025  106 lb/in2 (0.17 GPa).
12

Table 12—Effect of discard rate on properties and presence of pith and percentage of failures in 2×4 Stud

sample for various discard ratesa

Effect of discard rate

Pith or property Step No discard 20% discard 40% discard 60% discard 80% discard

Pith range 99–182 125–213 149–243 193–279 258–338

Pith mean 143 165 194 235 300

MOE mean (x106 lb/in2

 (GPa)) 1.487 (10.3) 1.477 (10.2) 1.463 (10.1) 1.442 (9.9) 1.411 (9.7)

MOR 5% (x103 lb/in2

 (MPa)) 3.245 (22.4) 3.205 (22.1) 3.161 (21.8) 3.106 (21.4) 3.036 (20.9)

Failures (%)

MOE 1 9.420 22.259 49.941 86.200 99.790

2 0.877 4.930 24.994 74.345 99.579

3 0.086 1.080 12.501 64.124 99.368

MOR 1 30.704 36.401 44.172 55.774 71.189

2 9.455 13.308 19.672 31.279 50.718

3 2.871 4.810 8.746 17.551 36.063

Pith 1 5.565 72.856 99.977 100 100

2 0.323 53.027 99.953 100 100

3 0.016 38.605 99.929 100 100

Proof load 1 2.078 2.999 4.872 8.735 18.033

2 0.049 0.088 0.215 0.760 3.254

3 0.002 0.004 0.008 0.075 0.577

a

Target MOE = 0.025  106 lb/in2 (0.17 GPa).

Table 13—Effect of discard rate on sample properties and presence of pith and percentage of failures in No. 8

2×4 sample for various discard ratesa

Effect of discard rate

Pith or property Step No discard 20% discard 40% discard 60% discard 80% discard

Pith range 56–131 70–149 93–171 123–218 201–284

Pith mean 91 107 132 170 241

MOE mean (x106 lb/in2

 (GPa) 1.543 (10.6) 1.539 (10.6) 1.533 (10.6) 1.524 (10.5) 1.506 (10.4)

MOR 5% (x103 lb/in2

 (MPa)) 2.580 (17.8) 2.577 (17.8) 2.573 (17.7) 2.567 (17.7) 2.553 (17.6)

Failures (%)

MOE 1 11.359 15.635 23.490 39.599 72.754

2 1.319 2.403 5.491 15.604 52.912

3 0.154 0.359 1.268 6.126 38.407

MOR 1 7.772 8.870 10.895 14.250 21.724

2 0.602 0.760 1.187 2.003 4.676

3 0.040 0.066 0.127 0.286 1.030

Pith 1 4.950 61.591 99.844 100 100

2 0.247 37.948 99.689 100 100

3 0.011 23.499 99.534 100 100

Proof load 1 5.186 5.490 6.021 6.850 8.531

2 0.272 0.309 0.365 0.446 0.722

3 0.008 0.017 0.021 0.037 0.068

a

Target MOE = 0.025  106 lb/in2 (0.17 GPa).
13

Table 14—Effect of discard rate on likelihood of detecting given targeted shift in MOE for SS 2x4 samplea

Effect of discard rate for various MOE means

No discard 20% discard 40% discard 60% discard 80% discard

MOE shift

(x106 lb/in2

 (GPa)) Step

1.824 ×

106

 lb/in2

(12.6 GPa)

1.819 ×

106

 lb/in2

(12.5 GPa)

1.812 ×

106

 lb/in2

(12.5 GPa)

1.799 ×

106

 lb/in2

(12.4 GPa)

1.771 ×

106

 lb/in2

(12.2 GPa)

0.02 (0.14) 1 10.545 16.9 30.338 60.375 97.357

2 1.082 2.846 9.235 36.389 94.776

3 0.111 0.469 2.821 21.878 92.273

0.04 (0.28) 1 0.635 1.445 4.102 17.020 76.828

2 0.006 0.021 0.172 2.947 58.983

3 0 0.002 0.005 0.496 45.318

0.05 (0.34) 1 0.083 0.257 0.985 6.025 55.308

2 0 0 0.007 0.336 30.640

3 0 0 0 0.024 16.902

0.10 (0.69) 1 0 0 0 0 0.194

20 0 0 0 0

30 0 0 0 0

a

Sample size = 413.

Table 15—Effect of discard rate on likelihood of detecting given targeted shift in MOE for No. 2 2x4 samplea

Effect of discard rate for various MOE means

No discard 20% discard 40% discard 60% discard 80% discard

MOE shift

(x106 lb/in2

 (GPa)) Step

1.530 ×

106

 lb/in2

(10.5 GPa)

1.520 ×

106

 lb/in2

(10.5 GPa)

1.505×

106

 lb/in2

(10.4 GPa)

1.482×

106

 lb/in2

(10.2 GPa)

1.438 ×

106

 lb/in2

(9.9 GPa)

0.02 (0.14) 1 17.204 35.523 67.899 96.445 100

2 2.891 12.601 46.120 93.011 100

3 0.480 4.431 31.283 89.705 100

0.04 (0.28) 1 1.990 6.899 25.467 75.225 99.933

2 0.029 0.479 6.506 56.600 99.865

3 0.001 0.026 1.628 42.576 99.797

0.05 (0.34) 1 0.443 2.043 11.149 54.673 99.622

2 0 0.038 1.246 30.017 99.245

3 0 0.001 0.125 16.417 98.871

0.10 (0.69) 1 0 0 0.007 0.302 39.460

2 0 0 0 0.001 15.634

3 0 0 0 0 6.161

a

Sample size = 413.
14

Implications of Simulations

The simulations indicate that “what if” scenarios can be

considered using normal statistics and existing data instead

of further simulations. If a constant is subtracted from the

MOE of every piece (Fig. 3), the probability that a test will

pick up that difference can be calculated. Equation (8) gives

the standard normal variate Z(1−β) for detecting an actual

shift of a given amount based on various targeted shifts.

n Z

σ

targeted actualshift

(1 )

− −β = (8)

Table 16 shows the likelihood of detecting a given actual

shift in MOE if the targeted shift is set at different levels. If

the actual shift equals the targeted shift, there is a 50%

chance of detecting the change. As the actual shift increases

or decreases with respect to the targeted shift, there is an

increase or decrease in the likelihood of detecting it. This

clearly indicates that there is very little chance that a minor

shift in MOE would be detected if the trigger level were set

to detect a targeted shift of 0.1  106

 lb/in2 (0.69 GPa).

Using Equation (9), the random chance of detecting a shift

when none had occurred for a given targeted shift is given in

Table 17.

n Zσ

targeted actual shift

( )

− α = (9)

These values, based on normal distribution statistics, are

comparable to those presented in Tables 2 to 5, which were

based on simulations. This information has been used as a

guide in developing a resource monitoring program at the

Southern Pine Inspection Bureau (SPIB).

SPIB Resource Monitoring

Program

The SPIB has conducted a resource monitoring program

annually since 1994. This program was developed as a means

of recognizing whether a significant change has occurred in

lumber strength properties. Both the SPIB Technical Committee and Board of Governors have shown solid support for

this program since its inception.

Method of Sampling

Mills are selected in a similar fashion to that used in the

original North American In-Grade program (Green and

others 1989). Each SPIB mill is assigned to a geographic

region and the production from each region is totaled. Based

on the proportion of production from each region, the number of pieces to be selected from that region is calculated.

The target minimum sample size is 360 pieces. Regardless of

the actual number of pieces required for a given region, a

minimum sample size of 10 pieces/mill and a maximum of

15 pieces/mill were established. Because of the minimum

sample size per mill, the actual sample size has ranged from

year to year from 380 to 405 pieces. Each year, approximately 30 mills are randomly selected from all of the SPIB

subscriber mills that produce No. 2 24 lumber (SPIB 1994).

Because of timing issues related to reporting production

figures and scheduling data collection for the monitoring

program, the regional production percentages are based on

the annual production figures 2 years prior to the testing. The

selection of mills to be sampled is conducted by the Forest

Products Laboratory. The mills in each region are randomly

ranked. The appropriate number of mills is then selected to

obtain the required sample size for each region.

The data collected for each piece include width, thickness,

length, moisture content, rings/inch, estimated percentage of

latewood, grade-controlling characteristic, maximum

strength-reducing characteristic, and two MOE values determined using a Metriguard E-Computer (Metriguard, Pullman, WA) . The E-Computer is calibrated using an 8-lb

(3.6 kg) brass weight, and the theoretical constant (79.4) to

maintain the “true, dynamic E” is used. All data are collected

at the individual mill sites. Ambient and wood temperature

data are also collected, and an effort is made to test the wood

at temperatures above 32°F (0°C).

After the data are collected for each annual program, several

data adjustments are made. First, the two E-Computer E

values are averaged to obtain a single value for each piece.

Because the E-Computer assumes nominal dimensions (that

is, 24 is 1.5 by 3.5 in.), the average E value is adjusted for

the actual dimensions of each piece. The E value is further

adjusted for moisture content to 15% using the moisture

content model in ASTM D1990.

In a separate, unpublished study conducted by SPIB, the

issue of adjusting a flatwise, E-Computer E value to be

equivalent to an edgewise, static bending E value was considered. Data were from a 1994 machine-stress-rated (MSR)

tension test program. The sample consisted of 24 to 210

lumber with a total sample size of 140 pieces. The

Frequency

0 μ1 μ0

Estimated MOE

Targeted

shift

Actual

shift H0:μ1 = μ0

H1:μ1 < μ0

Figure 3—Illustration of shifts in MOE.
15

Table 16—Likelihood of detecting actual shift for various targeted shifts for 24 samples

Likelihood (%) of detecting actual MOE shift for targeted shifts

Grade

Actual shift

in MOE

(x106

 lb/in2

(GPa))

–0.1 x

106 lb/in2

(–0.69 GPa)

–0.05 x

106 lb/in2

(–0.34 GPa)

–0.04 x

106 lb/in2

(–0.28 GPa)

–0.025 x

106 lb/in2

(–0.17 GPa)

–0.02 x

106 lb/in2

(–0.14 GPa)

SS Mean μ0 1.824 (12.6)

σ 0.332 (2.3)

n 413 –0.15

(–1.0)

99.9 100.0 100.0 100.0 100.0

–0.125

(–0.86)

93.7 100.0 100.0 100.0 100.0

–0.1

(–0.69)

50.0 99.9 99.9 100.0 100.0

–0.05

(–0.34)

0.1 50.0 72.9 93.7 96.7

–0.04

(–0.28)

0 27.1 50.0 82.1 88.9

–0.025

(–0.17)

0 6.3 17.9 50.0 62.2

–0.02

(–0.14)

0 3.3 11.1 37.8 50.0

–0.01

(–0.07)

0 0.7 3.3 17.9 27.1

No. 2 Mean μ0 1.531 (10.6)

σ 0.366 (2.5)

n 413 –0.15

(–1.0)

99.7 100.0 100.0 100.0 100.0

–0.125

(–0.86)

91.8 100.0 100.0 100.0 100.0

–0.1

(–0.69)

50.0 99.7 99.7 100.0 100.0

–0.05

(–0.34)

0.3 50.0 71.2 91.8 95.3

–0.04

(–0.28)

0 28.8 50.0 79.7 86.7

–0.025

(–0.17)

0 8.2 20.3 50.0 61.0

–0.02

(–0.14)

0 4.8 13.4 39.0 50.0

–0.01

(–0.07)

0 1.3 4.8 20.3 28.8

Table 17—Likelihood of detecting targeted shift when no shift had occurred for 24 samples

Actual shift Likelihood (%) of detecting actual MOE shift for targeted shifts

Grade

in MOE

(x106

 lb/in2

(GPa))

–0.1 x

106 lb/in2

(–0.69 GPa)

–0.05 x

106 lb/in2

(–0.34 GPa)

–0.04 x

106 lb/in2

(–0.28 GPa)

–0.025 x

106 lb/in2

(–0.17 GPa)

–0.02 x

106 lb/in2

(–0.14 GPa)

SS Mean μ0 1.824

(12.6)

σ 0.332

(2.3)

0 0.1 0.7 6.3 11.1

n 413

No. 2 Mean μ0 1.531

(10.6)

σ 0.366

(2.5)

0 0.3 1.3 8.2 13.4

n 413
16

E-Computer E value was the average of two lengthwise

orientations. Information on edgewise static E was collected

from a Metriguard 312 proof loader using a 21:1 span to

depth ratio. The results are plotted in Figure 4.

The data showed that for E values less than about

2.0  106

 lb/in2 (13.8 GPa), a slight upward adjustment to the

E-computer E value would be appropriate; for E values

greater than 2.0  106

 lb/in2 (13.8 GPa), a slight downward

adjustment would be appropriate. No adjustment was made

to convert E-Computer E values to edgewise E values because average E of the SPIB resource monitoring program

data was less than 2.0  106

 lb/in2 (13.8 GPa) and it would be

conservative to not make an adjustment.

Results to Date

The results of the SPIB resource monitoring program from

1994 to 1998 are presented in Table 18 and Figure 5. As a

basis for comparison, Table 18 and Figure 5 include data

from the original In-Grade test program (Green and Evans

1987) and from No. 2 24 tests in the FPL–64 Southern Pine

In-Grade program conducted in the 1960s (Doyle

and Markwardt 1966). The data for the In-Grade No. 2 24

sample, as well as the combined data for No. 2 of all sizes

converted to a 24 basis, are presented.

In general, the results are favorable and do not indicate a

significant departure from the results of the original In-Grade

testing program or the FPL–64 test program. In fact, the

observed MOE tends to be higher than that obtained in either

of these programs. This may be due in part to the fact that

fewer mills separated dense lumber after the In-Grade design

values were adopted in 1991.

Discussion

The potential for the resource to change continuously over

time indicates a critical need for a monitoring system to

identify shifts in mechanical properties. The monitoring of

In-Grade test results is a very complicated issue that lends

itself to many potential methods. For the methods examined,

the multiple-stage approach is apparently the most workable

system, considering current industry practice and procedures.

3.5

3.0

2.5

2.0

1.5

1.0

Edgewise MOE (106 lb/in2)

24.1

20.7

17.2

13.8

10.3

6.9

Edgewise MOE (GPa)

Edgewise E = 0.342 + 0.83 (E-computer E)

r2 = 0.85

E-computer MOE (106 lb/in2)

1.0 1.5 2.0 2.5 3.0 3.5

E-computer MOE (GPa)

6.9 10.3 13.8 17.2 20.7 24.1

Figure 4—Dynamic flatwise MOE (E-computer) as

opposed to edgewise static MOE.

3

2

1

0

Modulus of elasticity (106 lb/in2)

FPL64

Plus one standard deviation

Mean

Minus one standard deviation

20.7

13.8

6.9

0

Modulus of elasticity (GPa)

1994 1995 1996 1997 1998

SPIB Program

InGrade

Figure 5—Results of SPIB resource monitoring

program, 1994–1998.

Table 18—Summary of MOE test results for Southern Pine resource monitoring program

In-Grade testing program Resource monitoring program

Variable

FPL–64

No. 2 2x4 No. 2 2x4 No. 2 all sizes 1994 1995 1996 1997 1998

Sample size 100 413 2,605 405 405 405 390 380

Average E

(x106 lb/in2 (GPa))

1.540

(10.6)

1.531

(10.6)

1.563

(10.8)

1.660

(11.4)

1.585

(10.9)

1.678

(11.6)

1.655

(11.4)

1.593

(11.0)

COV (%) 19.0 23.9 — 22.6 24.0 24.1 25.1 27.4
17

The multiple-stage approach, with multiple steps at Stage I,

allows for small sample sizes with a high probability that the

selected trigger level is truly a change and did not occur by

random chance. The program initiated by the Southern Pine

Inspection Bureau is a fine initial attempt at monitoring

structural lumber. Ultimately, the decision of the best method

for determining changes in the resource lies in the hands of

the various grading agencies responsible for supervising the

implementation of the current visual grading rules.

There is a definite need for more study of monitoring possibilities. Additional work is needed to assess more fully the

economic impact of not recognizing a true shift in properties.

For example, if there is a concern that a change in the resource will primarily increase the coefficient of variability

(COV) of material properties, then a lower tail (that is, 5th

percentile value MOE) might be more sensitive to that

change. Other simulations could be conducted with existing

data to examine the impact of changes in production, such as

increases in MSR production at dimension mills, changes in

markets, or changing variability on reliability-based design

calculations. Finally, a large representative study of plantation material could be collected across the growth range of

the Southern Pine sample to obtain an accurate picture of the

impact of rapid growth on properties.

We hope that the most important impact of this publication

will be to provide a framework for discussing various options

of monitoring properties. We envision that this document

will serve as the starting point for determining appropriate

methods for monitoring structural lumber.

Conclusions

The simulations demonstrated the relative sensitivity of a

multiple-stage monitoring approach to sample size, juvenile

wood content, and selected trigger levels:

Differences in a uniform shift in MOE detected by monitoring procedures may be explained as clearly in closed-form

solutions based on normal distributions as by simulations.

The targeted shift of MOE should be less than

0.1  106

 lb/in2 (0.69 GPa).

For smaller target shifts, it is better to use a multiple-step

process to confirm any observed shifts.

A sample size of approximately 400 is very unlikely to give a

false positive indication of a shift for MOE after three steps.

Depending on the current relationship between MOE and

MOR, if a shift of one rounding rule in MOE is detected, it is

possible that many shifts in a rounding rule for MOR may

have occurred, particularly in the higher lumber grades.

A multiple-stage approach can be smoothly implemented by

a grading agency as part of its regular quality control

program.

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