Automatic Bulk Weighing Systems

EPO ABWS (Rev. 08/14) DRAFT Page 1

EPO No. 16

Appendix (Supplement 3)

Determining Scale Error When Applying the Alternative Substitution 

Test Method 

This supplement is intended to further clarify how scale error is determined from

hypothetical results, made up to imitate those that might be recorded by an official who 

applied the various steps of the alternative substitution test method to perform an 

increasing-load test on a scale with digital indication. The results of having applied each

step of the test are shown with sufficient notation to make clear how the substitution test 

loads were created and scale error determined from using error weights. Shading is used 

to differentiate between values associated with the most current step from those of 

previous steps. 

Types of Error:

When using the alternative substitution test method, there are two types of errors you will 

need to consider: 

1) The error associated with each step of the increasing-load test in which test 

weight is applied from a proper starting reference. These are referred to herein as 

“step errors.” You will see these errors recorded in the column of the example 

tables titled: “Error (En)”

2) The error associated with the cumulative results of one or more steps in which test 

weight is applied during of the increasing-load test. These errors are referred to 

herein as “cumulative errors.” Cumulative errors are determined by summing the 

results of consecutive increasing-load steps . You will see these errors recorded 

in the column of the example tables titled: “Error (∑En)”

Tolerance Application:

Tolerances apply to both types of error as follows:

1) Step Errors: Tolerances apply to the error corresponding to the test weight

portion of each test load applied during the increasing-load test, including test 

loads comprised of substituted material and test weight. 

2) Cumulative Errors: Tolerances apply to the error corresponding to the 

cumulative results of two or more consecutive increasing-load steps in which test 

weight is applied from a proper starting reference established at no load and each 

substitution load therefrom. 

Establish a proper reference at no load (high-level step 1)

Test 

Description

Test 

Weight

Substituted 

Bulk 

Starting 

Reference

Ending 

Reference

Scale 

Indication

Error 

(En)

Error

(∑En)
Automatic Bulk Weighing Systems

EPO ABWS (Rev. 08/14) DRAFT Page 2

(L) Material (Rs) (Re) (Ix)

Zero load 0 0 6 10/20

Apply the test weight load, establish proper reference, and determine the total amount 

of scale error (high level steps 2 and 3)

Test 

Description

Test 

Weight

(L)

Substituted 

Bulk 

Material

Starting 

Reference

(Rs)

Ending 

Reference

(Re)

Scale 

Indication

(Ix)

Error 

(En)

Error

(∑En)

Zero load 0 0 6 10/20

Increase 3 000 6 9 3 010/20 -3 -3 Step 1

The following formula is used to determine the amount of error (i.e., step error) in the 

scale at the first applied test weight load: 

En = Ie – Is – L + Rs – Re

Where:

“En” (Error) represents the amount of error in the scale relative to the applied test weight 

portion of the total applied test load;

“Ie” (Indication ending) represents the scale indication after the test weight has been 

applied and proper reference established;

“Is” (Indication start) represents the scale indication before the test weight was applied;

“L” (Load) represents the value of the applied test weight excluding any substituted load;

“Rs” (Reference start) represents the value of the error weights on the load-receiving

element that established proper reference prior to the test weight being applied; and

“Re” (Reference ending) represents the value of the error weights on the load-receiving 

element that established proper reference after the test weight had been applied. 

Thus, from the values recorded in the Table above:

“Ie” is equal to 3 015

“Is” is equal to 15

“L” is equal to 3 000

“Rs” is equal to 6

“Re” is equal to 9

To determine the amount of error in the scale, insert the appropriate corresponding values

obtained during testing into the formula and solve the equation as follows:

En = Ie – Is – L + Rs – Re
Automatic Bulk Weighing Systems

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Actual test result values (from Table above) inserted into the formula: 

En = 3 015 – 15 – 3 000 + 6 – 9

Completed formula calculation : Error = - 3

Evaluating the Results:

Since only test weights have been applied thus far during testing, the cumulative results

are the same as the error for Step 1. 

Verify return to no-load reference (high-level step 4)

Test 

Description

Test 

Weight

(L)

Substituted 

Bulk 

Material

Starting 

Reference

(Rs)

Ending 

Reference

(Re)

Scale 

Indication

(Ix)

Error 

(En)

Error

(∑En)

Zero load 0 0 6 10/20

Increase 3 000 6 9 3 010/20 -3 -3 Step 1

Zero Return 0 0 6 7 10/20 -1*

* Note from the shaded area that error weight in the amount of 6 pounds was initially 

balanced in to create proper reference at zero load. However, after the test weights 

were applied and then removed to verify zero return, 7 pounds of error weight was 

needed to duplicate proper reference, thus resulting in a - 1 pound balance change. 

Create the first substitution test load and establish proper reference (high-level step 5)

Test 

Description

Test 

Weight

(L)

Substituted 

Bulk 

Material

Starting 

Reference

(Rs)

Ending 

Reference

(Re)

Scale 

Indication

(Ix)

Error 

(En)

Error

(∑En)

Zero load 0 0 6 10/20

Increase 3 000 6 9 3 010/20 -3 -3 Step 1

Zero Return 0 0 6 7 10/20 -1

1st Sub. 2 980 1 2 980/90
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EPO ABWS (Rev. 08/14) DRAFT Page 4

Apply test weight to first substitution test load, establish proper reference, and 

determine the total amount of scale error (high-level steps 6 and 7)

Test 

Description

Test 

Weight

(L)

Substituted 

Bulk 

Material

Starting 

Reference

(Rs)

Ending 

Reference

(Re)

Scale 

Indication

(Ix)

Error 

(En)

Error

(∑En)

Zero load 0 0 6 10/20

Increase 3 000 6 9 3 010/20 -3 -3 Step 1

Zero Return 0 0 6 7 10/20 -1

1st Sub. 2 980 1 2 980/90

Increase 3 000 2 985 1 6 5 980/90 -5 -8 Step 2

To determine the amount of error in the scale corresponding to the test weight portion of 

the test load (i.e., step error), insert the appropriate values obtained during testing into the 

formula and solve the equation as follows:

En = Ie – Is – L + Rs – Re 

Actual test result values from the table above illustrating the results of high-level steps 6 

and 7 inserted into the formula: 

En = 5 985 – 2 985 – 3 000 + 1 – 6

Completed formula calculation : Error = - 5

Evaluating the Results:

Tolerances apply to:

1) the error corresponding to the test weight portion (i.e., 3 000 pounds) of the 

applied load for this particular increasing-load step; and

2) the error corresponding to the cumulative results of having applied the test weight 

twice; the first of which, resulted in a - 3 pound error, and the second of which,

resulted in a - 5 pound error. Thus, the cumulative error corresponding to the first 

two increasing-load steps is - 8 pounds.

In order for the example scale to meet applicable tolerances:

1) the result (error) associated with the addition of the test weight in each step of the 

increasing-load test (identified in the table as “Increase”) must be within 

applicable tolerance in relation to the test weight amount applied in each of those 

steps; and 

2) the cumulative results (error) of the two increasing-load steps completed thus far, 

must also be within tolerance. That is, the sum of the error recorded in each of 

the increasing-load steps completed thus far in relation to the sum of the test 

weight applied in each of those same steps must be within tolerance. In the two

increasing-load steps completed thus far, the cumulative error is - 8 pounds and 

the sum of the test weight applied is 6 000 pounds.

Create the second substitution test load and establish proper reference (high-level 

tep 8)
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EPO ABWS (Rev. 08/14) DRAFT Page 5

Test 

Description

Test 

Weight

(L)

Substituted 

Bulk 

Material

Starting 

Reference

(Rs)

Ending 

Reference

(Re)

Scale 

Indication

(Ix)

Error 

(En)

Error

(∑En)

Zero load 0 0 6 10/20

Increase 3 000 6 9 3 010/20 -3 -3 Step 1

Zero Return 0 0 6 7 10/20 -1

1st Sub. 2 980 1 2 980/90

Increase 3 000 2 985 1 6 5 980/90 -5 -8 Step 2

2nd Sub. 5 950 9 5 950/60

Apply test weight to the second substitution test load, establish proper reference, and 

determine the total amount of scale error (high-level steps 9 and 10)

Test 

Description

Test 

Weight

(L)

Substituted 

Bulk 

Material

Starting 

Reference

(Rs)

Ending 

Reference

(Re)

Scale 

Indication

(Ix)

Error 

(En)

Error

(∑En)

Zero load 0 0 6 10/20

Increase 3 000 6 9 3 010/20 -3 -3 Step 1

Zero Return 0 0 6 7 10/20 -1

1st Sub. 2 980 1 2 980/90

Increase 3 000 2 985 1 6 5 980/90 -5 -8 Step 2

2nd Sub. 5 950 9 5 950/60

Increase 3 000 5 955 9 8 8 950/60 +1 -7 Step 3

To determine the amount of error in the scale corresponding to the test weight portion of 

the test load (i.e., step error), insert the appropriate corresponding values obtained during 

testing into the formula and solve the equation as follows:

En = Ie – Is – L + Rs – Re 

Actual test result values from the table above illustrating the results of high-level steps 9 

and 10 inserted into the formula: 

En = 8 955 – 5 955 – 3 000 + 9 – 8

Completed formula calculation : Error = + 1

Evaluating the Results:

Tolerances apply to:

1) the error corresponding to the test weight portion (i.e., 3 000 pounds) of the total 

applied load for this particular step; and 

2) the error corresponding to the cumulative results of having applied the test weight 

three times (i.e., once in each of the three consecutive increasing-load steps). The

cumulative error corresponding to the three increasing-load steps completed thus 

far is - 7 pounds. 

In order for the example scale to meet applicable tolerances:

1) the result (error) associated with the addition of the test weight in each step of the 

increasing-load test (identified in the table as “Increase”) must be within 
Automatic Bulk Weighing Systems

EPO ABWS (Rev. 08/14) DRAFT Page 6

applicable tolerance in relation to the test weight amount applied in each of those 

steps; and 

2) the cumulative results (errors) of all increasing-load steps completed thus far, 

must also be within tolerance. That is, the sum of the error recorded in each of 

the increasing-load steps completed thus far in relation to the sum of the test 

weight applied in each of those same steps must be within tolerance. In the three 

increasing-load steps completed thus far, the cumulative error is - 7 pounds and 

the sum of the test weight applied in each of those same steps is 9 000 pounds. 

Create the third substitution test load and establish proper reference (high-level 

step 11)

Test 

Description

Test 

Weight

(L)

Substituted 

Bulk 

Material

Starting 

Reference

(Rs)

Ending 

Reference

(Re)

Scale 

Indication

(Ix)

Error 

(En)

Error

(∑En)

Zero load 0 0 6 10/20

Increase 3 000 6 9 3 010/20 -3 -3 Step 1

Zero Return 0 0 6 7 10/20 -1

1st Sub. 2 980 1 2 980/90

Increase 3 000 2 985 1 6 5 980/90 -5 -8 Step 2

2nd Sub. 5 950 9 5 950/60

Increase 3 000 5 955 9 8 8 950/60 +1 -7 Step 3

3rd Sub. 8 950 3 8 950/60

Apply the test weight to the third substitution load, establish proper reference, and 

determine the total amount of scale error (high-level steps 12 and 13)

Test 

Description

Test 

Weight

(L)

Substituted 

Bulk 

Material

Starting 

Reference

(Rs)

Ending 

Reference

(Re)

Scale 

Indication

(Ix)

Error 

(En)

Error

(∑En)

Zero load 0 0 6 10/20

Increase 3 000 6 9 3 010/20 -3 -3 Step 1

Zero Return 0 0 6 7 10/20 -1

1st Sub. 2 980 1 2 980/90

Increase 3 000 2 985 1 6 5 980/90 -5 -8 Step 2

2nd Sub. 5 950 9 5 950/60

Increase 3 000 5 955 9 8 8 950/60 +1 -7 Step 3

3rd Sub. 8 950 3 8 950/60

Increase 3 000 8 955 3 8 11 950/60 -5 -12 Step 4

To determine the amount of error in the scale corresponding to the test weight portion of 

the test load (i.e., step error), insert the appropriate corresponding values obtained during 

testing into the formula and solve the equation as follows:

En = Ie – Is – L + Rs – Re 

Actual test result values from the table above illustrating the results of high-level steps 12 

and 13 inserted into the formula: 

En = 11 955 – 8 955 – 3 000 + 3 - 8
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Completed formula calculation : Error = - 5

Evaluating the Results:

Tolerances apply to:

1) the error corresponding to the test weight portion (i.e., 3 000 pounds) of the total 

applied load for this particular step; and 

2) the error corresponding to the cumulative results of having applied the test 

weight four times (i.e., once in each of the four consecutive increasing-load 

steps). The cumulative error corresponding to the four increasing-load steps 

completed thus far is - 12 pounds.

In order for the example scale to meet applicable tolerances:

1) the result (error) of each individual step of the increasing-load test (identified in 

the table as “Increase”) must be within applicable tolerance in relation to the test 

weight amount applied in that particular step; and 

2) the cumulative results (errors) of all increasing-load steps completed thus far, 

must also be within tolerance. That is, the sum of the error recorded in each

individual increasing-load step completed thus far, in relation to the sum of the 

test weight applied in each of those same steps. In the four increasing-load steps 

completed thus far, the cumulative error of - 12 pounds and the sum of the test 

weight applied in each of those same steps is 12 000 pounds. 

Recording the Results of Additional Testing (If Necessary)

Note: If maximum test load has not been achieved after the test weights are applied to 

the third substitution test load, it will be necessary to develop additional substitution test 

loads and apply the test weights to those test loads as many additional times as needed to 

complete the test. These additional tests are to be performed in the same manner as those 

before them and the results recorded the same way.