Automatic Bulk Weighing Systems 

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

EPO No. 16

Appendix B (Supplement 2)

Determining Scale Error When Applying the 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 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 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:

The tolerances apply to the total cumulative test load for the successive increasing-load

tests. 

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

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

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

scale error (high level steps 2 and 3)
Automatic Bulk Weighing Systems 

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

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

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

En = 3 015 – 15 – 3 000 + 6 – 9

Completed formula calculation step 1: Error = - 3
Automatic Bulk Weighing Systems 

EPO ABWS (Rev. 08/14) DRAFT Page 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

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. 3 000 5 3 010/20 -3 -3

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. 3 000 5 3 010/20 -3 -3

Increase 3 000 3 000 5 9 6 010/20 -4 -7 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 = 6 015 – 3 015 – 3 000 + 5 – 9

Completed formula calculation step 2: Error = - 4

Evaluating the Results:
Automatic Bulk Weighing Systems 

EPO ABWS (Rev. 08/14) DRAFT Page 4

Tolerances apply to the cumulative results of the first two increasing-load steps 

which is - 7 pounds.

In order for the example scale to meet applicable tolerances 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 - 7

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 

step 8)

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. 3 000 5 3 010/20 -3

Increase 3 000 3 000 5 9 6 010/20 -4 -7 Step 2

2nd Sub. 6 000 3 6 010/20 -7

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. 3 000 5 3 010/20 -3

Increase 3 000 3 000 5 9 6 010/20 -4 -7 Step 2

2nd Sub. 6 000 3 6 010/20 -7

Increase 3 000 6 000 3 4 9 000/10 -11 -18 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 = 9 005 – 6 015 – 3 000 + 3 – 4

Completed formula calculation step 3: Error = - 11
Automatic Bulk Weighing Systems 

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

Evaluating the Results:

Tolerances apply to 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 - 18 pounds. 

In order for the example scale to meet applicable tolerances 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 - 18 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. 3 000 5 3 010/20 -3

Increase 3 000 3 000 5 9 6 010/20 -4 -7 Step 2

2nd Sub. 6 000 3 6 010/20 -7

Increase 3 000 6 000 3 4 9 000/10 -11 -18 Step 3

3rd Sub. 9 000 7 9 000/10 -18

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. 3 000 5 3 010/20 -3

Increase 3 000 3 000 5 9 6 010/20 -4 -7 Step 2

2nd Sub. 6 000 3 6 010/20 -7

Increase 3 000 6 000 3 4 9 000/10 -11 -18 Step 3

3rd Sub. 9 000 7 9 000/10 -18

Increase 3 000 9 000 7 5 11 980/90 -18 -36 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:
Automatic Bulk Weighing Systems 

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

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 = 11 985 – 9 005 – 3 000 + 7 - 5

Completed formula calculation step 4: Error = - 18

Evaluating the Results:

Tolerances apply to 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 - 36 pounds.

In order for the example scale to meet applicable tolerances 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 - 36 pounds and 

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

Additional Testing to Achieve Maximum Test Load (If Necessary)

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

substitution test load, remove the test weight and conduct a strain load to make possible 

additional testing. Up to three additional substitution tests may be conducted after proper 

reference has been established at any strain-load. The unshaded portion of the table 

below shows example results of a single strain-load and two substitution tests that were 

necessary to achieve a maximum test load to used capacity.

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. 3 000 5 3 010/20 -3

Increase 3 000 3 000 5 9 6 010/20 -4 -7 Step 2

2nd Sub. 6 000 3 6 010/20 -7

Increase 3 000 6 000 3 4 9 000/10 -11 -18 Step 3

3rd Sub. 9 000 7 9 000/10 -18

Increase 3 000 9 000 7 5 11 980/90 -18 -36 Step 4

Strain Load 5 18 300/10 N/A N/A

3 000 5 8 21 300/10 -3 -3 Step 1

1st Sub. 3 000 2 21 300/10 -3

Increase 3 000 3 000 2 6 24 300/10 -4 -7 Step 2

2nd Sub. 6 000 8 24 300/10 -7

Increase 3 000 6 000 8 8 27 290/00 -10 -17 Step 3
Automatic Bulk Weighing Systems 

EPO ABWS (Rev. 08/14) DRAFT Page 7

Tolerance application for increasing-load tests conducted from strain loads: With a 

strain load applied and proper reference established, the scale’s indication and the amount 

of error weight used to establish the proper reference provides a new starting point for 

additional increasing-load tests. For those additional tests, tolerances apply to the total 

cumulative test load for successive increasing load tests applied from the strain load, 

including substitution tests.