Council Directive of 19 December 1974 on the approximation of the laws of the Member States relating to bottles used as measuring containers (75/107/EEC)

3. APPLICATION OF THE RESULTS U.K.

3.1. Use of the standard deviation method U.K.

The number of measuring container bottles in the sample is 35.

3.1.1. Calculate as follows (see 3.1.4.): U.K.

3.1.1.1.

the average of the actual capacities x_i of the bottles in the sample,

3.1.1.2.

estimated standard deviation s of the actual capacities x_i of the bottles in the batch.

3.1.2. Calculate as follows: U.K.

3.1.2.1.

The upper limit T_s: the sum of the indicated capacity (see Annex I, Section 8) and of the maximum permissible error corresponding to this capacity.

3.1.2.2.

The lower limit T_i: the difference between the indicated capacity (see Annex I, Section 8) and the maximum permissible error corresponding to this capacity.

3.1.3. Acceptance criteria: U.K.

The batch shall be declared to comply with the Directive if the numbers and s verify simultaneously the following three inequations:

where k

=

1·57

and F

=

0·266

3.1.4. Calculation of the mean value and the estimated standard deviation s of the batch. U.K.

Calculate as follows:

• the sum of the 35 actual capacity measurements x = Σx_i

• the mean value of the 35 measurements

• the sum of the squares of the 35 measurements Σx_i ²

• the square of the sum of the 35 measurements (Σx_i)², then

• the corrected sum:

• the estimated variance

Hence the estimated standard deviation:

3.2. Use of the average range method U.K.

The number of measuring container bottles in the sample is 40.

3.2.1. Calculate as follows (see 3.2.4): U.K.

3.2.1.1.

the average of the actual capacities x of the bottles in the sample,

3.2.1.2.

the average range of the actual capacities x_i of the bottles in the sample.

3.2.2. Calculate as follows: U.K.

3.2.2.1.

the upper limit T_s the sum of the indicated capacity (see Annex I, Section 8) and the maximum permissible error corresponding to this capacity,

3.2.2.2.

the lower limit T_i:

difference between the indicated capacity (see Annex I, Section 8) and the maximum permissible error corresponding to this capacity.

3.2.3. Acceptance criterion: U.K.

The batch shall be declared to comply with the Directive if the numbers and verify simultaneously the following three inequations:

where k'

=

0·668,

and F'

=

0·628.

3.2.4. Calculation of the mean value and of the average range of of the 40 measuring container bottles in the sample. U.K.

3.2.4.1.

to obtain , calculate as follows:

• the sum of the 40 actual capacity measurements x_i: Σ x_i

• the mean value of these 40 measurements:

3.2.4.2.

To obtain

Divide the sample, in chronological order of selection, into eight sub-samples of five measuring container bottles each.

Calculate as follows:

• the range of each of the sub-samples, i.e. the difference between the actual capacity of the largest and the smallest of the five bottles in the sub-sample; eight ranges are thus obtained: R₁; R₂; ... R₈

• the sum of the ranges of the eight sub-samples:

  Σ R_i = R₁ + + ... + R₈

The average range is therefore: