# SPC Test

The SPC (Statistical Process Control) test assesses wether the tightening process is under control by analyzing the trend of torque and angle values in relation to a set of control limits, according to a series of standard rules.

With an SPC test, a pre-defined number of tightening values is collected in subgroups in order to determine the average of each subgroup. The averages' trend is then analyzed to monitor its behavior in relation to the set limits, and to verify whether the SPC rules are met or not.
This test makes it possible to get a trend of the tightening process performances in order to identify beforehand critical variations that might lead to assembling faulty joints.

## SPC test limits

UL | Upper Limit | LWL | Lower Warning Limit
UCL | Upper Control Limit | LCL | Lower Control Limit
UWL | Upper Warning Limit | LL | Lower Limit
T | Target (nominal) |  |

Upper Limit (UL) and Lower Limit (LL) are the limits the user configures for the test.

The other SPC test limits are calculated as follows:

Upper Control Limit = ((UL + LL) / 2) + (A · ((UL - LL) / 6))
Lower Control Limit = ((UL + LL) / 2) - (A · ((UL - LL) / 6))
Upper Warning Limit = ((UL + LL) / 2) + (2/3 · (UCL - ((UL + LL) / 2)))
Lower Warning Limit = ((UL + LL) / 2) - (2/3 · (((UL + LL) / 2) - LCL))
Range = D2 · ((UL - LL) / 6

In these formulas, A and D2 are coefficients that depend on the number of SPC tests performed:

Number of SPC tests | A | D2
--- | --- | ---
1 | 0.000 | 0.000
2 | 2.121 | 3.686
3 | 1.732 | 4.358
4 | 1.500 | 4.698
5 | 1.342 | 4.918
6 | 1.225 | 5.078
7 | 1.134 | 5.204
8 | 1.061 | 5.306
9 | 1.000 | 5.393
10 | 0.949 | 5.469
11 | 0.905 | 5.535
12 | 0.866 | 5.594
13 | 0.832 | 5.647
14 | 0.802 | 5.696
15 | 0.775 | 5.741
16 | 0.750 | 5.782
17 | 0.728 | 5.820
18 | 0.707 | 5.856
19 | 0.688 | 5.891
20 | 0.671 | 5.921
21 | 0.655 | 5.951
22 | 0.640 | 5.979
23 | 0.626 | 6.006
24 | 0.612 | 6.031
25 | 0.600 | 6.056

## SPC test rules

The following rules are applied to the last set of samples collected during a single SPC test:

- RULE1 - Verify whether the last average is out of control limits

| Diagnosis: The average is higher than the upper control limit, but it does not exceed the upper tolerance limit. |  | Diagnosis: The average is lower than the lower control limit, but it does not fall under the lower tolerance limit.

- RULE 6 - Verify whether the dispersion is too large

Dispersion is considered too large when the difference between the maximum and minimum value is greater than the Range (see Range formula above).

| Diagnosis: Excessive dispersion of the values prevents a proper calibration of the tool, but the measured values are still within the tolerance limits. |  | Diagnosis: Some measured values are out of tolerance limits. Excessive dispersion of the values prevents a proper calibration of the tool.

- RULE 7 - Verify whether at least one value is outside the tolerance limits

| Diagnosis: At least one value is higher than the upper tolerance limit. |  | Diagnosis: At least one value is lower than the lower tolerance limit.

- RULE 8 - Verify whether the dispersion is larger than the warning limits

| Diagnosis: Dispersion is larger than the warning limits and at least one value is outside the tolerance limits. |  | Diagnosis: Dispersion is larger than the warning limits but values are within the tolerance limits.

The following rules are applied to the last averages of the set of samples collected during an SPC test.
The device stores the last seven averages to analyze the trend according to these rules:

- RULE 3 - Verify whether the last 7 averages are over or under the nominal value

| Diagnosis: Averages are higher than the target value, but they do not exceed the upper tolerance limit. |  | Diagnosis: Averages are lower than the target value, but they do not fall under the lower tolerance limit.

- RULE 4 - Verify whether the last 7 averages are increasing or decreasing

| Diagnosis: Averages tend to be higher than the target value, but they do not exceed the upper tolerance limit. |  | Diagnosis: Averages tend to be lower than the target value, but they do not fall under the lower tolerance limit.

- RULE 5 - Verify whether the last 2 averages out of the warning limits

| Diagnosis: Averages are higher than the Upper Warning Limit, but they do not exceed the upper tolerance limit. |  | Diagnosis: Averages are lower than the Lower Warning Limit, but they do not fall under the lower tolerance limit.

- RULE 2 - Verify whether the last 4 averages are out of 1/3 of the control limits

| Diagnosis: Averages are higher than 1/3 of the Upper Control Limit, but they do not exceed the upper tolerance limit. |  | Diagnosis: Averages are below 1/3 of the Lower Control Limit, but they do not fall under the lower tolerance limit.