The product is called "Linearlight Source" for each unit of the product has seven (7) white light LEDs and seven (7) Infrared LEDs, in series and in line one after another (alternating). The product is a combined lighting and touch sensor for touch screens of Laptops and of GPS devices for vehicles.
Test procedure for this product is two-stage. First stage is the test for infrared LEDs' operating properties (basically wavelength and power) and the second stage is for white light LEDs' operating properties (basically Luminance and Chromaticity). Because of the physical configuration of the product, in both stages of the test, the product has to be manually positioned onto the jig of test handler before the operator presses the start button to commence the test. After the test, operator unloads the product and loads another unit.
The need to conduct Gage R&R arose when results of pre-operation calibrations started to incur large variations just between calibrations of intervals of just hours and initial analyses showed no discernable pattern in variations. It was further theorized that manual loading of the product onto the jig affects the readings due to possible variation in positioning the product.
Special consideration for this GR&R study is that the industry standard of maximum allowable Study Variance of 10%, is not applicable in this case, for the customer of this product, allows only +/- 2% maximum variation from the established true value of the calibration samples.
Objective of the Study
To effectively identify main factor causing the failures of pre-operation calibrations.
Methodology
To be effective in identifying the cause factor, this study will utilize the GRR ANOVA method. With this method, we will be able to breakdown total variation to its components and their respective per cent contributions.
Data and Computations
Table 1 | Raw Data ( Crossed Sampling )
Table 2 | Totals
| Gage R & R Raw Data ( Crossed ) | ||||||
| Part | Appraiser 1 | Appraiser 2 | Appraiser 3 | |||
| Run 1 | Run 2 | Run 1 | Run 2 | Run 1 | Run 2 | |
| 1 | 0.731 | 0.732 | 0.732 | 0.730 | 0.730 | 0.730 |
| 2 | 0.766 | 0.766 | 0.767 | 0.765 | 0.766 | 0.765 |
| 3 | 0.762 | 0.760 | 0.761 | 0.760 | 0.761 | 0.759 |
| 4 | 0.781 | 0.779 | 0.781 | 0.777 | 0.779 | 0.779 |
| 5 | 0.763 | 0.763 | 0.761 | 0.761 | 0.761 | 0.761 |
| 6 | 0.767 | 0.767 | 0.767 | 0.763 | 0.766 | 0.767 |
| 7 | 0.778 | 0.776 | 0.775 | 0.774 | 0.777 | 0.775 |
| 8 | 0.761 | 0.760 | 0.761 | 0.760 | 0.761 | 0.758 |
| 9 | 0.775 | 0.774 | 0.772 | 0.771 | 0.773 | 0.772 |
| 10 | 0.762 | 0.761 | 0.763 | 0.760 | 0.762 | 0.760 |
Table 2 | Totals
| Table of Totals | ||||
| Part | Appraiser 1 | Appraiser 2 | Appraiser 3 | Total |
| 1 | 1.463 | 1.462 | 1.459 | 4.385 |
| 2 | 1.531 | 1.531 | 1.531 | 4.594 |
| 3 | 1.522 | 1.520 | 1.520 | 4.562 |
| 4 | 1.560 | 1.558 | 1.557 | 4.675 |
| 5 | 1.525 | 1.522 | 1.521 | 4.569 |
| 6 | 1.534 | 1.530 | 1.533 | 4.597 |
| 7 | 1.554 | 1.549 | 1.552 | 4.655 |
| 8 | 1.521 | 1.521 | 1.520 | 4.561 |
| 9 | 1.548 | 1.543 | 1.545 | 4.636 |
| 10 | 1.524 | 1.523 | 1.522 | 4.569 |
| Total | 15.282 | 15.259 | 15.261 | 45.802 |
Table 3 | ANOVA Table ( Full Model )
| ANOVA Table ( Full Model ) | ||||||
| Source | DoF | SoS | MS | F Statistics | p-value | Significance |
| Appraiser | 2 | 1.567E -05 | 7.833E-06 | 4.454 | 0.020 | |
| Parts | 9 | 9.563E-03 | 1.063E-03 | 604.095 | 0.000 | most significant |
| Interaction | 18 | 1.434E-05 | 7.965E-07 | 0.453 | 0.960 | very insignificant |
| Gage Error | 30 | 5.277E-05 | 1.759E-06 | |||
| Total | 59 | 9.645E-03 | ||||
Table 4 | ANOVA ( Reduced Model )
| ANOVA ( Reduced Model ) | ||||||
| Source | DoF | SoS | MS | F Statistics | p-value | Significance |
| Appraiser | 2 | 1.567E-05 | 7.833E-06 | 5.603 | 0.006 | |
| Parts | 9 | 9.563E-03 | 1.063E-03 | 760.038 | 0.000 | most significant |
| Gage Error | 48 | 6.710E-05 | 1.398E-06 | |||
| Total | 59 | 9.654E-03 | ||||
Table 5 | Variance Decomposition
| Variance Decomposition | ||
| Source | Variance Component | % Contribution |
| Total GR&R | 0.00000172 | 0.96 % |
| Repeatability | 0.00000140 | 81.29 % |
| Reproducibility | 0.00000032 | 18.71 % |
| Part to Part | 0.00017685 | 99.04 % |
| Total Variance | 0.00017857 | 100.00 % |
Table 6 | Gage Repeatability and Reproducibility
| Gage Repeatability and Reproducibility | |||
| Source | Standard Deviation | Study Variance (6s) | % Study Variance |
| Total GRR | 0.00131138 | 0.00786828 | 9.81 % |
| Repeatability | 0.00118235 | 0.00709412 | 8.85 % |
| Reproducibility | 0.00056724 | 0.00340344 | 4.24 % |
| Part to Part | 0.01329852 | 0.07979113 | 99.52 % |
| Total | 0.01336302 | 0.08017814 | 100.00 % |
Table 7 | Gage Capability Ratio
| Gage Capability Ratio | |
| True Value | 0.760 |
| Upper Specification (+2%) | 0.775 |
| Lower Specification (-2%) | 0.745 |
| Tolerance Width | 0.030 |
| GCR (study variance of 6s) | 0.26 |
| % GCR | 26% |
| ndc | 14 |
Conclusion
Based on study variance of six (6) standard deviations, the Gage Capability Ratio of 0.26 is acceptable. This means that the Total Gage R&R consumes only 26 % of the tolerance given by the customer which is +/-2 % from the true value. The current measurement system is adequate since the number of distict categories (ndc) it can resolve is 14. AIAG 2002 standards, requires that ndc be at least 5.
What causes pre-operation calibrations to fail is the product itself. The part-to-part variation compose 99.58 % of the total variation. Therefore in this case, there is no need to calibrate the test machine nor re-train the operators.
