Arrhenius-Lognormal Model for Interval Data
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This example compares the results for the Arrhenius-Lognormal model with interval data.
Reference Case
The data set is from Example 19.11 on page 508 in the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.
Data
The data set for a new-technology IC Device is given below.
| Number in Group | Last Inspected (Hr) | State F/S | Time to State | Temperature (K) |
|---|---|---|---|---|
| 50 | 788 | S | 1536 | 423.15 |
| 50 | 788 | S | 1536 | 448.15 |
| 50 | 96 | S | 96 | 473.15 |
| 1 | 384 | F | 788 | 523.15 |
| 3 | 788 | F | 1536 | 523.15 |
| 5 | 1536 | F | 2304 | 523.15 |
| 41 | 1536 | S | 2304 | 523.15 |
| 4 | 192 | F | 384 | 573.15 |
| 27 | 384 | F | 788 | 573.15 |
| 16 | 788 | F | 1536 | 573.15 |
| 3 | 788 | S | 1536 | 573.15 |
Result
The following function is used for the Ln-Mean [math]\displaystyle{ \mu'\,\! }[/math] of the lognormal distribution:
- [math]\displaystyle{ \mu' = \beta_{0}+\beta_{1} \times \frac{11605}{T}\,\! }[/math]
where T is the temperature; [math]\displaystyle{ \beta_{1}\,\! }[/math] is the activation energy; 11605 is calculated from the reciprocal of the Boltzmann constant. This function can be written in the following way:
Results in ALTA