Tools › Reliability › Life Data › Accelerated Life › Example
Nelson's Class-B insulation data (SAS RELIABILITY procedure): Arrhenius-lognormal fit with quantiles at 130 °C
| Tool | Accelerated Life |
| Source | SAS Institute Inc. (2018). "The RELIABILITY Procedure: Analysis of Accelerated Life Test Data." SAS/QC User's Guide. Data from Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analyses. Wiley, New York, p. 243. |
| Level | Professional |
Problem
Forty Class-B insulation specimens were tested at 150, 170, 190 and 220 °C; 17 failed and 23 were removed unfailed. Fit a lognormal distribution with an Arrhenius relationship, report the parameter estimates with their standard errors, and estimate the median and the 10 % and 90 % life quantiles at the 130 °C design temperature with 95 % confidence limits.
Inputs to Enter
- Model Arrhenius, distribution lognormal, °C; use temperature 130 °C
- 150 °C: 10 units suspended at 8,064 h
- 170 °C: failures 1764, 2772, 3444, 3542, 3780, 4860, 5196 h; 3 suspended at 5,448 h
- 190 °C: failures 408, 408, 1344, 1344, 1440 h; 5 suspended at 1,680 h
- 220 °C: failures 408, 408, 504, 504, 504 h; 5 suspended at 528 h
Answers
- SAS (base-10 logs, x = 1000/T): intercept −6.0182 (s.e. 0.9467), slope 4.3103 (s.e. 0.4366), scale 0.2592 (s.e. 0.0473, 95 % 0.1812–0.3708), log-likelihood −12.96533
- At 130 °C: median 47,135.1 h (s.e. 16,125.5; 95 % 24,106.7–92,162.0), 10 % quantile 21,937.7 h (95 % 11,780.6–40,851.9), 90 % quantile 101,274 h
- Same fit in ReliaSoft's benchmark Example 1: σ = 0.59678 (Nelson 0.59673), B = 9,924.8 (Nelson 9,920.2), C = 9.590 × 10⁻⁷ (Nelson 9.695 × 10⁻⁷)
Notes
The tool prints natural-log parameters; SAS's base-10 values are the tool's divided by ln 10 and its slope is per 1000/T. SAS's log-likelihood is the density of log10 t without the Jacobian, so it differs from the tool's by a constant.