Accelerated life test calculations using the method of maximum likelihood: an improvement over least squares

Whitman, Charles S.

doi:10.1016/s0026-2714(03)00071-4

Cited by 13 publications

(6 citation statements)

References 1 publication

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“…Therefore, for our analyses, we mostly used a mixed-model framework (using Stata IC 10.0 for the Macintosh; Stata Corporation, College Station, Texas), which is readily amenable to complex data sets with hierarchical structure (Burton et al 1998;Goldstein et al 2002;Rabe-Hesketh and Skrondal 2005). This mixedmodeling approach has the added advantage of estimating parameters with maximum likelihood procedures (we used restricted maximum likelihood), which are often more accurate and more powerful than the traditional least squares estimates used in analyses of variance and other linear models (e.g., Goldschmidt and Timm 2003;Whitman 2003;Orton and Lark 2007). We coded the categorical variables song quality and trill performance as 0 (low quality and low performance) and 1 (high quality and high performance).…”

Section: Statistical Analysesmentioning

confidence: 99%

Female Lincoln's sparrows modulate their behavior in response to variation in male song quality

et al. 2010

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Sexually reproducing organisms should mate with the highest quality individuals that they can. When female songbirds choose a mate, they are thought to use several aspects of male song that reflect his quality. Under resource-limited environmental conditions, male Lincoln's sparrows (Melospiza lincolnii) vary among one another in several aspects of song quality, including song length, song complexity, and trill performance. In a 2-pronged approach, we tested whether variation in song quality of male Lincoln's sparrows influences the behavior of females that are in a reproductive-like state. Over two trials, we exposed females to songs from the high and low ends of the distribution of naturally occurring song quality variation and found a higher level of behavioral activity in females exposed to high-quality songs, especially when they had first been exposed to low-quality songs. We also examined female phonotaxis toward antiphonally played songs with experimentally elevated and reduced trill performance and found that females moved preferentially toward the songs with elevated trill performance. Contrary to most studies investigating the behavioral responses of wild, female songbirds to variation in male song, we obtained our results without administering exogenous estradiol, which can artificially perturb the female's physiology. Our results demonstrate that the behavior of female Lincoln's sparrows is modulated by the quality of male songs to which they are exposed and that trill performance plays a significant role in this behavioral modulation. Furthermore, as the order of song quality presentation matters, it appears that recent song experience also influences female behavior.

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Section: Statistical Analysesmentioning

confidence: 99%

Female Lincoln's sparrows modulate their behavior in response to variation in male song quality

et al. 2010

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“…As has been previously noted [10], least squares is a popular yet inefficient method for extrapolating lifetest data to use conditions. Figure 7 is an Arrhenius plot for the group A-low at temperature data showing both a least squares and ML fit.…”

Section: Comparison Between ML and Least Squaresmentioning

confidence: 99%

“…The method of maximum likelihood (ML) was used for all reliability calculations unless otherwise noted. Details ofthe method are described elsewhere [9,10]. One benefit of using the ML approach is that the estimates are normally distributed with a mean of the estimate itself and a variance found from an advanced likelihood approach [11].…”

Section: I Introductionmentioning

confidence: 99%

Reliability results of HBTs with an InGaP emitter

Whitman

2005

[Reliability of Compound Semiconductors] ROCS Workshop, 2005.

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0183 cwhitman@rfmd com 1. Abstract Accelerated lifetest results are presented on HBTs with InGaP emitters. The data from this experiment are analyzed in several ways. An Arrhenius plot indicates the existence of a tempemture dependent activation energy, E. A low Ea mechanism dominates above Tj 380°C and a high Ea mechanism dominates at lower temperature. The critical transition temperature between regimes is determined using the method of maximum likelihood. The difference in Ea's between low and high temperature regimes is statistically significant.The HBTs are divided into two groups, A and B. Group A contains a total of 116 devices from II wafer lots. The analysis suggests further splitting group A into high and low temperature subgroups.The A-high H-BTs are run stressed at Tj's of 379, 391 and 413 OC and A-low devices are tested at Tj's of 312, 355 and 367 OC. Group B is composed of HBTs from 7 lots from an earlier qualification and are stressed at Tj of285, 305 and 325 OC.A comparison is made between estimates from degradation measurements performed at temperature vs. 40°C for group A-low. No significant difference is observed indicating that beta degradation can be monitored at temperature only and cooling to low temperature is not necessary. Further, the predictions from group A-low and group B data are found to be in good agreement indicating that very high junction temperatures can still provide good estimates of lower temperature behavior.By the method of maximum likelihood, the group A-low data predicts a MTTF at T-= 125°C of 7.6 x 109 hours with 95% CBs of [6.4 x 108, 8.9 x I o'1. Given the typical industry standard of I x 1 06 hours, the reliability requirements are easily met.It is suggested that the standard of lx 106 hours does not adequately take failure time variation into account and that a better specification is in terms of FITs (fails in time). The 20 year average FIT rate at 125 IC is found to be negligible. Assuming a much higher junction temperature of 200 IC, the average failure rate climbs to 0.65 FITs with an upper 95% confidence bound of-6 FITs.

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“…In the literature, some authors suggested checking the validity of the stress independence assumption by a graphical procedure. Whitman et al 7 . showed that the slopes of the probabilities lines for the different stress levels are nearly parallel.…”

Section: Introductionmentioning

confidence: 98%

“…In the literature, some authors suggested checking the validity of the stress independence assumption by a graphical procedure. Whitman et al 7 showed that the slopes of the probabilities lines for the different stress levels are nearly parallel. Also, Barlow et al 8 showed that ALT data of Kevlar/Epoxy strands follow Weibull distribution with a stress-dependent shape parameter.…”

Section: Introductionmentioning

confidence: 99%

Discrimination between accelerated life models via Approximate Bayesian Computation

Rabhi

Abdessalem

Saintis

et al. 2023

Quality & Reliability Eng

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Accelerated life testing (ALT) is widely used in high-reliability product estimation to get relevant information about an item's performance and its failure mechanisms. To analyse the observed ALT data, reliability practitioners need to select a suitable accelerated life model based on the nature of the stress and the physics involved. A statistical model consists of (i) a lifetime distribution that represents the scatter in product life and (ii) a relationship between life and stress. In practice, several accelerated life models could be used for the same failure mode and the choice of the best model is far from trivial. For this reason, an efficient selection procedure to discriminate between a set of competing accelerated life models is of great importance for practitioners. In this paper, accelerated life model selection is approached by using the Approximate Bayesian Computation (ABC) method and a likelihood-based approach for comparison purposes. To demonstrate the efficiency of the ABC method in calibrating and selecting accelerated life model, an extensive Monte Carlo simulation study is carried out using different distances to measure the discrepancy between the empirical and simulated times of failure data. Then, the ABC algorithm is applied to real accelerated fatigue life data in order to select the most likely model among five plausible models. It has been demonstrated that the ABC method outperforms the likelihood-based approach in terms of reliability predictions mainly at lower percentiles particularly useful in reliability engineering and risk assessment applications. Moreover, it has shown that ABC could mitigate the effects of model misspecification through an appropriate choice of the distance function.

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Accelerated life test calculations using the method of maximum likelihood: an improvement over least squares

Cited by 13 publications

References 1 publication

Female Lincoln's sparrows modulate their behavior in response to variation in male song quality

Female Lincoln's sparrows modulate their behavior in response to variation in male song quality

Reliability results of HBTs with an InGaP emitter

Discrimination between accelerated life models via Approximate Bayesian Computation

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