65 research outputs found
Modern Statistical Models and Methods for Estimating Fatigue-Life and Fatigue-Strength Distributions from Experimental Data
Engineers and scientists have been collecting and analyzing fatigue data
since the 1800s to ensure the reliability of life-critical structures.
Applications include (but are not limited to) bridges, building structures,
aircraft and spacecraft components, ships, ground-based vehicles, and medical
devices. Engineers need to estimate S-N relationships (Stress or Strain versus
Number of cycles to failure), typically with a focus on estimating small
quantiles of the fatigue-life distribution. Estimates from this kind of model
are used as input to models (e.g., cumulative damage models) that predict
failure-time distributions under varying stress patterns. Also, design
engineers need to estimate lower-tail quantiles of the closely related
fatigue-strength distribution. The history of applying incorrect statistical
methods is nearly as long and such practices continue to the present. Examples
include treating the applied stress (or strain) as the response and the number
of cycles to failure as the explanatory variable in regression analyses
(because of the need to estimate strength distributions) and ignoring or
otherwise mishandling censored observations (known as runouts in the fatigue
literature). The first part of the paper reviews the traditional modeling
approach where a fatigue-life model is specified. We then show how this
specification induces a corresponding fatigue-strength model. The second part
of the paper presents a novel alternative modeling approach where a
fatigue-strength model is specified and a corresponding fatigue-life model is
induced. We explain and illustrate the important advantages of this new
modeling approach.Comment: 93 pages, 27 page
Non-destructive one-shot device testing under step-stress model with Weibull lifetime distributions
One-shot devices are product or equipment that can be used only once, so they
get destroyed when tested. However, the destructiveness assumption may not be
necessary in many practical applications such as assessing the effect of
temperature on some electronic components, yielding to the so called
non-destructive one-shot devices. Further, one-shot devices generally have
large mean lifetime to failure, and so accelerated life tests (ALTs) must be
performed for inference. The step-stress ALT shorten the lifetime of the
products by increasing the stress level at which units are subjected to
progressively at pre-specified times. Then, the non-destructive devices are
tested at certain inspection times and surviving units can continue within the
experiment providing extra information. Classical estimation methods based on
the maximum likelihood estimator (MLE) enjoy suitable asymptotic properties but
they lack of robustness. In this paper, we develop robust inferential methods
for non-destructive one-shot devices based on the popular density power
divergence (DPD) for estimating and testing under the step-stress model with
Weibull lifetime distributions. We theoretically and empirically examine the
asymptotic and robustness properties of the minimum DPD estimators and
Wald-type test statistics based on them. Moreover, we develop robust estimators
and confidence intervals for some important lifetime characteristics, namely
reliability at certain mission times, distribution quantiles and mean lifetime
of a device. Finally, we analyze the effect of temperature in three electronic
components, solar lights, medium power silicon bipolar transistors and LED
lights using real data arising from an step-stress ALT
Adjusted Empirical Likelihood Models with Estimating Equations for Accelerated Life Tests
This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate the advantage of the proposed methodology
Data Analysis and Experimental Design for Accelerated Life Testing with Heterogeneous Group Effects
abstract: In accelerated life tests (ALTs), complete randomization is hardly achievable because of economic and engineering constraints. Typical experimental protocols such as subsampling or random blocks in ALTs result in a grouped structure, which leads to correlated lifetime observations. In this dissertation, generalized linear mixed model (GLMM) approach is proposed to analyze ALT data and find the optimal ALT design with the consideration of heterogeneous group effects.
Two types of ALTs are demonstrated for data analysis. First, constant-stress ALT (CSALT) data with Weibull failure time distribution is modeled by GLMM. The marginal likelihood of observations is approximated by the quadrature rule; and the maximum likelihood (ML) estimation method is applied in iterative fashion to estimate unknown parameters including the variance component of random effect. Secondly, step-stress ALT (SSALT) data with random group effects is analyzed in similar manner but with an assumption of exponentially distributed failure time in each stress step. Two parameter estimation methods, from the frequentist’s and Bayesian points of view, are applied; and they are compared with other traditional models through simulation study and real example of the heterogeneous SSALT data. The proposed random effect model shows superiority in terms of reducing bias and variance in the estimation of life-stress relationship.
The GLMM approach is particularly useful for the optimal experimental design of ALT while taking the random group effects into account. In specific, planning ALTs under nested design structure with random test chamber effects are studied. A greedy two-phased approach shows that different test chamber assignments to stress conditions substantially impact on the estimation of unknown parameters. Then, the D-optimal test plan with two test chambers is constructed by applying the quasi-likelihood approach. Lastly, the optimal ALT planning is expanded for the case of multiple sources of random effects so that the crossed design structure is also considered, along with the nested structure.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201
Optimal designs of constant‐stress accelerated life‐tests for one‐shot devices with model misspecification analysis
The design of constant-stress accelerated life-test (CSALT) is important in reliability estimation. In reliability studies, practitioners usually rely on underlying distribution to design CSALTs. However, model misspecification analysis of optimal designs has not been examined extensively. This paper considers one-shot device testing data by assuming gamma, Weibull, lognormal and Birnbaum–Saunders (BS) lifetime distributions, which are popular lifetime distributions in reliability studies. We then investigate the effect of model misspecification between these lifetime distributions in the design of optimal CSALTs, in which the asymptotic variance of the estimate of reliability of the device at a specific mission time is minimized subject to a prefixed budget and a termination time of the life-test. The inspection frequency, number of inspections at each stress level, and allocation of the test devices are determined in optimal design for one-shot device testing. Finally, a numerical example involving a grease-based magnetorheological fluids (G-MRF) data set is used to illustrate the developed methods. Results suggest the assumption of lifetime distribution as Weibull or lognormal to be more robust to model misspecification, while the assumption of gamma lifetime distribution seems to be the most non-robust (or most sensitive) one
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