Search Results (36)

This study introduces a novel approach to accelerated life test experiments by examining competing risk factors using the Tampered Random Variable (TRV) model. This approach remains extensively unexplored in current research. The methodology is implemented for a simple step-stress life test (SSLT) model and accounts for various causes of failure. The Power Chris–Jerry (PCJ) distribution is utilized to model the lifetimes of units under different stress levels, incorporating unique shape parameters while maintaining a fixed-scale parameter. This study employs the TRV model to integrate constant tampering coefficients for each failure cause within step-stress data analysis. Maximum-likelihood estimates for model parameters and tampering coefficients are derived from SSLT data, and some confidence intervals are presented based on the Type-II censoring scheme. Furthermore, Bayesian estimation is applied to the parameters, supported by appropriate prior distributions. The robustness of the proposed method is validated through comprehensive simulations and real-world applications in different scientific domains. Full article

In this article, we discuss an unusual pattern in long-crack behavior at low stress intensity factor ranges ΔK (below ΔK_th), characterized by an initial dip, followed by a plateau, and then an acceleration in fatigue crack growth (FCG) rate. This unanticipated FCG behavior was first observed experimentally in the IMI 834 alloy and reported by Marci in 1996. Such an anomaly is only reported from experimental observation but cannot be understood or explained using the plasticity, roughness, or oxide-induced crack closure assumptions. It also has not been fully explained through either metallurgical analysis or failure mode investigation. The established application of fracture mechanics to the FCG rate (da/dN) assumes that the FCG rate decreases with decreasing ΔK towards the threshold of ΔKth with (da/dN) $\le$ 10⁻⁷ mm/cycle. Yet, some materials exhibit a lack of ΔK threshold dependence for long cracks when tested using constant-K_max or constant-R-ratio testing. An understanding of this anomaly and the related physics poses a scientific challenge. It is also relevant to predict the safe service life of structures subjected to high-frequency and low-amplitude vibrating loads. Here, we provide our interpretation and discuss the significant implications of this phenomenon in the context of damage-tolerant design. Full article

In lifetime tests, the waiting time for items to fail may be long under usual use conditions, particularly when the products have high reliability. To reduce the cost of testing without sacrificing the quality of the data obtained, the products are exposed to higher stress levels than normal, which quickly causes early failures. Therefore, accelerated life testing is essential since it saves costs and time. This paper considers constant stress-partially accelerated life tests under progressive Type II censored samples. This is realized under the claim that the lifetime of products under usual use conditions follows Vtub-shaped lifetime distribution, which is also known as log-log distribution. The log–log distribution is highly significant and has several real-world applications since it has distinct shapes of its probability density function and hazard rate function. A graphical description of the log–log distribution is exhibited, including plots of the probability density function and hazard rate. The log–log density has different shapes, such as decreasing, unimodal, and approximately symmetric. Several mathematical properties, such as quantiles, probability weighted moments, incomplete moments, moments of residual life, and reversed residual life functions, and entropy of the log–log distribution, are discussed. In addition, the maximum likelihood and maximum product spacing methods are used to obtain the interval and point estimators of the acceleration factor, as well as the model parameters. A simulation study is employed to assess the implementation of the estimation approaches under censoring schemes and different sample sizes. Finally, to demonstrate the viability of the various approaches, two real data sets are investigated. Full article

This article discusses different methods for estimating the shape and scale parameters of the generalized inverted exponential distribution (GIED) and the acceleration factor in constant stress partially accelerated life test (CSPALT) with general progressively Type-II censored samples. We obtain the maximum likelihood estimates for the three parameters and calculate correlated approximate confidence intervals. Bayesian point estimates and credible intervals are also determined using the importance sampling method. Monte-Carlo simulation studies are conducted to demonstrate and compare the effectiveness of the proposed parameter estimation techniques. Additionally, a real-life dataset is examined to highlight the practical utility of these methodologies. Our findings indicate that the GIED provides an appropriate and flexible model for the real lifetime data, and the Bayesian approach offers better estimation than classical methods under most scenarios, in terms of using generally progressively Type-II censored samples under CSPALT. Full article

This paper explores the inference for a constant-stress accelerated life test under a ranked set sampling scenario. When the lifetime of products follows the Fréchet distribution, and the failure times are collected under a maximum ranked set sampling with unequal samples, classical and Bayesian approaches are proposed, respectively. Maximum likelihood estimators along with the existence and uniqueness of model parameters are established, and the corresponding asymptotic confidence intervals are constructed based on asymptotic theory. Under squared error loss, Bayesian estimation and highest posterior density confidence intervals are provided, and an associated Monte-Carlo sampling algorithm is proposed for complex posterior computation. Finally, extensive simulation studies are conducted to demonstrate the performance of different methods, and a real-data example is also presented for applications. Full article

This study explores a new dimension of accelerated life testing by analyzing competing risk data through Tampered Random Variable (TRV) modeling, a method that has not been extensively studied. This method is applied to simple step-stress life testing (SSLT), and it considers multiple causes of failure. The lifetime of test units under changeable stress levels is modeled using Power Rayleigh distribution with distinct scale parameters and a constant shape parameter. The research introduces unique tampering coefficients for different failure causes in step-stress data modeling through TRV. Using SSLT data, we calculate maximum likelihood estimates for the parameters of our model along with the tampering coefficients and establish three types of confidence intervals under the Type-II censoring scheme. Additionally, we delve into Bayesian inference for these parameters, supported by suitable prior distributions. Our method’s validity is demonstrated through extensive simulations and real data application in the medical and electrical engineering fields. We also propose an optimal stress change time criterion and conduct a thorough sensitivity analysis. Full article

Thermo-oxidative stability testing plays a critical role in accurately predicting shelf life. These tests are performed in real time and under stress conditions, where degradation processes are accelerated by increasing storage conditions. In this study, high-performance liquid chromatography (HPLC) analyses were performed to evaluate the degradation of resveratrol in nutraceutical tablets as a function of time under different storage conditions in terms of temperature and relative humidity (RH), namely 25 °C/60% RH, 30 °C/65% RH, and 40 °C/75% RH. The latter is an accelerated test and is used to estimate shelf life for long-term storage. Resveratrol is present in both pure form and as a solid dispersion on magnesium dihydroxide microparticles (Resv@MDH). Degradation kinetic constants were determined at 25 °C, 30 °C, and 40 °C, and the Arrhenius behavior of the kinetic constants as a function of temperature was verified. The main results of this work are as follows: (i) the stability of resveratrol in nutraceutical tablets is affected by temperature; (ii) the dependence of the kinetic constants on temperature does not follow the Arrhenius equation, determining an overestimation of the degradation rate at 25 °C; in this regard a modified version of the Arrhenius equation that takes into account the deviation from linearity has been used to estimate the dependence of the kinetic constant on the temperature. These results suggest that accelerated testing does not provide a general model for predicting the shelf life of foods and dietary supplements. The reason may be due to possible matrix effects that result in different degradation mechanisms depending on the temperature. In this regard, symmetry relationships in the kinetics of chemical reactions resulting from microscopic reversibility and their relationship to the deviation from the Arrhenius equation are discussed. However, further research is needed to characterize the degradation mechanisms at different temperatures. The results of these studies would allow accurate prediction of food degradation to improve food safety and risk management and reduce food waste. In addition, knowledge of stability processes is necessary to ensure the maintenance of physiological processes by dietary supplements. Full article

A low-voltage circuit breaker thermal trip plays a role in power systems, including opening and closing, control, protection, and more. Their reliability directly affects the security and stability of the power distribution system. The Wiener process model is established according to the accelerated degradation data of thermal trips, and remaining life prediction is carried out. In this paper, firstly, the constant stress accelerated degradation test is carried out on a thermal trip with temperature as the accelerated stress and specific thermal deflection as the degradation eigenquantity to characterise the degradation trajectory according to the degradation data and analyse the degradation law; then, it is verified by the test of normal distribution that the degradation data of the thermal trip conform to the Wiener process. The Wiener process, using the great likelihood estimation method to estimate the parameters of the remaining life, calculates the remaining life probability density function and reliability function under different temperature stresses and obtains the remaining life of the thermal trip under each accelerated stress conditions; finally, the remaining life of the thermal trip at the initial moment is taken as the pseudo-failure life, and the Arrhenius accelerated model is utilised to launch the external thermal trip under normal stress. Finally, the Arrhenius acceleration model is used to extrapolate the lifespan of the thermal trip under normal stress. Full article

In this article, we characterize and review the unusual lack of threshold in fatigue crack growth (FCG) behavior for some alloys at low values of stress intensity factor ranges ΔK and its implications to damage-tolerant design approaches. This unusual behavior was first observed by Marci in 1996 in IMI 834 alloy. Conventional applications of linear elastic fracture mechanics to FCG analysis at constant R-ratio (or K_max) assumes that (da/dN) decreases monotonically with decreasing ΔK and approaches the threshold value of ΔK_th with (da/dN) $\le$ 10⁻⁷ mm/cycle for a given R (or K_max). However, instead of ΔK threshold behavior, some materials exhibit plateau or acceleration in da/dN rate with decreasing ΔK for long cracks tested in both constant R and K_max conditions. This unusual (da/dN)-ΔK behavior is only observed experimentally but not understood and represents a challenge to scientists and engineers to model the safe fatigue life prediction of structures under low amplitude vibrating loads. Full article

In addressing the design challenges for constant-stress accelerated life testing in non-rectangular experimental domains, we aim to optimize the precision in estimating parameters for the product reliability statistical model. Following the principles of regression orthogonal design theory to determine the combinations of stress levels, we constrain the maximum stress levels of each experimental stress along the boundary curve of the non-rectangular experimental domain. The remaining stress levels and the allocation ratios of specimens for each test serve as design variables in the optimization process. We establish a mathematical model for the optimal design of constant-stress accelerated life testing in non-rectangular experimental domains. The results of the optimized design for comprehensive stress accelerated life testing in non-rectangular experimental regions of aerospace electrical connectors indicate that, with the same sample size, the optimized testing scheme not only enhances the precision of model parameter estimation but also reduces the number of required tests. At an equivalent number of tests and testing duration, the optimization scheme proposed in this study demonstrates an improvement of over 63% in the precision of model parameter estimation compared to the EM-optimized testing scheme in non-rectangular experimental regions. Using the mean, standard deviation, and coefficient of variation of the determinant values of the information matrix as criteria for evaluating the precision and robustness of experimental designs, a simulated evaluation was conducted for the optimized experimental design, a conventional experimental design, and an EM experimental design. The results indicate that the optimal experimental design outperforms both the conventional experimental design and the EM experimental design in terms of precision and robustness. Full article

In this research, the degradation behavior and failure mechanism of silicone rubber seal rings under the synergistic effects of multiple factors in the marine atmosphere are fully investigated. Firstly, four aging factors of air, temperature, compressive stress, and chemical medium were determined by analyzing the service environment profile of silicone rubber seal under a marine atmosphere environment. Secondly, to better simulate the actual service environment of silicone rubber and shorten the test period, an artificially accelerated aging test was designed and carried out in the laboratory. In this paper, temperature is utilized as the accelerating stress. According to the results of the pre-test, the accelerating stress level is finally determined to be 110–150 ${}^{\circ }$C. In addition, the compression set applied is consistent with the constant compression permanent deformation value of 28% of the silicone rubber in the actual service process. Finally, through the macroscopic physical properties and microstructure analysis of the samples before and after aging, the corresponding test results are given, and the failure mechanism is analyzed and discussed in detail. Through the above test results and discussion, it can be concluded that the aging process of multi-factor coupling on the lower silicone rubber seal ring is uneven, and its aging process is not a simple superposition of multiple environmental factors. More importantly, the above test data and results are of great significance for evaluating the service life of silicone rubber seals, which can be utilized in the future to improve the reliability and durability of related equipment in the marine environment. Full article

Monitoring life-testing trials for a product or substance often demands significant time and effort. To expedite this process, sometimes units are subjected to more severe conditions in what is known as accelerated life tests. This paper is dedicated to addressing the challenge of estimating the power hazard distribution, both in terms of point and interval estimations, during constant- stress partially accelerated life tests using progressive first failure censored samples. Three techniques are employed for this purpose: maximum likelihood, two parametric bootstraps, and Bayesian methods. These techniques yield point estimates for unknown parameters and the acceleration factor. Additionally, we construct approximate confidence intervals and highest posterior density credible intervals for both the parameters and acceleration factor. The former relies on the asymptotic distribution of maximum likelihood estimators, while the latter employs the Markov chain Monte Carlo technique and focuses on the squared error loss function. To assess the effectiveness of these estimation methods and compare the performance of their respective confidence intervals, a simulation study is conducted. Finally, we validate these inference techniques using real-life engineering data. Full article

This paper discusses inferential approaches for the problem of constant-stress accelerated life testing when the failure data are progressive type-I interval censored. Both frequentist and Bayesian estimations are carried out under the assumption that the log-normal location parameter is nonconstant and follows a log-linear life-stress model. The confidence intervals of unknown parameters are also constructed based on asymptotic theory and Bayesian techniques. An analysis of a real data set is combined with a Monte Carlo simulation to provide a thorough assessment of the proposed methods. Full article

The analysis of the constant-stress partially accelerated life test was considered under progressive Type-II censoring when the lifetime of the products follows a two-parameter bathtub-shaped distribution. The maximum likelihood estimates of the unknown parameters were established, where the expectation–maximization iterative solution is proposed for the estimation. The approximate confidence intervals were also constructed based on asymptotic theory via the Fisher information matrix. For comparison purposes, the bootstrap (i.e., Studentized-t and percentile) confidence intervals of the unknown parameters were also obtained. Finally, simulation studies and a real-life data example are presented to examine the performance of the different results. Full article

This paper assumes constant-stress accelerated life tests when the lifespan of the test units follows the XLindley distribution. In addition to the maximum likelihood estimation, the Bayesian estimation of the model parameters is acquired based on progressively Type-II censored samples. The point and interval estimations of the model parameters and some reliability indices under normal operating conditions at mission time are derived using both estimation methods. Using the Markov chain Monte Carlo algorithm, the Bayes estimates are calculated using the squared error loss function. Simulating the performances of the different estimation methods is performed to illustrate the proposed methodology. As an example of how the proposed methods can be applied, we look at two real-life accelerated life test cases. According to the numerical outcomes and based on some criteria, including the root of the mean square error and interval length, we can conclude that the Bayesian estimation method based on the Markov chain Monte Carlo procedure performs better than the classical methods in evaluating the XLindley parameters and some of its reliability measures when a constant-stress accelerated life test is applied with progressively Type-II censoring. Full article