Step-stress Accelerated Life Testing Research Articles

Implant-abutment fit influences the mechanical performance of single-crown prostheses

ObjectivesTo evaluate the three-dimensional fit of abutments fabricated by the industry to those either milled or cast by a commercial laboratory and to correlate the implant-abutment connection fit with stress at fatigue failure of prostheses. Probability of survival (reliability) and fractography to characterize failure modes were also performed for cemented and screw-retained prostheses. MethodsOne-hundred and twenty-six maxillary central incisor crowns were milled to restore implants and divided in 3 cemented and 3 screwed-retained groups (n = 21/each), as follows: [Digital-Sc]: milled one-piece monolithic abutment/crown; [TiB-Sc]: milled crowns cemented onto Ti-base abutments; [UCLA]: screw-retained crown using UCLA abutments; [Digital-Ce]: milled two-piece assembly comprised by screwed monolithic abutment and a cemented crown; [TiB–Ce]: milled coping cemented onto Ti-base abutments to receive a cemented crown; [UCLA-Ce]: UCLA abutments that received an overcast coping and a cemented crown. Implant-abutment volume misfit was assessed by micro-computed tomography using the silicone replica technique. Implant/crown systems were subjected to step-stress accelerated life testing (SSALT) in water. The use-level probability Weibull curves and reliability for a mission of 50,000 cycles at calculated stress at failure of 2,300, 3300 and 4300 MPa were plotted. Fractographic analysis was performed with scanning electron microscopy. Internal misfit was analyzed through one-way ANOVA following post-hoc comparisons by Tukey test (p < 0.05). Correlation between misfit volume and the stress at fatigue failure was assessed by Pearson test. ResultsSimilar misfit volumes were observed for TiB-Sc (0.458 mm3), TiB–Ce (0.461 mm3), UCLA (0.471 mm3) and UCLA-Ce (0.480 mm3), which were significantly lower than Digital-Sc (0.676 mm3) and Digital-Ce (0.633 mm3). The mean β values were: 1.68, 1.39, 1.48, 2.41, 2.27 and 0.71 for Digital-Sc, TiB-Sc, UCLA, Digital-Ce, TiB–Ce and UCLA-Ce, respectively, indicating that fatigue was an accelerating factor for failure of all groups. Higher stress at failure decreased the reliability of all groups, more significantly for screw compared to cement-retained groups, especially for Digital-Sc that demonstrated the lowest reliability. The failure mode was restricted to abutment screw fracture. A negative correlation was observed between misfit values and stress at failure (r = -0.302, p = 0.01). ConclusionsAbutments milled by a commercial lab presented higher misfit compared to those provided by the industry and a moderate correlation was observed between higher misfit and lower stress at failure during fatigue. Probability of survival decreased at higher stress, especially for screw compared to cement-retained groups, and failures were confined to abutment screws.

Optimal design of simple step-stress accelerated life tests for one-shot devices under Weibull distributions

One-shot devices, such as rockets, airbags of automobiles, and electro-explosive devices, can be used only once and will be extensively destroyed. The actual lifetimes of the devices cannot be observed, no matter whether the outcomes are successful or not. Step-stress accelerated life tests, which are useful for shortening the lifetimes of devices and quickly collecting lifetime data in a limited time, are widely adopted in engineering reliability studies. However, optimal designs of step-stress accelerated life tests for one-shot devices have not been well studied. This paper provides a procedure of determining optimal designs of simple step-stress accelerated life tests for one-shot devices by minimizing the asymptotic variance of the maximum likelihood estimate of reliability at normal operating conditions under Weibull distributions, with respect to inspection times and sample allocations. Comprehensive simulation studies are carried out to study the optimal designs under Weibull distributions with various hazard rates, showing that the optimal designs can maintain the simulated standard deviations at the nominal level of standard error. Besides, sensitivity analysis is conducted to evaluate the robustness of determined designs when mis-specification on planning values of model parameters exists. Finally, an application in grease-based magnetorheological fluids is presented to illustrate the optimal designs.

Optimal Designs for Step-Stress Models Under Interval Censoring

This article proposes new approaches for optimal planning of step-stress accelerated life testing models. The experiment considered is time constrained with the tested items not monitored continuously but inspected at particular time points instead. The inspection points are primarily the points of stress level change and the experiment’s termination point, but the inclusion of additional intermediate inspection points is possible. The underlying lifetimes in each stress level follow a general-scale family of distributions having, among others, the exponential and the Weibull as special cases. For this model, the optimal allocation of the inspection points is studied in terms of the classical A-, C-, D- and E-optimality criteria, as well as in the context of minimizing the probability of nonexistence of the maximum likelihood estimators of the model’s parameters. For the determination of the inspection intervals’ length, a deterministic and a hazard rate-based approach are introduced. Simulation study results indicate that these new approaches outperform the standard ones of equal spacing and equal probability. All the considered designs are comparatively evaluated and discussed on the basis of simulation studies.

On the Existence of the Optimal Step-Stress Accelerated Life Tests Under Progressive Type-I Censoring

In reliability engineering, the accelerated life test is not only getting increasingly popular but also necessary as it quickly yields information on the lifetime distribution of a highly reliable product in a short period of time by conducting the life test at more extreme stress levels than normal operating conditions. Through extrapolation, the lifetime distribution at the usage stress is then estimated with an appropriate regression model. In this paper, we revisit the problem of the design optimization for a general k-level step-stress accelerated life test under progressive Type-I censoring with an equispaced step duration Δ for the design simplicity. Allowing the intermediate censoring to take place at each stress change time point (viz., iΔ, i = 1, 2, . . . , k), the existence of the optimal stress duration is demonstrated under various design criteria including A- and E-optimality in addition to D-, T-, and C-optimalities. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable, and the effect of the intermediate censoring proportion on the design efficiency is numerically studied.

Inference for a simple step-stress model based on ordered ranked set sampling

In this paper, we considered the inference problem on simple step-stress accelerated life test data from one-parameter exponential distribution under type-I censored ordered ranked set sample with cumulative exposure model. The Bayesian estimators and credible intervals for the model parameters are developed and compared with the corresponding estimators based on simple random sampling. Two real data sets and numerical simulation evaluations are presented to illustrate all the results developed here. The simulation study indicated that the proposed Bayes estimators and credible intervals based on ordered ranked set sampling performed better than their counterparts using simple random sampling.

Bayesian analysis for dependent competing risks model with masked causes of failure in step-stress accelerated life test under progressive hybrid censoring

This article considers the statistical analysis of dependent competing risks model with masked causes of failure in step-stress accelerated life test, where the failure times of the competing risks at each stress level follow Weibull distribution and they are related to the Khamis–Higgins model assumptions. In the usual step-stress experiment, the expected lifetime of the experimental unit is shortened as the stress level increases. We provided Bayesian inference of the unknown parameters under this restriction using the prior assumption. In addition, Bayesian predictive estimates and prediction intervals for the future observations are obtained. Finally, simulations are performed to demonstrate the performances of the estimates, and one data set has been analyzed for illustrative purposes.

Applying the copula approach on step stress accelerated life test under type II censoring

The copula approach is a way to describe the dependence structure between variables. This could be done through splitting the analysis of the joint distribution of a multivariate random vector into two parts: the analysis of the marginals and the analysis of a copula which describes the dependence structure. An important field of reliability in which the copula approach could be applied, is the accelerated life testing (ALT). When a test unit fails under ALT, there are often more than one fatal cause for the failure. In this paper, we consider the simple step-stress ALT (SSALT) under type II censoring when the lifetime distribution of the different risks are dependent. The dependence structure between the competing risks is described using the copula approach. The point estimates of the unknown parameters are obtained using the maximum likelihood method. Also, the interval estimates for the unknown parameters are constructed using the asymptotic distributions and the parametric bootstrap method. Numerical analysis including simulated data and a real life data set is conducted to study the performance of the estimates.

The copula-based method for statistical analysis of step-stress accelerated life test with dependent competing failure modes

Competing risk usually exists in engineering applications; thus, the study of the statistical inference of accelerated life testing with competing failure modes is of great significance. In this article, we address the statistical analysis of a step-stress accelerated life test in the presence of dependent competing failure modes. The dependence structure among distributions of lifetimes is constructed by copula function with unknown copula parameter. The parametric maximum likelihood estimation is developed to obtain the estimates of underlying parameters. The asymptotic standard errors and asymptotic confidence interval of estimates are also obtained by missing information principle. An extensive simulation study and a real data analysis are carried out to observe the performance of the proposed method. The results of the case studies show that our proposed method is valid and effective for the statistical analysis of step-stress accelerated life test with dependent competing failure modes.

Fatigue behavior and crack initiation of CAD/CAM resin composite molar crowns

ObjectiveThe aim of this study was to evaluate long-term fatigue behavior using an in vitro step-stress accelerated life test (SSALT), and to determine the crack initiation point using in silico finite element analysis for computer-aided designed and manufactured (CAD/CAM) molar crowns fabricated from three commercial CAD/CAM resin composite blocks: Cerasmart (CS; GC, Tokyo, Japan), Katana Avencia Block (KA; Kuraray Noritake Dental, Niigata, Japan), and Shofu Block HC (HC; Shofu, Kyoto, Japan). MethodsFifty-one mandibular first molar crowns luted on a resin core die were embedded in acrylic resin and covered with a polyvinyl chloride tube. Single compressive tests were performed for five crowns. SSALT was conducted for 36 crowns using three profiles and reliabilities at 120,000 cycles, and a Weibull analysis was conducted. The maximum principal strain of each CAD/CAM resin composite crown model was analyzed by three-dimensional finite element analysis. ResultsFracture loads of CS and KA (3784±144N and 3915±313N) were significantly greater than that of HC (2767±227N) (p<0.05). Fracture probabilities at 120,000 cycles were 24.6% (CS), 13.7% (KA), and 14.0% (HC). Maximum principal strain was observed around the mesiolingual cusps of CS and KA and the distobuccal cusp of HC. SignificanceCAD/CAM resin composite molar crowns containing nano-fillers with a higher fraction of resin matrix exhibited higher fracture loads and greater longevity, suggesting that these crowns could be used as an alternative to ceramic crowns in terms of fatigue behavior.

Amari–Chentsov structure on the statistical manifold of models for accelerated life tests

The invariant geometric structures on the statistical manifold under sufficient statistics have played an important role in both statistical inference and information theory. In this paper, we focus on one of the commonly used invariant geometric structures, the Amari–Chentsov structure, on a statistical manifold. The manifold is derived from statistical models for accelerated life tests (ALTs) with censoring based on the exponential family of distributions. The constant-stress ALTs and step-stress ALTs are considered. We show that the statistical manifold still belongs to the exponential family of distributions, but the cumulant generating function depends on a random variable related to the experimental design of the ALT, which is different from the usual situation. We also investigate the Bregman divergence and Riemannian metric. The relationships between the Riemannian metric and the expected Fisher information metric are studied. The dual coordinate system is studied by using the Legendre transformation. Then, the Amari–Chentsov structure is derived based on the two different coordinate systems. The methodologies are illustrated by using two distributions, the exponential and gamma distributions, in the exponential family of distributions. Finally, using the results of Fisher information metric, optimal designs of the two types of ALTs are presented with different optimal criteria. Finally, numerical examples are provided to demonstrate the practical applications of the results developed in this paper.

The effect of DLC-coating deposition method on the reliability and mechanical properties of abutment’s screws

ObjectiveTo characterize the mechanical properties of different coating methods of DLC (diamond-like carbon) onto dental implant abutment screws, and their effect on the probability of survival (reliability). MethodsSeventy-five abutment screws were allocated into three groups according to the coating method: control (no coating); UMS – DLC applied through unbalanced magnetron sputtering; RFPA-DLC applied through radio frequency plasma-activated (n=25/group). Twelve screws (n=4) were used to determine the hardness and Young’s modulus (YM). A 3D finite element model composed of titanium substrate, DLC-layer and a counterpart were constructed. The deformation (μm) and shear stress (MPa) were calculated. The remaining screws of each group were torqued into external hexagon abutments and subjected to step-stress accelerated life-testing (SSALT) (n=21/group). The probability Weibull curves and reliability (probability survival) were calculated considering the mission of 100, 150 and 200N at 50,000 and 100,000 cycles. ResultsDLC-coated experimental groups evidenced higher hardness than control (p<0.05). In silico analysis depicted that the higher the surface Young’s modulus, the higher the shear stress. Control and RFPA showed β<1, indicating that failures were attributed to materials strength; UMS showed β>1 indicating that fatigue contributed to failure. High reliability was depicted at a mission of 100N. At 200N a significant decrease in reliability was detected for all groups (ranging from 39% to 66%). No significant difference was observed among groups regardless of mission. Screw fracture was the chief failure mode. SignificanceDLC-coating have been used to improve titanium’s mechanical properties and increase the reliability of dental implant-supported restorations.

OPTIMAL DESIGN OF SIMPLE STEP-STRESS ACCELERATED LIFE TESTS FOR ONE-SHOT DEVICES UNDER EXPONENTIAL DISTRIBUTIONS

This paper considers simple step-stress accelerated life tests (SSALTs) for one-shot devices. The one-shot device is an item that cannot be used again after the test, for instance, munitions, rockets, and automobile air-bags. Either left-or right-censored data are collected instead of actual lifetimes of the devices under test. An expectation-maximization algorithm is developed here to find the maximum likelihood estimates of the model parameters based on one-shot device testing data collected from simple SSALTs. Furthermore, the asymptotic variance of the mean lifetime under normal operating conditions is determined under the expectation-maximization framework. On the other hand, the optimal design that minimizes the asymptotic variance of the estimate of the mean lifetime under normal operating conditions in terms of three decision variables, including stress levels, inspection times, and sample allocation is discussed. A procedure then is presented to determine the decision variables when a range of stress levels and the termination time of the test as well as normal operating conditions of the devices are given. The properties of the optimal design and the effects of errors in pre-specified planning values of the model parameters are also investigated. Comprehensive simulation studies show that the procedure is quite reliable for the design of simple SSALTs.

Analysis and Optimum Plan for 3-Step Step-Stress Accelerated Life Tests with Lomax Model Under Progressive Type-I Censoring

In this paper, the optimum test plan and parameter estimation for 3-step step-stress accelerated life tests in the presence of modified progressive Type-I censoring are discussed. It is assumed that the lifetime of test units follows a Lomax distribution with log of characteristic life being quadratic function of stress level. The maximum likelihood and Bayesian method are used to obtain the point and interval estimators of the model parameters. The Bayes estimates are obtained using Markov chain Monte Carlo simulation based on Gibbs sampling. The optimum plan for 3-step step-stress test under modified progressive Type-I censoring is developed which minimizes the asymptotic variance of the maximum likelihood estimators of log of scale parameter at design stress. Finally, the numerical study with sensitivity analysis is presented to illustrate the proposed study.

Bayesian planning of optimal step-stress accelerated life test for log-location-scale distributions

This paper introduces some Bayesian optimal design methods for step-stress accelerated life test planning with one accelerating variable, when the acceleration model is linear in the accelerated variable or its function, based on censored data from a log-location-scale distributions. In order to find the optimal plan, we propose different Monte Carlo simulation algorithms for different Bayesian optimal criteria. We present an example using the lognormal life distribution with Type-I censoring to illustrate the different Bayesian methods and to examine the effects of the prior distribution and sample size. By comparing the different Bayesian methods we suggest that when the data have large(small) sample size B1(τ) (B2(τ)) method is adopted. Finally, the Bayesian optimal plans are compared with the plan obtained by maximum likelihood method.

Maximum likelihood estimation of the parameters of a multiple step-stress model from the Birnbaum-Saunders distribution under time-constraint: A comparative study

ABSTRACTThe cumulative exposure model (CEM) is a commonly used statistical model utilized to analyze data from a step-stress accelerated life testing which is a special class of accelerated life testing (ALT). In practice, researchers conduct ALT to: (1) determine the effects of extreme levels of stress factors (e.g., temperature) on the life distribution, and (2) to gain information on the parameters of the life distribution more rapidly than under normal operating (or environmental) conditions. In literature, researchers assume that the CEM is from well-known distributions, such as the Weibull family. This study, on the other hand, considers a p-step-stress model with q stress factors from the two-parameter Birnbaum-Saunders distribution when there is a time constraint on the duration of the experiment. In this comparison paper, we consider different frameworks to numerically compute the point estimation for the unknown parameters of the CEM using the maximum likelihood theory. Each framework implements at least one optimization method; therefore, numerical examples and extensive Monte Carlo simulations are considered to compare and numerically examine the performance of the considered estimation frameworks.

Optimal Plan for Step-Stress Accelerated Life Test with Two Stress Variables for Lognormal Data

A simple step-stress accelerated life testing plan with two stress variables is considered, when the failure times in each level of stress follow the lognormal distribution. The lognormal distribution is commonly used to model certain types of data that arise in several fields of engineering such as, for example, different types of lifetime data or coefficients of wear and friction. The problem of choosing the optimal times to change the stress level is investigated by minimizing the asymptotic variance of the reliability estimate and maximizing the determinant of Fisher information matrix. In this paper, we obtain the optimal bivariate step-stress accelerated life test using both the criteria. Due to the nonlinearity and complexity of problem, the particle swarm optimization algorithm is developed to calculate the optimal hold times. In this method, the research speed is very fast and the optimization ability is more. To illustrate the effect of the initial estimates on the optimal values, sensitivity analysis is performed. Finally, numerical studies are discussed to illustrate the proposed criterion. Simulation results show that the proposed optimum plan is robust.

Influence of platform diameter in the reliability and failure mode of extra-short dental implants.

To evaluate the influence of implant diameter in the reliability and failure mode of extra-short dental implants. Sixty-three extra-short implants (5mm-length) were allocated into three groups according to platform diameter: Ø4.0-mm, Ø5.0-mm, and Ø6.0-mm (21 per group). Identical abutments were torqued to the implants and standardized crowns cemented. Three samples of each group were subjected to single-load to failure (SLF) to allow the design of the step-stress profiles, and the remaining 18 were subjected to step-stress accelerated life-testing (SSALT) in water. The use level probability Weibull curves, and the reliability (probability of survival) for a mission of 100,000 cycles at 100MPa, 200MPa, and 300MPa were calculated. Failed samples were characterized in scanning electron microscopy for fractographic inspection. No significant difference was observed for reliability regarding implant diameter for all loading missions. At 100MPa load, all groups showed reliability higher than 99%. A significant decreased reliability was observed for all groups when 200 and 300MPa missions were simulated, regardless of implant diameter. At 300MPa load, the reliability was 0%, 0%, and 5.24%, for Ø4.0mm, Ø5.0mm, and Ø6.0mm, respectively. The mean beta (β) values were lower than 0.55 indicating that failures were most likely influenced by materials strength, rather than damage accumulation. The Ø6.0mm implant showed significantly higher characteristic stress (η = 1,100.91MPa) than Ø4.0mm (1,030.25MPa) and Ø5.0mm implant (η = 1,012.97MPa). Weibull modulus for Ø6.0-mm implant was m = 7.41, m = 14.65 for Ø4.0mm, and m = 11.64 for Ø5.0mm. The chief failure mode was abutment fracture in all groups. The implant diameter did not influence the reliability and failure mode of 5mm extra-short implants.

A Bayes Inference for Step-Stress Accelerated Life Testing

In this article, we present a Bayesian analysis with convex tent priors for step-stress accelerated life testing (SSALT) using a proportional hazard (PH) model. As flexible as the cumulative exposure (CE) model in fitting step-stress data and its attractive mathematical properties, the PH model makes Bayesian inference much more accessible than the CE model. Two sampling methods through Markov chain Monte Carlo algorithms are employed for posterior inference of parameters. The performance of the methodology is investigated using both simulated and real data sets.

Data analysis of step-stress accelerated life tests with heterogeneous group effects

ABSTRACTStep-Stress Accelerated Life Testing (SSALT) is a special type of experiment that tests a product′s lifetime with time-varying stress levels. Typical testing protocols deployed in SSALTs cannot implement complete randomization of experiments; instead, they often result in grouped structures of experimental units and, thus, correlated observations. In this article, we propose a Generalized Linear Mixed Model (GLMM) approach to take into account the random group effect in SSALT. Failure times are assumed to be exponentially distributed under any stress level. Two parameter estimation methods, Adaptive Gaussian Quadrature (AGQ) and Integrated Nested Laplace Approximation (INLA), are introduced. A simulation study is conducted to compare the proposed random effect model with the traditional model, which pools data groups together, and with the fixed effect model. We also compare AGQ and INLA with different priors for parameter estimation. Results show that the proposed model can validate the existence of group-to-group variation. Lastly, the GLMM model is applied to a real data and it shows that disregarding experimental protocols in SSALT may result in large bias in the estimation of the effect of stress variable.

Microstructural analysis and reliability of monolithic zirconia after simulated adjustment protocols

ObjectiveTo investigate the microstructural properties and reliability of zirconia partially stabilized by yttrium oxide (Y-TZP) for use in monolithic form (Vita YZ HT, Vita Zahnfabrik, Germany) after different clinical adjustment protocols simulation. One-hundred and sixty two Y-TZP discs of high translucency were divided into 6 groups (n=27), according to simulated adjustments: S-Y-TZP as sintered; G-glazed Y-TZP; DbG-Y-TZP with diamond bur adjustment simulation followed by glaze application; GDb-glazed Y-TZP adjusted with diamond bur; DbDrG-Y-TZP with adjustment simulation with diamond bur and polishing kit (diamond rubber), followed by glaze; GDbDr-glazed Y-TZP with adjustment simulation with diamond bur followed by polishing kit. MethodsAfter monotonic testing under biaxial flexure (n=3), remaining specimens were distributed into 3:2:3 ratio and tested under step-stress accelerated life testing. Specimens were evaluated in a stereomicroscope and SEM. Microstructure was analyzed by X-ray diffraction and mean surface roughness (Ra). Survival data were used to calculate Weibull's beta value (β) and reliability for missions of 300,000 and 600,000 cycles at 200N. Ra data were statistically analyzed by 1-way ANOVA and Tukey’s test (both, a=5%). ResultsThe untreated HT zirconia (S) presented a lower probability of survival after 600,000 cycles at 200N, compared to HT zirconia adjusted with diamond bur and glazed (DbG), and after final polishing with polishing kit (GDbDr). Final polishing with diamond rubber (GDbDr) resulted in a more homogeneous surface compared to glazed samples (G, DbG and DbDrG). SignificanceHT zirconia is more likely to present increased survival when glazed after diamond adjustments (DbG) or when it is finished with polishing kit (GDbDr).