Step-stress Accelerated Life Testing Research Articles

Cyclic fatigue behavior of Y‐TZP nanostructures with non‐homogeneous yttria distribution

AbstractNanostructured Y‐TZP samples with Non‐Homogeneous Yttria Distribution (NNHYD) were prepared by mixing co‐precipitated 3Y‐TZP powder (Tosoh TZ‐3Y) with yttria‐free monoclinic powder (Tosoh TZ‐0), yielding an overall yttria content of 2 mol%. The cyclic fatigue behavior of NNHYD was evaluated by Step‐Stress Accelerated Life Testing (SSALT) and mechanical cycling in a biaxial flexural strength test (BFST) setup and compared to Conventional Submicrometric 3Y‐TZP (CS). Physical, structural, microstructural, and mechanical characterizations of all groups were also evaluated and compared before and after artificial aging in autoclave. NNHYD presented a higher capacity for damage accumulation and maintenance of phase transformation potential than CS, associated with elevated resistance to the propagation of Low‐Temperature Degradation (LTD). A nanostructured 3Y‐TZP surface layer introduced in NNHYD by dip coating (DC‐NNHYD) improved resistance to LTD at the cost of reduced reliability under cyclic fatigue by increasing the stability of the tetragonal phase. This surface alteration highlights the impact of surface properties on mechanical performance. The results of this study present practical possibilities to help achieve the ideal balance between strength, toughness, and LTD resistance to improve the lifetime of zirconia‐based biomaterials.

Aging Intensity for Step-Stress Accelerated Life Testing Experiments.

The aging intensity (AI), defined as the ratio of the instantaneous hazard rate and a baseline hazard rate, is a useful tool for the describing reliability properties of a random variable corresponding to a lifetime. In this work, the concept of AI is introduced in step-stress accelerated life testing (SSALT) experiments, providing new insights to the model and enabling the further clarification of the differences between the two commonly employed cumulative exposure (CE) and tampered failure rate (TFR) models. New AI-based estimators for the parameters of a SSALT model are proposed and compared to the MLEs in terms of examples and a simulation study.

Optimal test plans for accelerated life tests based on progressive type-I censoring with engineering applications

In reliability engineering studies, the accelerated life tests with optimal test design that balances cost constraints is particularly important since the lifetimes of electro-mechanical, electronic, and mechanical goods are typically modelled with this characteristic. Comparative optimal test plans for accelerated life tests are developed in a variety of applications, including engineering, biological, medical, and other related fields. In this study, we compare, under cost restriction with a specified budget, optimum multiple constant stress and step stress accelerated life tests based on progressive-type-I censoring. The goal is to assess the advantage provided by step-stress testing over constant-stress testing. In order to conduct an accelerated life test effectively, stress durations need to be carefully specified during the design stage due to limited resources in engineering practice. The estimated accuracy of the parameters of interest and the expense of the experiment are directly impacted by the stress durations. Under a prespecified budget and cost constraints, this article examines the optimal stress durations based on D-, E-, T-, C-, R-, and P-optimal criteria. These criteria are also contrasted together. We illustrate the application of the optimal durations using numerical and simulation examples. A study is conducted to determine how sensitive the optimal duration is to model parameter misspecification.

Bivariate step-stress accelerated life test for a new three-parameter model under progressive censored schemes with application in medical

<abstract><p>In this article, a new three-parameter lifetime model called the Gull alpha power exponentiated exponential (GAPEE) distribution is introduced and studied by combining the Gull alpha power family of distributions and the exponentiated exponential distribution. The shapes of the probability density function (PDF) for the GAPEE distribution can be asymmetric shapes, like unimodal, decreasing, and right-skewed. In addition, the shapes of the hazard rate function (hrf) for the GAPEE distribution can be increasing, decreasing, and upside-down shaped. Several statistical features of the GAPEE distribution are computed. Eight estimation methods such as the maximum likelihood, Anderson-Darling, right-tail Anderson-Darling, left-tailed Anderson-Darling, Cramér-von Mises, least-squares, weighted least-squares, and maximum product of spacing are discussed to estimate the parameters of the GAPEE distribution. The flexibility and the importance of the GAPEE distribution were demonstrated utilizing three real-world datasets related to medical sciences. The GAPEE distribution is extremely adaptable and outperforms several well-known statistical models. A bivariate step-stress accelerated life test based on progressive type-I censoring using the model is presented. Minimizing the asymptotic variance of the maximum likelihood estimate of the log of the scale parameter at design stress under progressive type-I censoring yields an expression for the ideal test plan under progressive type-I censoring.</p></abstract>

Accelerated testing of soft soldered, small-diameter, thin-walled CuNi pipes subjected to cyclic internal pressure loading

Small-diameter, thin-walled pipes have applications in a wide range of industries including high-energy physics, heat transfer, nuclear, medical and communications. However, there are currently no standards that exist for permanently joining these components either via welding (melting the base material) or soldering. As such it is difficult to determine the likely performance of a thin-walled pipe connection. Porosity is largely inevitable in soldered joints and is a determining factor in the performance of a connection.This study focused on characterisation of failure initiation and propagation within soft soldered CuNi thin-walled pipe joints under cyclic internal pressure loading. A step-stress accelerated life testing regime (SSALT) was developed to simulate the loads the joints would experience over their operational lifetime, in a shorter timescale.10 soldered joints were studied in total, with varying levels of porosity within the soldered joints prior to testing. Pressurised Nitrogen gas was used to internally pressurise the samples, with cyclic loading between atmospheric conditions and a prescribed maximum pressure value.The results of the SSALT showed that the soldered samples experienced early failure through crack initiation and propagation through the solder. Cracks, or failures, were seen to initiate from existing voids, or porosity, within the soft-soldered joints.From this work, it can be concluded that the performance of soft-soldered joints under cyclic, internal pressure loading is strongly influenced by the presence of voids that are created during the manufacture of such soldered connections.

Statistical Analysis of Step Stress Acceleration Test Data

The step stress accelerated life test is the selection of a set of accelerated stress levels that are higher than normal stress levels. At the beginning of the test, a certain number of samples are placed under a certain stress level for life testing. After some time, the stress level is increased, and this continues until a certain number of samples fail. In this paper, the acceleration coefficient is used to convert the failure data under each acceleration stress level into life data. The life distribution is exponential distribution, Weibull distribution, and logarithmic normal distribution. Under a certain number of samples, the statistical analysis of step stress accelerated life test data is completed, and the estimation of each reliability index is calculated.

Ultrathin lithium disilicate and translucent zirconia crowns for posterior teeth: Survival and failure modes.

To evaluate the reliability and failure modes of ultrathin (0.5 mm) lithium disilicate, translucent and ultra-translucent zirconia crowns for posterior teeth restorations. Fifty-four mandibular first molar crowns of three ceramic materials: (1) Lithium disilicate (e.max CAD, Ivoclar Vivadent), (2) 3Y-TZP (Zirconn Translucent, Vipi), and (3) 5Y-PSZ (Cercon XT, Dentsply Sirona), with 0.5 mm of thickness were milled and cemented onto composite resin abutments. Eighteen samples of each group were tested under mouth-motion step-stress accelerated life testing in a humid environment using mild, moderate, and aggressive profiles. Data was subjected to Weibull statistics. Use level curves were plotted and reliability was calculated for a given mission of 100,000 cycles at 100, 200, and 300 N. Fractographic analyses of representative samples were performed in scanning electron microscope. Beta (β) values suggest that failures were dictated by material's strength for lithium disilicate and by fatigue damage accumulation for both zirconias. No significant differences were detected in Weibull modulus and characteristic strength among groups. At a given mission of 100,000 cycles at 100 N, lithium disilicate presented higher reliability (98% CB: 95-99) regarding 3Y-TZP and 5Y-PSZ groups (84% CB: 65%-93% and 79% CB: 37&-94%, respectively). At 200 N, lithium disilicate reliability (82% CB: 66%-91%) was higher than 5Y-PSZ (20% CB: 4%-44%) and not significantly different from 3Y-TZP (54% CB: 32%-72%). Furthermore, at 300 N no significant differences in reliability were detected among groups, with a notable reduction in the reliability of all materials. Fractographic analyses showed that crack initiated at the interface between the composite core and the ceramic crowns due to tensile stress generated at the intaglio surface. Ultrathin lithium disilicate crowns demonstrated higher reliability relative to zirconia crowns at functional loads. Lithium disilicate and zirconia crown's reliability decreased significantly for missions at higher loads and similar failure modes were observed regardless of crown material. The indication of 0.5 mm thickness crowns in high-load bearing regions must be carefully evaluated. Ultraconservative lithium disilicate and zirconia crowns of 0.5 mm thickness may be indicated in anterior restorations and pre-molars. Their clinical indication in high-load requirement regions must be carefully evaluated.

Designing efficient Bayesian sampling plans for exponential distributions based on samples under a (n, t) simple step-stress test

This article studies a method about how to design an efficient Bayesian sampling plan based on samples collected through a (n, t)-sampling scheme with a simple step-stress accelerated life test (ALT). For brevity, such a step-stress accelerated life test is called (n, t)-SSALT. A Bayesian sampling plan (BSP) derived through the (n, t)-SSALT is called BSPA. First, we derive the BSPA with data collected through a (n, t)-SSALT for a general loss function. Given gamma and Jeffreys prior distributions, an explicit expression of the Bayes decision function under a certain loss function is derived. By applying a curtailment procedure to the preceding Bayes decision function, an on-line new Bayes decision function and Bayesian sampling plan, called an efficient Bayesian sampling plan (EBSPA), are constructed. It is shown that the Bayes risk of EBSPA is less than or equal to that of BSPA. This indicates that the EBSPA is more efficient than the BSPA. Comparisons among some BSPAs and the proposed EBSPA are given. The numerical results indicate that, in terms of Bayes risks, the EBSPA significantly outperforms the BSPA.

Reliability and Failure Mode of Ti-Base Abutments Supported by Narrow/Wide Implant Systems.

To assess the reliability and failure modes of Ti-base abutments supported by narrow and wide-diameter implant systems. Narrow (Ø3.5 × 10 mm) and wide (Ø5 × 10 mm) implant systems of two different manufacturers with internal conical connections (16°) and their respective Ti-base abutments (3.5 and 4.5 mm) were evaluated. Ti-base abutments were torqued to the implants, standardized metallic maxillary incisor crowns were cemented, and step stress accelerated life testing of eighteen assemblies per group was performed in three loading profiles: mild, moderate, and aggressive until fracture or suspension. Reliability for missions of 100,000 cycles at 100 and 150 N was calculated, and fractographic analysis was performed. For missions at 100 N for 100,000 cycles, both narrow and wide implant systems exhibited a high probability of survival (≥99%, CI: 94-100%) without significant differences. At 150 N, wide-diameter implants presented higher reliability (≥99%, CI: 99-100%) compared to narrow implants (86%, CI: 61-95%), with no significant differences among manufacturers. Failure mode predominantly involved Ti-base abutment fractures at the abutment platform. Ti-base abutments supported by narrow and wide implant systems presented high reliability for physiologic masticatory forces, whereas for high load-bearing applications, wide-diameter implants presented increased reliability. Failures were confined to abutment fractures.

Non-destructive one-shot device test under step-stress experiment with lognormal lifetime distribution

Dealing with censored data is an important concern in reliability and survival analysis. Non-destructive one-shot devices are an extreme case of interval censoring, wherein we only know if a device has failed or not before an inspection time. Besides, non-destructive one-shot devices are frequently highly reliable with large lifetimes, and then long experimentation times would be needed for inference under normal operating conditions. Alternatively, accelerated life tests (ALTs) shorten the lifetime of the devices by increasing one or more stress factors causing failure. Then, after suitable inference, results can be extrapolated to normal conditions. In particular, step-stress ALT designs increase the stress level at which devices are tested throughout the experiment at some fixed times. Under the non-destructive one-shot device set-up, the number of failures is recorded at some inspection times, including the times of stress change, then resulting in censored data. Among the most popular lifetime distributions used to analyze survival data, the lognormal distribution has hazard function with an increasing–decreasing behavior, which is encountered often in practice as units usually experience early failure and then stabilize over time in terms of performance. However, the classical maximum likelihood estimator (MLE) of parameters of the lognormal lifetime distribution may get highly influenced by data contamination. In this paper we propose a family of divergence-based robust estimators for non-destructive one-shot device step-stress experiments under the lognormal lifetime distribution. Further, from the robust estimators, a generalization of the popular Wald-type test statistic based on the MLE for testing composite null hypothesis is defined, resulting in a robust divergence-based family of test statistics.

In vitro analysis of durability of S-PRG filler-containing composite crowns for primary molar restoration.

To evaluate the reliability, maximum principal stress, shear stress, and crack initiation of a computer-aided design/computer-aided manufacturing (CAD/CAM) resin composite (RC) incorporating surface pre-reacted glass (S-PRG) filler for primary molar teeth. Mandibular primary molar crowns fabricated by experimental (EB) or commercially available CAD/CAM RCs (HC) were prepared and cemented to a resinous abutment tooth using an adhesive resin cement (Cem) or a conventional glass-ionomer cement (CX). These specimens were subjected to a single compressive test (n=5/each) and the step-stress accelerated life testing (SSALT) (n=12/each). Data was evaluated using Weibull analyses and reliability was calculated. Afterwards, the maximum principal stress and crack initiation point of each crown was analyzed by finite element analysis. To evaluate bonding of EB and HC to dentin, microtensile bond strength (μTBS) testing was conducted using primary molar teeth (n=10/each). There was no significant difference between the fracture loads of EB and HC for either cement (p>0.05). The fracture loads of EB-CX and HC-CX were significantly lower than EB-Cem and HC-Cem (p<0.05). The reliability at 600N for EB-Cem was greater than that for EB-CX, HC-Cem, and HC-CX. The maximum principal stress concentrated on EB was lower than that on HC. The shear stress concentrated in the cement layer for EB-CX was higher than that for HC-CX. There was no significant difference among the μTBSs of EB-Cem, EB-CX, HC-Cem, and HC-CX (p>0.05). The crowns fabricated with the experimental CAD/CAM RC incorporating S-PRG filler yielded greater fracture loads and reliability than the crowns manufactured with commercially available CAD/CAM RC regardless of the luting materials. These findings suggest that the experimental CAD/CAM RC crown may be clinically useful for the restoration of primary molars.

Reliability estimation of thin film platinum resistance MEMS thermal mass flowmeter by step-stress accelerated life testing

Assuring reliability is a key aspect of sensor quality. In this article, we introduce the reliability test results of thin film platinum resistance (TFPR) MEMS thermal mass flowmeter based on accelerated life testing (ALT). The influences of temperature stress (Ts) and temperature-voltage double-stress ((T + V)s) on sensor reliability are assessed through ageing experiments using a climatic chamber. According to the performance in ageing test, we chose output voltage as a characteristic parameter. We analyze the causes for degradation of the characteristic parameter. In addition, based on Arrhenius model and Weibull distribution (WD), we predict the lifetime and estimate the reliability of the TFPR MEMS thermal mass flowmeter. The average lifetime of Ts group is 1.826 × 104 h (2.085 years) in 85 °C test conditions; and the (T + V)s group is 1.003 × 104 h (1.145 years). The reliability of Ts group is 87 %, and the (T + V)s group is 80 %, in the first working year. The results reveal the temperature and voltage stress influences on lifetime. This research provides a good way for reliability analysis of thermal mass flowmeter units.

Single geometry abutment for narrow and extra-narrow implant systems: Survival and failure modes

The use of identical prosthetic components for all implant diameters could reduce the production costs by companies and the complexity of component selection for the clinician and his team. However, it would imply in reduction of thickness of the cervical walls of tapered internal connection implants, which could compromise the reliability of narrow and extra-narrow implants. Therefore, this study aims to evaluate the probability of survival and failure modes of extra-narrow implant systems with the same internal diameter as standard-diameter implants using the same prosthetic components. It was used eigth different implant system configurations, including narrow (Ø 3.3 mm) (N) extra-narrow (Ø 2.9 mm) (EN) and extra-narrow-scalloped (Ø 2.9 mm) (ENS) implants, both with cementable abutments (Ce) or titanium bases (Tib) and one-piece implants (Ø 2.5 mm and Ø 3.0 mm) (OP) (Medens, Itu, SP, Brazil), comprising the following groups: OP 3.0; OP 2.5; N Ce; N Tib; EN Ce, EN Tib, ENS-Ce and ENS-Tib. The implants were embedded using polymethylmethacrylate acrylic resin in a 15 mm matrix. Standardized maxillary central incisor crowns were virtually designed and milled to fit on the different studied abutments and cemented using a dual self-adhesive resin cement. The specimens were submitted to SSALT (Step Stress Accelerated Life Testing) at 15 Hz in water until failure or suspension of the test, until a maximum load of 500 N. Fractographic analysis of the failed specimens were realized in scanning electron microscopy. All implant systems demonstrated high probability of survival (90–100%) for missions at 50 and 100 N and values of characteristic strength superior to 139 N. Failure modes were restricted to the abutment in all the implant configurations tested. Therefore, the use extra-narrow implants with standardized prosthetic components for different implant diameters is a viable option for the replacement of anterior teeth.

Reliability and lifetime of lithium disilicate, 3Y-TZP, and 5Y-TZP zirconia crowns with different occlusal thicknesses.

To assess the probability of survival of crowns made with a 3Y-TZP, a 5Y-TZP, and a lithium disilicate. CAD-CAM premolar crowns with occlusal thicknesses of 1.0mm or 1.5mm and cemented on a metal dye. Step-stress accelerated life testing (SSALT) was performed to access the use level probability Weibull curves and reliability were calculated for the completion of a mission of 100,000 cycles at 300 to 1200 N. All ceramics showed a high probability of survival (87-99%) at 300 N, irrespective of thickness. 3Y-TZP shows no significant decrease in the probability of survival up to 1200 N (83-96%). Lithium disilicate presented lower reliability than zirconia under the 600 N mission. 5Y-TZP showed lower reliability than 3Y-TZP at 1200 N. There was no significant difference in the Weibull modulus (3.23-7.12). 3Y-TZP had the highest characteristic strength (2483-2972 N), followed by 5Y-TZP (1512-1547 N) and lithium disilicate (971-1154 N). Zirconia ceramics have a high probability of survival (up to 900 N-load), while lithium disilicate survives up to 300 N load only, irrespective of the thickness (1.0mm or 1.5mm). The probability of survival of posterior crowns made with zirconia ceramics resists extreme loads whileglass ceramics resist normal chewing loads. In addition, crowns withthinner occlusal face showed sufficient mechanical behavior.

Order restricted inference for a multiple step‐stress model with long‐term survivors for a general family of distributions

AbstractIn this article, we propose a failure rate based step‐stress accelerated life testing (SSALT) model assuming that the time‐to‐event distribution belongs to a fairly general family of distributions and the underlying population consists of long term survivors. With increase in stress levels, it is expected that the mean time to the event of interest gets shortened leading to an order restriction among the mean times‐to‐event. We propose here a method of obtaining order restricted maximum likelihood estimators (MLEs) based on expectation maximization (EM) algorithm coupled with the method of generalized isotonic regression technique. Additionally, we address the testing of hypothesis problem for the presence of long term survivors in the underlying population based on both asymptotic and non‐asymptotic approaches. To illustrate the effectiveness of the proposed method, extensive simulation experiments are carried out and a real data set is analyzed.

Inference and optimal design for the k-level step-stress accelerated life test based on progressive Type-I interval censored power Rayleigh data.

In this paper, a new generalization of the one parameter Rayleigh distribution called the Power Rayleigh (PRD) was employed to model the life of the tested units in the step-stress accelerated life test. Under progressive Type-I interval censored data, the cumulative exposure distribution was considered to formulate the life model, assuming the scale parameter of PRD has the inverse power function at each stress level. Point estimates of the model parameters were obtained via the maximum likelihood estimation method, while interval estimates were obtained using the asymptotic normality of the derived estimators and the bootstrap resampling method. An extensive simulation study of $ k = 4 $ levels of stress in different combinations of the life test under different progressive censoring schemes was conducted to investigate the performance of the obtained point and interval estimates. Simulation results indicated that point estimates of the model parameters are closest to their initial true values and have relatively small mean squared errors. Accordingly, the interval estimates have small lengths and their coverage probabilities are almost convergent to the 95% significance level. Based on the Fisher information matrix, the D-optimality and the A-optimality criteria are implemented to determine the optimal design of the life test by obtaining the optimum inspection times and optimum stress levels that improve the estimation procedures and give more efficient estimates of the model parameters. Finally, the developed inferential procedures were also applied to a real dataset.

Exact inference for progressively Type-I censored step-stress accelerated life test under interval monitoring

Exact inference for progressively Type-I censored step-stress accelerated life test under interval monitoring

Bayesian analysis for multiple step-stress accelerated life test model under gamma lifetime distribution and type-II censoring

PurposeThe step-stress accelerated test is the most appropriate statistical method to obtain information about the reliability of new products faster than would be possible if the product was left to fail in normal use. This paper presents the multiple step-stress accelerated life test using type-II censored data and assuming a cumulative exposure model. The authors propose a Bayesian inference with the lifetimes of test item under gamma distribution. The choice of the loss function is an essential part in the Bayesian estimation problems. Therefore, the Bayesian estimators for the parameters are obtained based on different loss functions and a comparison with the usual maximum likelihood (MLE) approach is carried out. Finally, an example is presented to illustrate the proposed procedure in this paper.Design/methodology/approachA Bayesian inference is performed and the parameter estimators are obtained under symmetric and asymmetric loss functions. A sensitivity analysis of these Bayes and MLE estimators are presented by Monte Carlo simulation to verify if the Bayesian analysis is performed better.FindingsThe authors demonstrated that Bayesian estimators give better results than MLE with respect to MSE and bias. The authors also consider three types of loss functions and they show that the most dominant estimator that had the smallest MSE and bias is the Bayesian under general entropy loss function followed closely by the Linex loss function. In this case, the use of a symmetric loss function as the SELF is inappropriate for the SSALT mainly with small data.Originality/valueMost of papers proposed in the literature present the estimation of SSALT through the MLE. In this paper, the authors developed a Bayesian analysis for the SSALT and discuss the procedures to obtain the Bayes estimators under symmetric and asymmetric loss functions. The choice of the loss function is an essential part in the Bayesian estimation problems.

Optimal Test Plan of Step-Stress Model of Alpha Power Weibull Lifetimes under Progressively Type-II Censored Samples

In this study, the estimation of the unknown parameters of an alpha power Weibull (APW) distribution using the concept of an optimal strategy for the step-stress accelerated life testing (SSALT) is investigated from both classical and Bayesian viewpoints. We used progressive type-II censoring and accelerated life testing to reduce testing time and costs, and we used a cumulative exposure model to examine the impact of various stress levels. A log-linear relation between the scale parameter of the APW distribution and the stress model has been proposed. Maximum likelihood estimators for model parameters, as well as approximation and bootstrap confidence intervals (CIs), were calculated. Bayesian estimation of the parameter model was obtained under symmetric and asymmetric loss functions. An optimal test plan was created under typical operating conditions by minimizing the asymptotic variance (AV) of the percentile life. The simulation study is discussed to demonstrate the model’s optimality. In addition, real-world data are evaluated to demonstrate the model’s versatility.

Bivariate Step-Stress Accelerated Life Tests for the Kavya–Manoharan Exponentiated Weibull Model under Progressive Censoring with Applications

A new three-parameter survival model is proposed using the Kavya–Manoharan (KM) transformation family and the exponentiated Weibull (EW) distribution. The shapes of the pdf for the new model can be asymmetric and symmetric shapes, such as unimodal, decreasing, right-skewed and symmetric. In addition, the shapes of the hrf for the suggested model can be increasing, decreasing, constant and J-shaped. Statistical properties are obtained: quantile function, mode, moments, incomplete moments, residual life time, reversed residual life time, probability weighted moments, order statistics and entropy. We discuss the maximum likelihood estimation for the model. The relevance and flexibility of the model are demonstrated using two real datasets. The distribution is very flexible, and it outperforms many known distributions, such as the three-parameter exponentiated Weibull, the modified Weibull model, the Kavya–Manoharan Weibull, the extended Weibull, the odd Weibull inverse Topp–Leone and the extended odd Weibull inverse Nadarajah–Haghigh model. A bivariate step-stress accelerated life test based on progressive type-I censoring (PTIC) using the model is presented. This pattern is noticed when a particular number of lifetime test units are routinely eliminated from the test at the conclusion of each post-test period of time. Minimizing the asymptotic variance of the MLE of the log of the scale parameter at design stress under PTIC yields an expression for the ideal test plan under PTIC.