Step-stress Accelerated Life Testing Research Articles

Optimal accelerated life tests under a cost constraint with non-uniform stress durations

ABSTRACTTo collect the information about the lifetime distribution of a product, a standard life testing method at normal working conditions is impractical when the product has a substantially long lifespan. Accelerated life testing solves this problem by subjecting the test units at higher stress levels for quicker and more failure data. Due to constrained resources in practice, several decision variables such as the allocation proportions and stress durations must be determined carefully at the design stage in order to run an accelerated life test efficiently. These decision variables directly affect the experimental cost as well as the estimate precision of the parameters of interest. This article investigates these optimal decision variables based on several well-known optimality criteria under the constraint that the total experimental cost does not exceed a pre-specified budget. A general scale family of distributions is considered for the underlying lifetimes to accommodate different lifetime models at different stress levels for flexible modeling. The constant-stress and step-stress accelerated life tests are then studied in detail with linearly decreasing stress durations as the stress level progresses. Under the identical budget constraint, the efficiencies of these two stress loading schemes are compared using two case studies.

In vitro fatigue tests and in silico finite element analysis of dental implants with different fixture/abutment joint types using computer-aided design models

PurposeThe aim of this study was to evaluate fatigue resistance of dental fixtures with two different fixture-abutment connections by in vitro fatigue testing and in silico three-dimensional finite element analysis (3D FEA) using original computer-aided design (CAD) models. MethodsDental implant fixtures with external connection (EX) or internal connection (IN) abutments were fabricated from original CAD models using grade IV titanium and step-stress accelerated life testing was performed. Fatigue cycles and loads were assessed by Weibull analysis, and fatigue cracking was observed by micro-computed tomography and a stereomicroscope with high dynamic range software. Using the same CAD models, displacement vectors of implant components were also analyzed by 3D FEA. Angles of the fractured line occurring at fixture platforms in vitro and of displacement vectors corresponding to the fractured line in silico were compared by two-way ANOVA. ResultsFatigue testing showed significantly greater reliability for IN than EX (p<0.001). Fatigue crack initiation was primarily observed at implant fixture platforms. FEA demonstrated that crack lines of both implant systems in vitro were observed in the same direction as displacement vectors of the implant fixtures in silico. ConclusionsIn silico displacement vectors in the implant fixture are insightful for geometric development of dental implants to reduce complex interactions leading to fatigue failure.

Fracture strength and probability of survival of narrow and extra-narrow dental implants after fatigue testing: In vitro and in silico analysis

PurposeTo assess the probability of survival (reliability) and failure modes of narrow implants with different diameters. Materials and methodsFor fatigue testing, 42 implants with the same macrogeometry and internal conical connection were divided, according to diameter, as follows: narrow (Ø3.3×10mm) and extra-narrow (Ø2.9×10mm) (21 per group). Identical abutments were torqued to the implants and standardized maxillary incisor crowns were cemented and subjected to step-stress accelerated life testing (SSALT) in water. The use-level probability Weibull curves, and reliability for a mission of 50,000 and 100,000 cycles at 50N, 100, 150 and 180N were calculated. For the finite element analysis (FEA), two virtual models, simulating the samples tested in fatigue, were constructed. Loading at 50N and 100N were applied 30° off-axis at the crown. The von-Mises stress was calculated for implant and abutment. ResultsThe beta (β) values were: 0.67 for narrow and 1.32 for extra-narrow implants, indicating that failure rates did not increase with fatigue in the former, but more likely were associated with damage accumulation and wear-out failures in the latter. Both groups showed high reliability (up to 97.5%) at 50 and 100N. A decreased reliability was observed for both groups at 150 and 180N (ranging from 0 to 82.3%), but no significant difference was observed between groups. Failure predominantly involved abutment fracture for both groups. FEA at 50N-load, Ø3.3mm showed higher von-Mises stress for abutment (7.75%) and implant (2%) when compared to the Ø2.9mm. ConclusionsThere was no significant difference between narrow and extra-narrow implants regarding probability of survival. The failure mode was similar for both groups, restricted to abutment fracture.

Using accelerated life tests data to predict warranty cost under imperfect repair

For new products that have not been put on the market, manufacturers usually want to predict the warranty cost to forecast its influence on future profit. In the test phase of new products, accelerated life tests (ALT) are commonly used to predict the lifetime under use condition. In this paper, we present a framework to predict the warranty cost and risk under one-dimensional warranty by analyzing ALT experimental data. Two sources of variability are considered to make inferences of predicted warranty cost: the uncertainty of estimated parameters from ALT data and the variation in field conditions. Under these assumptions, the expected warranty cost and warranty risk is computed by Markov chain Monte Carlo (MCMC) sampling based on the approximated lifetime distribution. We assume that the warranty guarantees imperfect repairs. The framework could be easily repeated for ALT data based on log-location-scale lifetime distributions and both constant-stress and step-stress ALT data. Compared with original Monte Carlo (MC) simulation, the proposed method provides comparable prediction accuracy with significantly less computational effort. A numerical example with sensitivity analysis is given to illustrate the effectiveness of the proposed methods.

Point and interval estimation for a simple step-stress model with Type-I censored data from geometric distribution

The estimation problem of expected time to failure of units is studied in a discrete set up. A simple stepstress accelerated life testing is considered with a Type-I censored sample from geometric distribution that is a commonly used distribution to model the lifetime of a device in discrete case. Maximum likelihood estimators as well as the associated distributions are derived. Exact, approximate and bootstrap approaches construct confidence intervals that are compared via a simulation study. Optimal confidence intervals are suggested in view of the expected width and coverage probability criteria. An illustrative example is also presented to explain the results of the paper. Finally, some conclusions are stated.

Fatigue Failure of Narrow Implants with Different Implant-Abutment Connection Designs.

To evaluate the reliability of narrow diameter dental implants (NDIs) with similar macrogeometry and 3 implant-abutment connection designs. Eighty-four NDIs (3.5 × 10 mm) were selected and divided into 4 groups (n = 21/group) according to implant-abutment connection design, as follows: EH - external hexagon, IH - internal hexagon, IC - internal conical, and IC-M - internal conical connected to a monolithic titanium abutment. Identical abutments were torqued to the implants, and standardized maxillary incisor crowns were cemented and subjected to step-stress accelerated life testing (SSALT) in water. Use of level probability Weibull curves, and reliability for a mission of 50,000 cycles at 75 N and 200 N were calculated. The beta (β) values were: 1.48 for IC, 1.40 for IC-M, 8.54 for EH, and 1.98 for IH, indicating that damage accumulation was an acceleration factor for failure of all groups. At 75 N the probability of survival was not significantly different between groups. A decrease in reliability was observed for all groups at 200 N with no significant differences between IC (81.71%) and IC-M (94.28%), or between EH and IH (0%) which presented the lowest values. EH failures were primarily restricted to the screw, while IH involved screw and implant fracture. IC and IC-M were restricted to prosthetic failures (fracture and bending). Narrow implants with external or internal hexagon connections presented the lowest reliability at high loads compared to internal conical connections. Failure modes differed among connections.

Estimation in Step-Stress Accelerated Life Testing for Lindely Distribution with Progressive First-Failure Censoring

Based on progressive first-failure censoring, step-stress partially accelerated life tests are considered when the li fetime of a product follows Weibull distribution. The maximum likelihood estimates (MLEs) are obtained for the distribution parameters and the acceleration factor. In addition, asymptotic variance and covariance matrix of the estimators are given. Furthermore, confidence intervals of the estimators are presented. The optimal stre ss change time for the step-stress partially accelerated li fe test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results a re carried out to study the precision of the MLEs for the parameters involved.

Analysis of simple step-stress accelerated life test data from Lindley distribution under type-I censoring

This article introduces step-stress accelerated life time model with Lindley lifetime under type-I censoring. The corresponding likelihood function is developed and parameter estimation by maximum likelihood approach is discussed. Also, parametric bootstrap confidence intervals are constructed for the unknown parameters. Simulation study is carried out to evaluate performance of the estimators of the proposed model.

Survival and failure modes: platform-switching for internal and external hexagon cemented fixed dental prostheses.

This study evaluated the probability of survival (reliability) of platform-switched fixed dental prostheses (FDPs) cemented on different implant-abutment connection designs. Eighty-four-three-unit FDPs (molar pontic) were cemented on abutments connected to two implants of external or internal hexagon connection. Four groups (n=21 each) were established: external hexagon connection and regular platform (ERC); external hexagon connection and switched platform (ESC); internal hexagon and regular platform (IRC); and internal hexagon and switched platform (ISC). Prostheses were subjected to step-stress accelerated life testing in water. Weibull curves and probability of survival for a mission of 100,000 cycles at 400N (two-sided 90% CI) were calculated. The beta values of 0.22, 0.48, 0.50, and 1.25 for groups ERC, ESC, IRC, and ISC, respectively, indicated a limited role of fatigue in damage accumulation, except for group ISC. Survival decreased for both platform-switched groups (ESC: 74%, and ISC: 59%) compared with the regular matching platform counterparts (ERC: 95%, and IRC: 98%). Characteristic strength was higher only for ERC compared with ESC, but not different between internal connections. Failures chiefly involved the abutment screw. Platform switching decreased the probability of survival of FDPs on both external and internal connections. The absence in loss of characteristic strength observed in internal hexagon connections favor their use compared with platform-switched external hexagon connections.

Optimum simple accelerated life tests based on progressively Type-I hybrid censoring

This paper presents the process of the optimum test design for simple constant-stress and step-stress accelerated life tests under the progressively Type-I hybrid censoring data. Considering the constant-stress and step-stress accelerated models, the explicit conditional density functions of order statistics under progressively Type-I hybrid censoring scheme are given to obtain the expected Fisher information matrix. By minimizing the asymptotic variance of the mean life under the use stress, the optimum test design is completed by determining the test units allocated to each stress in constant-stress accelerated life test and the changing time to severer accelerated stress in step-stress accelerated life test. Finally, an example is shown to illustrate the optimum test design. The numerical results show that the step-stress accelerated life test is a better choice.

Reliability nonparametric Bayesian estimation for the masked data of parallel systems in step-stress accelerated life tests

The accelerated life tests with two groups of step-stress levels are considered for the parallel systems, in which the masked data are observed. We assume the power function as accelerated function for the life transformation between different stress levels, which covers the shortage of linear accelerated function. Then the estimators of coefficient vectors in accelerated function are obtained. The relationship among survival and subsurvival functions of components is discussed under a regular condition. It does not require that the discontinuity points of survival functions have to be disjointed. With the help of that transformational relationship, nonparametric Bayesian estimators of reliability functions corresponding to any components’ set are derived. Due to the complexity of masked data, a group of computational algorithms are developed to obtain the estimates. Finally, a simulated example is presented to illustrate the proposed nonparametric Bayesian method.

Parametric inference on step-stress accelerated life testing for the extension of exponential distribution under progressive type-II censoring

In this paper, a simple step-stress accelerated life test (ALT) under progressive type-II censoring is considered. Progressive type-II censoring and accelerated life testing are provided to decrease the lifetime of testing and lower test expenses. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are also obtained. In addition, a real dataset is analyzed to illustrate the proposed procedures. Approximate, bootstrap and credible confidence intervals (CIs) of the estimators are then derived. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.

Optimum quadratic step-stress accelerated life test plan for Weibull distribution under type-I censoring

This paper presents the optimum stress changing times for 3-step, step stress accelerated life testing under the cumulative exposure model with type-I censoring. The lifetimes of test units are assumed to follow Weibull distribution. The scale parameter of the Weibull failure time at constant stress level is assumed to be a log-quadratic function of the stress level. We derive an optimum test plans to minimize the asymptotic variance of maximum likelihood estimator of given pth percentile of the distribution at a design stress. The optimum test plan based on simulated observations is illustrated through a numerical example. The maximum likelihood estimates and asymptotic interval estimates are obtained using R software.

Estimation of the extended Weibull parameters and acceleration factors in the step-stress accelerated life tests under an adaptive progressively hybrid censoring data

ABSTRACTBased on the tampered failure rate model under the adaptive Type-II progressively hybrid censoring data, we discuss the maximum likelihood estimators of the unknown parameters and acceleration factors in the general step-stress accelerated life tests in this paper. We also construct the exact and unique confidence interval for the extended Weibull shape parameter. In the numerical analysis, we describe the simulation procedures to obtain the adaptive Type-II progressively hybrid censoring data in the step-stress accelerated life tests and present an experimental data to illustrate the performance of the estimators.

A Critical Perspective on Mechanical Testing of Implants and Prostheses.

The degree of interplay among variables in dental implant treatment presents a challenge to randomized clinical trials attempting to answer questions in a timely, unbiased, and economically feasible fashion. Further adding complexity to the different scenarios is the varied implant designs and related bone response, area of implantation, implant bulk material, restoration, abutments and related screws, fixation mode (screwed, fixed, or a combination), and horizontal implant-abutment matching geometry. This article critically appraises the most common mechanical testing methods used to characterize the implant-prostheses complex. It attempts to provide insight into the process of construction of an informed database of clinically relevant questions regarding preclinical evaluation of implant biomechanics and failure mechanisms. The use of single load to failure, fatigue life, fatigue limit, and step-stress accelerated life testing is discussed with emphasis on their deliverables, weaknesses, and strengths. Fractographic analysis and challenges in the correlation between laboratory- and in-service-produced failures of dental ceramics, resin composites, and titanium are introduced. In addition, examples are presented of mechanical characterization studies used in our laboratory to assess some implant-supported rehabilitation variables.

Optimum Step-Stress Accelerated Life Test Plan for Lomax Distribution with an Adaptive Type-II Progressive Hybrid Censoring

The adaptive type -II progressive hybrid censoring has the advantage of saving both t he total test time and the cost of the experiment; also it increases the effi ciency of the statistical analysis. This article discuss es k-level step stress accelerated life tests based on an ad aptive type-II progressive hybrid censoring with product ' s life time following Lomax distribution. The scale param eter of the Lomax failure time distribution at constant levels is assumed to be a log line ar function of the stress level. Maximum likelihood estimators of the model parameters are derive d. Based on normal approximation to the asymptotic distribution of maximum likelihood estimators, t he approximate confidence intervals for model parameters are obtained. The optimal times of changing stress levels are discussed under Doptimality and A-optimality criteria. Such methods maximize the determinant and the trace of Fisher's information matrix for the model parameters. Analysis of t he numerical data has been presented for illustrative proposes.

Optimum Step-Stress Accelerated Life Test Plan for Lomax Distribution with an Adaptive Type-II Progressive Hybrid Censoring

The adaptive type -II progressive hybrid censoring has the advantage of saving both t he total test time and the cost of the experiment; also it increases the effi ciency of the statistical analysis. This article discuss es k-level step stress accelerated life tests based on an ad aptive type-II progressive hybrid censoring with product ' s life time following Lomax distribution. The scale param eter of the Lomax failure time distribution at constant levels is assumed to be a log line ar function of the stress level. Maximum likelihood estimators of the model parameters are derive d. Based on normal approximation to the asymptotic distribution of maximum likelihood estimators, t he approximate confidence intervals for model parameters are obtained. The optimal times of changing stress levels are discussed under Doptimality and A-optimality criteria. Such methods maximize the determinant and the trace of Fisher's information matrix for the model parameters. Analysis of t he numerical data has been presented for illustrative proposes.

Estimation for Birnbaum–Saunders Distribution in Simple Step Stress–accelerated Life Test with Type-II Censoring

This paper develops the Bayesian estimation for the Birnbaum–Saunders distribution based on Type-II censoring in the simple step stress–accelerated life test with power law accelerated form. Maximum likelihood estimates are obtained and Gibbs sampling procedure is used to get the Bayesian estimates for shape parameter of Birnbaum–Saunders distribution and parameters of power law–accelerated model. Asymptotic normality method and Markov Chain Monte Carlo method are employed to construct the corresponding confidence interval and highest posterior density interval at different confidence level, respectively. At last, the results are compared by using Monte Carlo simulations, and a numerical example is analyzed for illustration.

Reliability and failure modes of narrow implant systems.

Narrow implants are indicated in areas of limited bone width or when grafting is nonviable. However, the reduction of implant diameter may compromise their performance. This study evaluated the reliability of several narrow implant systems under fatigue, after restored with single-unit crowns. Narrow implant systems were divided (n=18 each), as follows: Astra (ASC); BioHorizons (BSC); Straumann Roxolid (SNC), Intra-Lock (IMC), and Intra-Lock one-piece abutment (ILO). Maxillary central incisor crowns were cemented and subjected to step-stress accelerated life testing in water. Use level probability Weibull curves and reliability for a mission of 100,000 cycles at 130- and 180-N loads (90% two-sided confidence intervals) were calculated. Scanning electron microscopy was used for fractography. Reliability for 100,000 cycles at 130N was ∼99% in group ASC, ∼99% in BSC, ∼96% in SNC, ∼99% in IMC, and ∼100% in ILO. At 180N, reliability of ∼34% resulted for the ASC group, ∼91% for BSC, ∼53% for SNC, ∼70% for IMC, and ∼99% for ILO. Abutment screw fracture was the main failure mode for all groups. Reliability was not different between systems for 100,000 cycles at the 130-N load. A significant decrease was observed at the 180-N load for ASC, SNC, and IMC, whereas it was maintained for BSC and ILO. The investigated narrow implants presented mechanical performance under fatigue that suggests their safe use as single crowns in the anterior region.

Optimal Design for a Bivariate Simple Step-Stress Accelerated Life Testing Model with Type-II Censoring and Gompertz Distribution

This paper deals with the optimal designing of step-stress accelerated life test (SSALT) for two stress variables. The lifetime of the items follows the Gompertz distribution and the test is subject to termination at a predetermined number of failures of test items (Type II censoring). Furthermore, we model the effects of changing stress as a cumulative exposure (CE) function. This test is presented to obtain the optimal hold times for each combination of stress levels. The optimal test plan with the minimum asymptotic variance (AV) of the maximum likelihood estimator (MLE) of reliability at time [Formula: see text] is determined. Due to nonlinearity and complexity of the objective function, the particle swarm optimization (PSO) algorithm is developed to calculate the optimal hold times. In this method, the research speed is very fast and optimization ability is more. Finally, simulation results are discussed to illustrate the proposed criteria. For some selected values of the parameters, the effect of initial estimates on optimal values has been studied.