Step-stress Accelerated Life Testing Research Articles

The step-stress tampered failure rate model under interval monitoring

A step-stress accelerated life testing model is constructed that deals with type-I censored experiments for which a continuous monitoring of the tested items is infeasible and only their inspection at particular time points is possible, producing thus grouped data. A general scale family of distributions is considered for the underlying lifetimes, which allows for flexible modeling by permitting different lifetime distributions for different stress levels. The maximum likelihood estimators of its parameters and their density functions are derived explicitly only when the inspection points coincide with the points of stress-level change. In case of additional inspection points, the estimates are obtained numerically. Asymptotic, exact (whenever possible) and bootstrap confidence intervals (CIs) are considered. For the bootstrap CIs a smoothing-modification is introduced, accounting for the categorical nature of the data.

Mechanical Evaluation of Two Grades of Titanium Used in Implant Dentistry.

To investigate the effect of core dental implant materials supporting single crowns on the probability of survival and failure modes. Thirty-six standard external-hex titanium implants (4.0 mm in diameter) were selected to restore single crowns and divided into two groups according to core material: commercially pure grade 2 titanium (G2) and grade 5 titanium-aluminum-vanadium alloy (Ti-6Al-4V) (G5). Abutments were screwed to the implants, and standardized maxillary central incisor metal crowns were cemented and subjected to step-stress accelerated life testing in water. Use-level probability Weibull curves and reliability for missions of 100,000 cycles at 150 N and 200 N (with 90% two-sided confidence intervals [CIs]) were calculated. Polarized light and scanning electron microscopes were used to determine the failure modes. Use-level probability Weibull calculations showed beta values of 0.59 (CI, 0.31 to 1.11) and 1.22 (CI 0.81 to 1.84) for G2 and G5, respectively, and significantly higher characteristic strength and Weibull modulus for G5. The calculated reliability (90% CIs) for a mission of 100,000 cycles at 150 N showed that cumulative damage would lead to survival of 45% of implant-supported crowns of G2 and 98% of G5. At 200 N the probability of survival decreased to 0.03% for G2 and 21% for G5. Abutment screw fracture was the failure mode for all groups. Reliability, characteristic strength, and Weibull modulus were significantly higher for Ti-6Al-4V dental implants than for commercially pure (grade 2) titanium implants. Failure modes were similar for both groups.

Effect of Diamondlike Carbon Coating on Reliability of Implant-Supported Crowns.

To evaluate the effect of diamondlike carbon (DLC) coating on abutments and/or abutment screws on the reliability, characteristic strength, and Weibull modulus of implant-supported single crowns. Seventy-two external hexagon implants (Emfills Implant 4 mm diameter, 10 mm length, Emfills) were divided into four groups (n = 18 each), according to the presence or not of a DLC coating in the abutment and/or abutment screw, as follows: abutment without coating, screw without coating (AwcSwc); abutment without coating with coated screw (AwcSC); abutment coated with noncoated screw (ACSwc), and coated abutment with coated screw (ACSC). Abutments and screws were evaluated with scanning electron microscopy. The specimens were subjected to step-stress accelerated life testing in water. Use-level probability Weibull curves and reliability for a mission of 100,000 cycles at 150 N (90% two-sided confidence intervals) were calculated. Polarized light and scanning electron microscopes were used for fractographic analysis. For a mission of 100,000 cycles at 150 N, reliability was 0.45 (0.20 to 0.67), 0.12 (0.00 to 0.47), 0.56 (0.17 to 0.82), and 0.44 (0.07 to 0.77) for AwcSwc, AwcSC, ACSwc, and ACSC, respectively. The probability Weibull calculation showed a Weibull modulus (m) of m = 5.50, m = 11.64, m = 16.96, and m = 15.08 and the characteristic strengths (η, which indicates the load at which 63.2% of the specimens of each group fail) of η = 202.67 N, ŋ = 206.64 N, ŋ = 192.54 N, and ŋ = 203.59 N for AwcSwc, AwcSC, ACSwc, and ACSC, respectively. Abutment screw fracture was the chief failure outcome in all groups. Characteristic strength values were not different among groups; neither was reliability. However, an increase in Weibull modulus (indicating low variability of the results) was observed with DLC coating of abutment or screw or both.

An Approximate E-Bayesian Estimation of Step-stress Accelerated Life Testing with Exponential Distribution

The data analysis problem of step-stress accelerated life testing with exponential distribution is discussed. At the step-stress accelerated life testing conditions, an approximate E-Bayesian parameter estimation of step-stress acceler- ated life testing with exponential distribution is given by considering the prior distributions of the hyperparameters and us- ing Gibbs sampling method. Finally, a simulation example is given, the results show that the Gibbs sampling method is simple and the convergence is better. E-Bayesian parameter estimation is more effective than the maximum likelihood es- timation.

Bayesian Analysis of Step-Stress Accelerated Life Tests and Its Use in Planning

ABSTRACTA Bayesian analysis of step-stress accelerated life test data is introduced and illustrated by an experiment on cryogenic cables. A cumulative damage model is used to describe the cumulative distribution function of Weibull lifetimes. The analysis methodology can then be used to evaluate a step-stress accelerated life test plan through simulation and calculation of appropriate criteria. Such planning is illustrated with the cryogenic cable example.

Planning simple step-stress accelerated life tests using reference optimality criterion

A reference optimality criterion has been proposed by Xu and Tang based on the expected Kullback–Leibler divergence between the posterior and the prior distributions of the parameters of interest. In this paper, we use the reference optimality criterion to plan simple step-stress accelerated life tests for log-location-scale distributions. Monte Carlo algorithms are developed to find the optimal plans. Effects of the priors on the optimal plans are also investigated. Results indicate that the optimal Bayesian plans are robust to the choice of the priors.

Time and cost constrained optimal designs of constant-stress and step-stress accelerated life tests

By running life tests at higher stress levels than normal operating conditions, accelerated life testing quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. To conduct an accelerated life test efficiently with constrained resources in practice, several decision variables such as the sample allocation proportions and the stress durations should be determined carefully at the design stage. These decision variables affect not only the experimental cost but also the estimate precision of the lifetime parameters of interest. In this work, under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal decision variables are determined based on C/D/A-optimality criteria. In particular, the constant-stress and step-stress accelerated life tests are considered with the exponential failure data under time constraint as well. We illustrate the proposed methods using two real case studies, and under the identical budget constraint, the efficiencies of these two stress loading schemes are compared in terms of the ratio of optimal objective functions based on the information matrix.

Digitally produced fiber-reinforced composite substructures for three-unit implant-supported fixed dental prostheses.

This study aimed to evaluate the probability of survival, Weibull modulus, characteristic strength, and failure modes of computer-aided design/computer-assisted manufacture (CAD/CAM) fiber-reinforced composite (FRC) substructures used for implant-supported fixed dental prostheses (ISFDPs). Three-unit ISFDPs (first molar pontic) fabricated as a monolithic composite piece or as composite veneered on a CAD/CAM FRC substructure with either a 12-mm² or 3-mm² connector area (n = 18 each) were subjected to step-stress accelerated life testing in water. Use-level probability Weibull curves and the probability of survival were calculated. Fractographic analysis was performed under polarized light and scanning electron microscopy. Fatigue did not accelerate the failure of any group, whereas prosthesis strength was the main factor in increased failure (β < 1). The probability Weibull contour plot showed no differences between the ISFDPs with 12 mm² and the monolithic composite ISFDP in characteristic strength (η = 643.5 N and 742.7 N, respectively) or Weibull modulus (6.7 and 5.8, respectively), whereas both were significantly higher than 3 mm² (444.91 N and 9.57). The probability of survival was not statistically different between groups at 100,000 mission cycles at 300 N. Differences were observed in fatigue failures above 800 N; monolithic composite ISFDPs failed catastrophically, whereas those with CAD/CAM FRC substructures presented veneer/composite cohesive or adhesive failures. Cracks evolved from the occlusal contact toward the margins of the cohesively failed composite, and in CAD/CAM FRC prostheses, competing failure modes of cracks developing at the connector area with those at the indentation contact were observed. The probability of survival did not differ between CAD/CAM FRC with either 3-mm² or 12-mm² connector areas, monolithic composite, or metal-ceramic ISFDPs previously tested under the same methodology. However, differences in failure modes were detected between groups.

Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring

Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs) of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.

Optimal three step-stress accelerated life tests for Type-I hybrid censored data

Optimal three step-stress accelerated life tests for Type-I hybrid censored data

Mathematical Modeling of Optimum 3 Step Stress Accelerated Life Testing for Generalized Pareto Distribution

This article contains the optimum 3 step stress accelerated life test under cumulative exposure model. The lifetimes of test units are assumed to follow a generalized Pareto distribution. The scale parameter of the used failure time distribution at the constant stress level is assumed to have a log-linear and quadratic relationship with the stress. A comparison between linear plan and quadratic plan by maximum likelihood estimators for the different sample sizes is shown in the table. The optimum test plans is obtained by minimizing the asymptotic variance of the maximum likelihood estimator of the percentile of the lifetime distribution at normal stress condition for the model parameters. Tables of optimum times of changing stress level for both plans are also obtained.

A Study on the Storage Reliability of LSINS Based on Step-stress Accelerated Life Test

Based on the step-stress accelerated life test and the laser strap-down inertial navigation system, this paper studies the accelerated life model and the test method, provides the likelihood function, the likelihood equation and the two-order derivative when the stress level is k, evaluates the effectiveness of the method with the simulation test model established by MATLAB, applies the research findings in the storage reliability study of the XX laser strap-down inertial navigation system, and puts forward an effective evaluation method of the storage life of the inertial navigation system.

Reliability and failure modes of two Y-TZP abutment designs.

Fracture strength and accelerated fatigue reliability of two zirconia abutment systems were tested. Thirty-six implants with a Morse taper (MT; n = 18) or cone (C; n = 18) design were restored with metallic crowns. Loads were applied as single load to failure (SLF) or mouth-motion cycles using a step-stress accelerated life testing (SALT) method. SLF mean values were 690 ± 430 N and 209 ± 25 for MT and C groups, respectively. In terms of the SALT results, 8 specimens survived (50,000 cycles) and 7 failed (maximum load 400 N) in the MT group; whereas for the C group all abutments failed before the maximum number of cycles. Failure mode was fracture of the Y-TZP abutments for both groups. Higher reliability for a mission of 50,000 cycles at 175 N for MT versus C designs was determined, and significant differences in fracture modes were observed.

Effects of implant diameter and prosthesis retention system on the reliability of single crowns.

The probability of survival of implant-supported prostheses may be affected by the interplay between different implant diameters supporting screwed or cemented crowns. The purpose of this study was to investigate the effect of implant diameter and prosthesis retention system on the reliability and failure modes of single crowns. Internal-hexagon implants were divided into six groups (n = 21 each) according to implant diameter (3.3, 4.0, or 5.0 mm) and crown retention system (screwed or cemented). Abutments were torqued to the implants, and crowns were then fixed and subjected to step-stress accelerated life testing in water. Use-level probability Weibull curves and reliability for missions of 50,000 cycles at 100, 150, and 200 N were calculated. Failure analysis was performed. Cemented systems presented higher reliability than screwed ones, except between 3.3-mm-diameter cemented and screwed systems at a load of 100 or 150 N. Failure modes were restricted to the abutment screw and varied with implant diameter only in the cement-retained groups. Higher reliability was observed for cement-retained crowns and implants of larger diameter compared to screw-retained and smaller diameter. Failure modes differed between groups.

Durability Reliability Demonstration Test Methods

A complete product design cycle should include the following three stages: target setting, product design and development, and product validation. In the first target setting stage, it is required to understand the voice of customers (VOC), define the extreme customer usage conditions, acquire the duty cycle or customer usage data for the target, and cascade the top-down VOC targets from vehicle to system and component levels. In the second stage of product design and development, the multi-objective design optimization in the virtual analysis domain needs to be performed, where the analytical tools to design the products for various design criteria should have been developed and in place for analyses. In the final product validation stage, the test methods with a limited sample size are required to demonstrate the reliability of the product population for meeting the specific design functional and performance requirements. Since the test results exhibit significant statistical variations, these test methods (named the reliability demonstration test methods) are the most important mechanism to ensure a successful product launch for durability, reliability and quality. Again, due to the limited sample size for testing, a specific reliability and confidence target should be predetermined to be demonstrated by these test methods.The focus of this paper is to review the theoretical background and discuss the pros and cons of commonly used reliability demonstration test methods. Depending on the failure criterion in product validation testing, these reliability demonstration test methods can be categorized into the methods for non-repairable and repairable systems. For a non-repairable system, the test is considered complete, censored or suspended as the system fails, while a repairable system allows the actions required to restore/renew a failed system to operational status. The methods of interest for non-repairable systems include the test-to-failure method, the test-to-bogey method, the extended life test bogey method, and the step-stress accelerated life test method. Repairable systems are often modeled with the non-homogeneous Poisson process which includes the Duane and the Crow reliability growth models.

Equivalent step-stress accelerated life tests with log-location-scale lifetime distributions under Type-I censoring

Accelerated Life Testing (ALT) is used to provide timely estimates of a product's lifetime distribution. Step-Stress ALT (SSALT) is one of the most widely adopted stress loadings and the optimum design of a SSALT plan has been extensively studied. However, few research efforts have been devoted to establishing the theoretical rationale for using SSALT in lieu of other types of stress loadings. This article proves the existence of statistically equivalent SSALT plans that can provide equally precise estimates to those derived from any continuous stress loading for the log-location-scale lifetime distributions with Type-I censoring. That is, for any optimization criterion based on the Fisher information matrix, SSALT is identical in comparison to other continuous stress loadings. The Weibull and lognormal distributions are introduced as special cases. For these two distributions, the relationship among statistical equivalencies is investigated and it is shown that two equivalent ALT plans must be equivalent in terms of the strongest version of equivalency for many objective functions. A numerical example for a ramp-stress ALT, using data from an existing study on miniature lamps, is used to illustrate equivalent SSALT plans. Results show that SSALT is not only equivalent to the existing ramp-stress test plans but also more cost-effective in terms of the total test cost.

A Full Bayesian Approach for Masked Data in Step-Stress Accelerated Life Testing

Bayesian analysis of the series system failure data under step-stress accelerating life testing is proposed when the cause of failure may not have been identified but has only been narrowed down to a subset of all potential risks. A general Bayesian formulation is investigated for the log-location-scale distribution family that includes most commonly used parametric lifetime distributions. Reparameterization is introduced for estimating the lifetime under the use condition stress and other parameters directly. The posterior analysis is done by Markov chain Monte Carlo sampling. The methodology is illustrated through the Weibull distributions, and a numerical example.

Research on Accelerated Life Test System for Water Quality Analyzer

This research proposes an Accelerated Life Test System and has realized the reliability test of water quality analyzer. ALT (Accelerated Life Test) system is based on the principle of step stress accelerated life test and takes temperature as the accelerated stress. The system includes lower computer PLC and upper computer software of MCGS. In this research, Upper computer using configuration software to connect with the SIEMENS S7-300 PLC, in order to realize data acquisition and system control. This system improves the reliability test efficiency of the water quality analyzer, reduces the cost of test and has good economic efficiency.

Asymptotic Comparison Between Constant-stress Testing and Step-stress Testing for Type-I Censored Data from Exponential Distribution

By running the life tests at higher stress levels than normal operating conditions, accelerated life testing quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. In constant-stress testing, a unit is tested at a fixed stress level until failure or the termination time point of the test, while step-stress testing allows the experimenter to gradually increase the stress levels at some pre-fixed time points during the test. In this article, the optimal k-level constant-stress and step-stress accelerated life tests are compared for the exponential failure data under Type-I censoring. The objective is to quantify the advantage of using the step-stress testing relative to the constant-stress one. A log-linear relationship between the mean lifetime parameter and stress level is assumed and the cumulative exposure model holds for the effect of changing stress in step-stress testing. The optimal design point is then determined under C-optimality, D-optimality, and A-optimality criteria. The efficiency of step-stress testing compared to constant-stress testing is discussed in terms of the ratio of optimal objective functions based on the information matrix.

Bayesian Analysis of Masked Data in Step-stress Accelerated Life Testing

This article considers a k level step-stress accelerated life testing (ALT) on series system products, where independent Weibull-distributed lifetimes are assumed for the components. Due to cost considerations or environmental restrictions, causes of system failures are masked and type-I censored observations might occur in the collected data. Bayesian approach combined with auxiliary variables is developed for estimating the parameters of the model. Further, the reliability and hazard rate functions of the system and components are estimated at a specified time at use stress level. The proposed method is illustrated through a numerical example based on two priors and various masking probabilities.