Permissible noninformative priors for the accelerated life test model with censored data

With the increasing marketplace demand for decreasing test time and cost, constant‐stress accelerated life testing (CSALT) is widely used for reliability demonstration in practice. The existing accelerated acceptance sampling plans (AASPs) do not consider the uncertainty of accelerated factor (AF), which makes it difficult to accurately describe the producer's and consumer's risks. Previous AASP studies on CSALT were mainly carried out under a fixed accelerated stress level, and the influence of accelerated stress level is not concerned. Therefore, considering the uncertainty of AF and taking the lognormal distribution as an example, the AASP design method with time‐censoring is proposed, where the life‐stress relationship between the location parameter and stress level is expressed by an inverse power law model. First, considering the uncertainty of AF expressed by a distribution, the acceptance probability can be obtained by the mathematic expectation of conditional acceptance probability, and the producer's and consumer's risks can be accurately expressed. Then, to reduce the total cost furtherly, the accelerated stress level is considered as a new decision variable, the optimum AASP including the sampling plan and the decision‐making criterion can be designed by minimizing the total cost and solving the risk constraint equations of both sides. A real case study of white organic light‐emitting diodes is carried out to verify the effectiveness of the proposed method.

Accelerated life tests are used to explore the lifetime of extremely reliable items by subjecting them to elevated stress levels from stressors to cause early failures, such as temperature, voltage, pressure, and so on. The alpha power inverse Weibull (APIW) distribution is of great significance and practical applications due to its appealing characteristics, such as its flexibilities in the probability density function and the hazard rate function. We analyze the step stress partially accelerated life testing model with samples from the APIW distribution under adaptive type II progressively hybrid censoring. We first obtain the maximum likelihood estimates and two types of approximate confidence intervals of the distributional parameters and then derive Bayes estimates of the unknown parameters under different loss functions. Furthermore, we analyze three probable optimum test techniques for identifying the best censoring under different optimality criteria methods. We conduct simulation studies to assess the finite sample performance of the proposed methodology. Finally, we provide a real data example to further demonstrate the proposed technique.

Hydraulic piston pumps are important mechanical power conponents, and accelerated life tests (ALT) of them are widely conducted. After an ALT, ALT model is needed to give the lifetime of hydraulic piston pumps under baseline condition with ALT data. This paper proposes a physics-statistics-based ALT model for hydraulic piston pumps. After studying the structure and failure mechanism of hydraulic piston pumps, this paper uses Gumbel-Hougaard copula function to describe the dependency of the subcomponents in them. Dependence model with Gumbel-Hougaard copula function is built, the survival function of hydraulic piston pumps is derived and the whole ALT model is built.

Geometry of an accelerated model with censored data

Methods on reliability estimation and mechanism consistency test for accelerated degradation data are established in the paper. Firstly, according to the characteristics of the accelerated degradation data, the integrated degradation model is established with the Arrhenius relationship, which is used commonly in reliability engineering. Secondly, the confidence interval of percentile lifetime is given via Fisher information matrix. Via the effective usage of data under different accelerated stress levels, the accuracy of reliability estimation and lifetime prediction for product are improved. Additionally, a mechanism consistency test method is proposed which would ensure the validity of the integrated model. Finally, an example is presented which can illustrate the performance of the proposed method.

In the case of operating conditions in a much shorter time, the accelerated life test models are commonly used method since these models let the experimenters control the higher stress levels to be used for components or items in the life tests. Among different accelerated life test methods, constant stress accelerated life test models have a relationship between “failure time” and “stress” and these models are quite popular since they help the experimenters save time and cost. In this study, we evaluate the performances of the parameter estimations of the two-parameter bathtub-shaped lifetime distribution introduced by Chen (Stat Probab Lett 49(2):155–161, 2000) under the constant stress accelerated life test model using the well-known eight different inference methods. Then, we investigate the optimal stress levels using some popular criteria. Then, the performances of the estimations are compared with simulation schemes. Simulation results showed that the maximum likelihood method provides better estimation performances than others. The estimation performances of the other methods can be changed according to the stress level of the accelerated life test model. Further, it is observed that increasing stress levels provide optimal accelerated life test schemes under fixed first stress levels. Finally, we use a real data example to illustrate the theoretical outcomes.

In Malaysia, PILC cable has been used for more than 25 years. Based on the cable manufacturers' recommendation, the chronological lifetime of PILC is 40 years. However, the physical age of the cable may be lower due to various stresses experienced by the cables. Since there are 41,911 km of PILC cables in the system (more than 50% population), there must be a strategy to prioritize the replacement of PILC cables. Therefore the aim of this study is to determine the remaining life of the existing PILC in Malaysia. Based on the literature review, a well-known method to estimate remaining life is to use Accelerated Life Testing (ALT). ALT is a method used in this project to accelerate the aging of the samples to fail faster than normal aging. The data collected from the ALT are analyzed using Weibull Distribution and Inverse Power Law formula to predict remaining life of the PILC cables.

The basic idea of Accelerated Life Testing (ALT) is to expose a limited number of test units of a product to harsher-than-normal operating conditions to expedite failures. Based on the failure time data collected in a short time period, an ALT model incorporating the underlying failure time distribution and life–stress relationship can be developed for predicting the reliability of the product under the normal operating condition. However, ALT experiments often consume significant amounts of energy due to the harsher-than-normal operating conditions created and controlled by test equipment. In this article, a new ALT design methodology is developed that has the objective of improving the statistical and energy efficiency of ALT experiments. The resulting statistically and energy-efficient ALT plan depends not only on the reliability of the product to be evaluated, but also on the physical characteristics of the test equipment and its controller. Particularly, the statistical efficiency of each candidate ALT plan needs to be evaluated and the corresponding controller capable of providing the required stress loadings must be designed and simulated to evaluate the total energy consumption of the ALT plan. In this article, mathematical formulations, computational algorithms, and simulation tools are provided to handle such complex experimental design problems. Numerical examples are provided to demonstrate the effectiveness of the proposed methodology in energy reduction in ALT.

In addition to conventional censoring schemes such as Type-I or Type-II censoring, progressively censoring is a useful method to reduce cost and obtain additional reliability information in accelerated life testing. Statistical inference for accelerated life testing (ALT) with Weibull distribution and progressively censoring is found to be difficult. This paper develops generalized fiducial inference techniques for the constant-stress ALT model with Weibull distribution and progressively Type-II censoring. Simulation studies reveal the good performance of the proposed inference methods. An example is given for illustration.

Combined with the actual project, a grating ruler accelerated life test device is designed, which can simulate the actual loads, including temperature, humidity and speed stress. An accelerated life test scheme based on stepped stress loading is proposed, and 6 grating rulers are tested based on time-censored test method. An accelerated life model based on Weibull distribution used for evaluating the lifetime is established. Related experimental techniques also can be typical application cases for innovative practical teaching.

An accelerated life test model for solid lubricated bearings based on dependence analysis and proportional hazard effect

The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration.

Thanks to continuously advancing technology and manufacturing processes, the products and devices are becoming highly reliable. However, performing the life tests of these products at normal operating conditions becomes extremely difficult, if not impossible, due to their long life spans. This can result in missed opportunities to introduce the products to the market in a timely manner and eventually loss of the market share. This problem is solved by accelerated life tests where the test units are subjected to higher stress levels than the normal usage level so that information on the lifetime parameters can be obtained more quickly. The lifetime at the design condition is then estimated through extrapolation using a regression model. In this work, the design optimization of a simple step‐stress accelerated life test under progressive type I censoring is studied with nonuniform step durations for assessing the reliability characteristics of a solar lighting device. Allowing the intermediate censoring to take place at the stress change time point, the nature of the optimal stress duration is demonstrated under various design criteria including D‐optimality, C‐optimality, A‐optimality, and E‐optimality. 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 is assessed on the design efficiency.

The optimal plan of a time-censored accelerated life test (ALT) depends on unknown parameters in the ALT model. The general strategy for coping with this problem is to replace the unknown parameters with their a priori estimated values, after which we can design test plans that are robust to deviations of the estimated values. In an ALT with log-location-scale lifetime distribution and linear acceleration relation function, the slope parameter of the acceleration relation function usually has the highest uncertainty. Instead of prespecifying the slope parameter in the ALT design, in this article, we propose a new design criterion that minimizes the risk of misclassifying whether the product's pth quantile meets the design specification. Through a case study of a circular electric connector, we illustrate the proposed method, and compare it with other test criteria. The comparison result shows that the proposed plan exhibits good performance in both estimating and s-testing the product's pth quantile.

Inference on adaptive progressive hybrid censored accelerated life test for Gompertz distribution and its evaluation for virus-containing micro droplets data