Geometry of an accelerated model with censored data

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 this paper, the Jeffreys priors for the step-stress partially accelerated life test with Type-II adaptive progressive hybrid censoring scheme data are considered. Given a density function family satisfied certain regularity conditions, the Fisher information matrix and Jeffreys priors are obtained. Taking the Weibull distribution as an example, the Jeffreys priors, posterior analysis and its permissibility are discussed. The results, which present that how the accelerated stress levels, censored size, hybrid censoring time and stress change time etc. affect the Jeffreys priors, are obtained. In addition, a theorem which shows there exists a relationship between single observation and multi observations for permissible priors is proved. Finally, using Metroplis with in Gibbs sampling algorithm, these factors are confirmed by computing the frequentist coverage probabilities.

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.

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.

An imprecise statistical method for accelerated life testing using the power-Weibull model

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

Accelerated life tests (ALTs) are aimed at revealing and understanding the physics of the expected or occurred failures, i.e., are able to detect the possible failure modes and mechanisms. Another objective of the ALTs is to accumulate representative failure statistics. Adequately designed, carefully conducted, and properly interpreted ALTs provide a consistent basis for obtaining the ultimate information of the reliability of a product—the predicted probability of failure after the given time of service in the given conditions. Such tests can dramatically facilitate the solution to the cost effectiveness and time-to-market problems. ALTs should play an important role in the evaluation, prediction and assurance of the reliability of microelectronics and optoelectronics devices and systems. In the majority of cases, ALTs should be conducted in addition to the qualification tests required by the existing standards. There might also be situations when ALTs can be (and, probably, should be) used as an effective substitution for such standards, or, at least, as the basis for the improvement of the existing qualification specifications. We describe different types (categories) of accelerated tests, with an emphasis on the role that ALTs should play in the development, design, qualification, and manufacturing of microelectronics and photonics products. We discuss the challenges associated with the implementation and use of the ALTs, potential pitfalls (primarily those associated with possible “shifts” in the mechanisms and modes of failure), and the interaction of the ALTs with other types of accelerated tests. The role of the nondestructive evaluations is also briefly outlined. The case of a laser welded optoelectronic package assembly is used to illustrate some concepts addressed. “All life is an experiment. The more experiments you make the better” Ralph Waldo Emerson “In the long run we are all dead” John Maynard Keynes

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.

This paper aims to study the efficiency of recombinant DNA insulin via models for accelerated life tests. The potency loss of these insulin products was evaluated periodically, subject to the conditions of temperature of 8°C, 25°C and 37°C. Insulin samples with potency at less than 100% were considered unfit for consumption, which characterizes the event of interest. Samples suitable for consumption were considered to be censored. The response variable was observed periodically for 736 days. For data analysis, statistical models of stress-response regression were used. The deterministic part of these models is the Arrhenius model because the stress variable is the temperature, while the probabilistic part was comprised of the Exponential, Weibull, and Log-normal models. The techniques of accelerated life tests proved adequate to address the time of potency loss of the insulin for the various temperature levels. The times of occurrence of the events were treated in three different ways, which were compared in this study. First, interval censoring was considered, or only the upper and lower limits of the interval in which the failure occurred were known. Then, the midpoint of this interval was considered as a failure time. Finally, only the lower limit of the interval in which the failure occurred was considered. According to the results, it is concluded that the use of the interval lower limit is more appropriate for estimating the reliability curves, as the estimates are closer to those using interval censoring then using the midpoint of the interval. For the specific case of the recombinant DNA insulin data, it was observed that the Arrhenius-Weibull model and the Arrhenius-lognormal are suitable for adjusting the data. It follows also that the temperature affects the power of the insulin: The higher the temperature are, the lesser the efficiency.

Producing predictions of the probabilistic risks of operating materials for given lengths of time at stated operating conditions requires the assimilation of existing deterministic creep life prediction models (that only predict the average failure time) with statistical models that capture the random component of creep. To date, these approaches have rarely been combined to achieve this objective. The first half of this paper therefore provides a summary review of some statistical models to help bridge the gap between these two approaches. The second half of the paper illustrates one possible assimilation using 1Cr1Mo-0.25V steel. The Wilshire equation for creep life prediction is integrated into a discrete hazard based statistical model—the former being chosen because of its novelty and proven capability in accurately predicting average failure times and the latter being chosen because of its flexibility in modelling the failure time distribution. Using this model it was found that, for example, if this material had been in operation for around 15 years at 823 K and 130 MPa, the chances of failure in the next year is around 35%. However, if this material had been in operation for around 25 years, the chance of failure in the next year rises dramatically to around 80%.

A hydraulic gear motor for pump oil may be run as a component in an endurance type of accelerated life test (ALT) with several different applied stresses. The main failure modes may be first established and the life test developed based upon the failure modes. The purpose of an accelerated test is to demonstrate a minimum life in a simulated customer environment. The operating temperature range for his type of pump is typically -40/spl deg/C to 60/spl deg/C with a steady operating pressure load. The results of a hypothetical 1000 hour life test are shown for clarity. This closes the loop on the larger improvement process. The ALT results in the real world depend upon the applied stresses and should be well-behaved when the test conditions are not excessive or unusual. Simple reliability models may be employed to extrapolate the ALT to other customer conditions. Limits and conditions of the ALT are noted for this type of gear pump operating at pressures of greater than 100 PSI.

Most proteins interact with small-molecule ligands such as metabolites or drug compounds. Over the past several decades, many of these interactions have been captured in high-resolution atomic structures. From a geometric point of view, most interaction sites for grasping these small-molecule ligands, as revealed in these structures, form concave shapes, or 'pockets', on the protein's surface. An efficient method for comparing these pockets could greatly assist the classification of ligand-binding sites, prediction of protein molecular function and design of novel drug compounds. We introduce a computational method, APoc (Alignment of Pockets), for the large-scale, sequence order-independent, structural comparison of protein pockets. A scoring function, the Pocket Similarity Score (PS-score), is derived to measure the level of similarity between pockets. Statistical models are used to estimate the significance of the PS-score based on millions of comparisons of randomly related pockets. APoc is a general robust method that may be applied to pockets identified by various approaches, such as ligand-binding sites as observed in experimental complex structures, or predicted pockets identified by a pocket-detection method. Finally, we curate large benchmark datasets to evaluate the performance of APoc and present interesting examples to demonstrate the usefulness of the method. We also demonstrate that APoc has better performance than the geometric hashing-based method SiteEngine. The APoc software package including the source code is freely available at http://cssb.biology.gatech.edu/APoc.

Accelerated life testing is a method for estimating the reliability of products at normal use conditions from the failure data obtained at the severe conditions. In this paper, constant-stress accelerated life testing is considered when the lifetime of a product follows a two- parameter Birnbaum-Saunders distribution. Based on type-II censoring. A certain conditions (stress) are assumed to affect the scale parameter through the inverse power law model. Maximum likelihood estimators (MLEs) of an accelerated life tests model are derived. Prediction of the scale parameter under usual conditions is obtained. Moreover, the reliability function at a certain mission time under the same conditions is also predicted. Simulation results are carried out to study the precision of the MLEs for the parameters involved.

A newly designed hinge kit system (HKS) of a commercial refrigerator was subjected to a robust reliability methodology during the design phase of the system. This methodology included setting the overall parametric accelerated life test (ALT) plan of product and identifying failure mechanisms and modes in field. The ALT included a sample size equation to improve several of the HKS design parameters. Reliability of the new HKS was targeted to be 10 years over B1. Failure sites in the HKS were identified through returned products from the field. The first ALT confirmed a failure that occurred at the housing of HKS. The missing design parameters of HKS housing for the refrigerator were that it had no support ribs in the original design. The supporting structure of HKS in the refrigerator was modified based on the action plan. Cracks were identified in a second ALT that was generated in the torsional shaft. Due to it having squared off corners, the HKS torsional shaft did not have not enough strength to withstand repetitive stresses. The shaft was modified as a consequence of the ALTs. The reliability of redesigned HKS is now guaranteed as B1 10 years. The design methods - load analysis and three ALTs were very effective in identifying the missing design parameters during the design phase. The robust design method presented in this paper might be applicable to the other mechanical systems.

An accelerated life test (ALT) is often well planned to yield the most statistical information given limited test resources. Nevertheless, ALT planning requires rough estimates of the model parameters as an input, called planning values. The discrepancy between the planning values and the true values may result in insufficient or even no failures at the low-stress level, making the subsequent data analysis difficult. Motivated by the need in the ALTs of data acquisition devices used in smart grids, an adaptive ALT scheme is proposed. The key idea is based on the observation that, when the product reliability is underestimated during the ALT design phase, it is unlikely to observe failures at the early stage of the test. Therefore, the low-stress level should be elevated to protect against insufficient failures. Under this adaptive ALT framework, order statistics techniques are used to derive the likelihood function by assuming a general log-location-scale distribution for the product lifetime. Confidence intervals for the parameters are constructed based on the large-sample approximation as well as the accelerated bootstrap method. A simulation study is conducted to demonstrate the advantages of the adaptive ALT compared with the simple constant-stress ALT. Its application is illustrated using the motivating example from smart grids.