Non-destructive one-shot device testing under step-stress model with Weibull lifetime distributions

One-shot devices are product or equipment that can be used only once, so they get destroyed when tested. However, the destructiveness assumption may not be necessary in many practical applications such as assessing the effect of temperature on some electronic components, yielding to the so called non-destructive one-shot devices. Further, one-shot devices generally have large mean lifetime to failure, and so accelerated life tests (ALTs) must be performed for inference. The step-stress ALT shorten the lifetime of the products by increasing the stress level at which units are subjected to progressively at pre-specified times. Then, the non-destructive devices are tested at certain inspection times and surviving units can continue within the experiment providing extra information. Classical estimation methods based on the maximum likelihood estimator (MLE) enjoy suitable asymptotic properties but they lack of robustness. In this paper, we develop robust inferential methods for non-destructive one-shot devices based on the popular density power divergence (DPD) for estimating and testing under the step-stress model with Weibull lifetime distributions. We theoretically and empirically examine the asymptotic and robustness properties of the minimum DPD estimators and Wald-type test statistics based on them. Moreover, we develop robust estimators and confidence intervals for some important lifetime characteristics, namely reliability at certain mission times, distribution quantiles and mean lifetime of a device. Finally, we analyze the effect of temperature in three electronic components, solar lights, medium power silicon bipolar transistors and LED lights using real data arising from an step-stress ALT

Inferencia estadística robusta basada en divergencias para dispositivos de un sólo uso

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 30-06-2021A one-shot device is a unit that performs its function only once and, after use, the device either gets destroyed or must be rebuilt. For this kind of device, one can only know whether the failure time is either before or after a speci c inspection time, and consequently the lifetimes are either left- or right-censored, with the lifetime being less than the inspection time if the test outcome is a failure (resulting in left censoring) and the lifetime being more than the inspection time if the test outcome is a success (resulting in right censoring). An accelerated life test (ALT) plan is usually employed to evaluate the reliability of such products by increasing the levels of stress factors and then extrapolating the life characteristics from high stress conditions to normal operating conditions. This acceleration process will shorten the life span of devices and reduce the costs associated with the experiment. The study of one-shot device from ALT data has been developed considerably recently, mainly motivated by the work of Fan et al. [2009]...Los dispositivos de un solo uso (one shot devices en ingles), son aquellos que, una vez usados, dejan de funcionar. La mayor dificultad a la hora de modelizar su tiempo de vida es que solo se puede saber si el momento de fallo se produce antes o despues de un momento específico de inspeccion. As pues, se trata de un caso extremo de censura intervalica: si el tiempo de vida es inferior al de inspeccion observaremos un fallo (censura por la izquierda), mientras que si el tiempo de vida es mayor que el tiempo de inspeccion, observaremos un exito (censura por la derecha). Para la observacion y modelizacion de este tipo de dispositivos es comun el uso de tests de vida acelerados. Los tests de vida acelerados permiten evaluar la fiabilidad de los productos en menos tiempo, incrementando las condiciones a las que se ven sometidos los dispositivos para extrapolar despues estos resultados a condiciones mas normales. El estudio de los dispositivos de un solo uso por medio de tests de vida acelerados se ha incrementado considerablemente en los ultimos a~nos motivado, principalmente, por el trabajo de Fan et al. [2009]...Fac. de Ciencias MatemáticasTRUEunpu

Robust estimation based on one-shot device test data under log-normal lifetimes

In this paper we present robust estimators for one-shot device test data under lognormal lifetimes. Based on these estimators, confidence intervals and Wald-type tests are also developed. Their robustness feature is illustrated through a simulation study and two numerical examples

Optimal designs of constant‐stress accelerated life‐tests for one‐shot devices with model misspecification analysis

The design of constant-stress accelerated life-test (CSALT) is important in reliability estimation. In reliability studies, practitioners usually rely on underlying distribution to design CSALTs. However, model misspecification analysis of optimal designs has not been examined extensively. This paper considers one-shot device testing data by assuming gamma, Weibull, lognormal and Birnbaum–Saunders (BS) lifetime distributions, which are popular lifetime distributions in reliability studies. We then investigate the effect of model misspecification between these lifetime distributions in the design of optimal CSALTs, in which the asymptotic variance of the estimate of reliability of the device at a specific mission time is minimized subject to a prefixed budget and a termination time of the life-test. The inspection frequency, number of inspections at each stress level, and allocation of the test devices are determined in optimal design for one-shot device testing. Finally, a numerical example involving a grease-based magnetorheological fluids (G-MRF) data set is used to illustrate the developed methods. Results suggest the assumption of lifetime distribution as Weibull or lognormal to be more robust to model misspecification, while the assumption of gamma lifetime distribution seems to be the most non-robust (or most sensitive) one

One-Shot Device Testing Data Analysis under Logistic-Exponential Lifetimes with an Application to SEER Gallbladder Cancer Data

In the literature, the reliability analysis of one-shot devices is found under accelerated life testing in the presence of various stress factors. The application of one-shot devices can be extended to the bio-medical field, where we often evidence that inflicted with a certain disease, survival time would be under different stress factors like environmental stress, co-morbidity, the severity of disease etc. This work is concerned with a one-shot device data analysis and applies it to SEER Gallbladder cancer data. The two-parameter logistic exponential distribution is applied as a lifetime distribution. For robust parameter estimation, weighted minimum density power divergence estimators (WMDPDE) is obtained along with the conventional maximum likelihood estimators (MLE). The asymptotic behaviour of the WMDPDE and the robust test statistic based on the density power divergence measure are also studied. The performances of estimators are evaluated through extensive simulation experiments. Later those developments are applied to SEER Gallbladder cancer data. Citing the importance of knowing exactly when to inspect the one-shot devices put to the test, a search for optimum inspection times is performed. This optimization is designed to minimize a defined cost function which strikes a trade-off between the precision of the estimation and experimental cost. The search is accomplished through the population-based heuristic optimization method Genetic Algorithm

Robust inference for non-destructive one-shot device testing under step-stress model with exponential lifetimes

One-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one-shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step-stress tests allow the experimenter to increase the stress levels at pre-fixed times gradually during the life-testing experiment. The cumulative exposure model is commonly assumed for step-stress models, relating the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. In this paper, we develop robust estimators and Z-type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for non-destructive one-shot devices under the step-stress ALTs with exponential lifetime distribution. We study asymptotic and robustness properties of the estimators and test statistics, yielding point estimation and conffidence intervals for different lifetime characteristic such as reliability, distribution quantiles and mean lifetime of the devices. A simulation study is carried out to assess the performance of the methods of inference developed here and some real-life data sets are analyzed ffinally for illustrative purpose

Practical reliability. Volume 3 - Testing

Application of testing to hardware program

RELIABILITY TESTING & BAYESIAN MODELING OF HIGH POWER LEDS FOR USE IN A MEDICAL DIAGNOSTIC APPLICATION

While use of LEDs in fiber optics and lighting applications is common, their use in medical diagnostic applications is rare. Since the precise value of light intensity is used to interpret patient results, understanding failure modes is very important. The contributions of this thesis is that it represents the first measurements of reliability of AlGaInP LEDs for the medical environment of short pulse bursts and hence the uncovering of unique failure mechanisms. Through accelerated life tests (ALT), the reliability degradation model has been developed and other LED failure modes have been compared through a failure modes and effects criticality analysis (FMECA). Appropriate ALTs and accelerated degradation tests (ADT) were designed and carried out for commercially available AlGaInP LEDs. The bias conditions were current pulse magnitude and duration, current density and temperature. The data was fitted to both an Inverse Power Law model with current density J as the accelerating agent and also to an Arrhenius model with T as the accelerating agent. The optical degradation during ALT/ADT was found to be logarithmic with time at each test temperature. Further, the LED bandgap temporarily shifts towards the longer wavelength at high current and high junction temperature. Empirical coefficients for Varshini's equation were determined, and are now available for future reliability tests of LEDs for medical applications. In order to incorporate prior knowledge, the Bayesian analysis was carried out for LEDs. This consisted of identifying pertinent prior data and combining the experimental ALT results into a Weibull probability model for time to failure determination. The Weibull based Bayesian likelihood function was derived. For the 1st Bayesian updating, a uniform distribution function was used as the Prior for Weibull á-â parameters. Prior published data was used as evidence to get the 1st posterior joint á-â distribution. For the 2nd Bayesian updating, ALT data was used as evidence to obtain the 2nd posterior joint á-â distribution. The predictive posterior failure distribution was estimated by averaging over the range of á-â values. This research provides a unique contribution in reliability degradation model development based on physics of failure by modeling the LED output characterization (logarithmic degradation, TTF â<1), temperature dependence and a degree of Relevance parameter `R' in the Bayesian analysis

Reliability demonstration of a multi-component Weibull system under zero-failure assumption.

This dissertation is focused on finding lower confidence limits for the reliability of systems consisting of Wei bull components when the reliability demonstration testing (RDT) is conducted with zero failures. The usual methods for the parameter estimation of the underlying reliability functions like maximum likelihood estimator (MLE) or mean squares estimator (MSE) cannot be applied if the test data contains no failures. For single items there exists a methodology to calculate the lower confidence limit (LCL) of reliability for a certain confidence level. But there is no comparable method for systems. This dissertation provides a literature review on specific topics within the wide area of reliability engineering. Based on this and additional research work, a first theorem for the LCL of system reliability of systems with Weibull components is formulated. It can be applied if testing is conducted with zero observed failures. This theorem is unique in that it allows for different Wei bull shape parameters for components in the system. The model can also be applied if each component has been exposed to different test durations. This can result from accelerated life testing (AL T) with test procedures that have different acceleration factors for the various failure modes or components respectively. A second theorem for Ex -lifetime, derived from the first theorem, has been formulated as well. The first theorem on LCL of system reliability is firstly proven for systems with two components only. In the following the proof is extended towards the general case of n components. There is no limitation on the number of components n. The proof of the second theorem on Bx - lifetime is based on the first proof and utilizes the relation between Bx and reliability. The proven theorem is integrated into a model to analyze the sensitivity of the estimation of the Wei bull shape parameter p. This model is also applicable if the Weibull parameter is subject to either total uncertainty or of uncertainty within a defined range. The proven theorems can be utilized as the core of various models to optimize RDT plans in a way that the targets for the validation can be achieved most efficiently. The optimization can be conducted with respect to reliability, Bx -lifetime or validation cost. The respective optimization models are mixed-integer and highly non-linear and therefore very difficult to solve. Within this research work the software package LINGO™ was utilized to solve the models. There is a proposal included of how to implement the optimization models for RDT testing into the reliability process in order to iteratively optimize the RDT program based on failures occurred or changing boundary conditions and premises. The dissertation closes with the presentation of a methodology for the consideration of information about the customer usage for certain segments such as market share, annual mileage or component specific stress level for each segment. This methodology can be combined with the optimization models for RDT plans

Reliability Abstracts and Technical Reviews January-December 1967

No abstract availabl