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

Accelerated life testing provides an interesting challenge for quantification of the uncertainties involved, in particular due to the required linking of the units’ failure times, or failure time distributions, at different stress levels. This paper provides an initial exploration of the use of statistical methods based on imprecise probabilities for accelerated life testing. We apply nonparametric predictive inference at the normal stress level, in combination with an estimated parametric power-Weibull model linking observations at different stress levels. To provide robustness with regard to this assumed link between different stress levels, we introduce imprecision by considering an interval around the parameter estimate, leading to observations at stress levels other than the normal level to be transformed to intervals at the normal level. The width of such intervals is increasing with the difference between the stress level at which a unit is tested and the normal level. The resulting inference method is predictive, so it explicitly considers the random failure time of a future unit tested at the normal level. We perform simulation studies to investigate the performance of our imprecise predictive method and to get insight into a suitable amount of imprecision for the linking between levels. We also explain how simulation studies can assist in choosing imprecision in order to provide robustness against specific biases or model misspecifications

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

Accelerated life testing provides an interesting challenge for quantification of the uncertainties involved, in particular due to the required linking of the units’ failure times, or failure time distributions, at different stress levels. This paper provides an initial exploration of the use of statistical methods based on imprecise probabilities for accelerated life testing. We apply nonparametric predictive inference at the normal stress level, in combination with an estimated parametric power-Weibull model linking observations at different stress levels. To provide robustness with regard to this assumed link between different stress levels, we introduce imprecision by considering an interval around the parameter estimate, leading to observations at stress levels other than the normal level to be transformed to intervals at the normal level. The width of such intervals is increasing with the difference between the stress level at which a unit is tested and the normal level. The resulting inference method is predictive, so it explicitly considers the random failure time of a future unit tested at the normal level. We perform simulation studies to investigate the performance of our imprecise predictive method and to get insight into a suitable amount of imprecision for the linking between levels. We also explain how simulation studies can assist in choosing imprecision in order to provide robustness against specific biases or model misspecifications

Imprecise Statistical Methods for Accelerated Life Testing

Accelerated Life Testing (ALT) is frequently used to obtain information on the lifespan of devices. Testing items under normal conditions can require a great deal of time and expense. To determine the reliability of devices in a shorter period of time, and with lower costs, ALT can often be used. In ALT, a unit is tested under levels of physical stress (e.g. temperature, voltage, or pressure) greater than the unit will experience under normal operating conditions. Using this method, units tend to fail more quickly, requiring statistical inference about the lifetime of the units under normal conditions via extrapolation based on an ALT model. This thesis presents a novel method for statistical inference based on ALT data. The method quantifies uncertainty using imprecise probabilities, in particular it uses Nonparametric Predictive Inference (NPI) at the normal stress level, combining data from tests at that level with data from higher stress levels which have been transformed to the normal stress level. This has been achieved by assuming an ALT model, with the relation between different stress levels modelled by a simple parametric link function. We derive an interval for the parameter of this link function, based on the application of classical hypothesis tests and the idea that, if data from a higher stress level are transformed to the normal stress level, then these transformed data and the original data from the normal stress level should not be distinguishable. In this thesis we consider two scenarios of the methods. First, we present this approach with the assumption of Weibull failure time distributions at each stress level using the likelihood ratio test to obtain the interval for the parameter of the link function. Secondly, we present this method without an assumed parametric distribution at each stress level, and using a nonparametric hypothesis test to obtain the interval. To illustrate the possible use of our new statistical method for ALT data, we present an application to support decisions on warranties. A warranty is a contractual commitment between consumer and producer, in which the latter provides post-sale services in case of product failure. We will consider pricing basic warranty contracts based on the information from ALT data and the use of our novel imprecise probabilistic statistical method

Fuzzy reliability prediction of rotating machinery product with accelerated testing data

For machinery product experienced several operating conditions, this paper proposes a framework of fuzzy reliability analysis of machinery accelerated testing. Due to the non-stationary of the vibration signals, a Gaussian mixture model (GMM) method is introduced to obtain the degradation index through calculating the overlap between current feature set and the historical baseline set. The features in four domains are extracted. Considered that the uncertainties exit in feature extraction and health assessment, a fuzzy regression model is used to describe the degradation path at each operating condition and compute fuzzy quasi time to failures (q-TTFs). Meanwhile, the relationship between q-TTFs and environmental variables are identified by a linear model, through which the fuzzy reliability analysis can be conducted with the most appropriate lifetime distribution. An industrial application is used to verify the effectiveness of the proposed framework and the results have confirmed a good consistency with the true values

Trends in the Statistical Assessment of Reliability

Changes in technology have had and will continue to have a strong effect on changes in the area of statistical assessment of reliability data. These changes include higher levels of integration in electronics, improvements in measurement technology and the deployment of sensors and smart chips into more products, dramatically improved computing power and storage technology, and the development of new, powerful statistical methods for graphics, inference, and experimental design and reliability test planning. This paper traces some of the history of the development of statistical methods for reliability assessment and makes some predictions about the future

Addressing failure rate uncertainties of marine energy converters

publication-status: Publishedtypes: ArticleThe interest in marine renewable energy is strong, but has not led to significant commercial-scale investment and deployment, yet. To attract investors and promote the development of a marine renewable industry a clear concept of project risk is paramount, in particular issues relating to device reliability are critical. In the public domain, reliability information is often scarce or inappropriate at this early stage of development, as little operational experience has been gained. Thus, reliability estimates are fraught with large uncertainties. This paper explores sources and magnitudes of failure rate uncertainty and demonstrates the effect on reliability estimates for a notional marine energy converter. If generic failure rate data forms the basis of a reliability assessment, reliability estimates are not robust and may significantly over- or underestimate system reliability. The Bayesian statistical framework provides a method to overcome this issue. Generic data can be updated with more specific information that could not be statistically incorporated otherwise. It is proposed that adopting such an approach at an early stage in an iterative process will lead to an improved rate of certainty

Breakdown voltage modelling for leatherite paper dielectrics using fuzzy logic technique & estimating the lifetime using step-stress test

OBJECTIVE The real insulation systems are often heterogeneous and some times nonlinear. Quality of insulation is accessed in terms of break down strengths. Partial discharge caused in insulation system by local defects and the resultant overstressing caused by them ultimately lead to breakdown. So the estimation has to be done properly to save insulation from failure. The use of modern computers in bdv analysis has lead to the estimation based on fuzzy logic modeling. The mamdani fuzzy logic using triangular and trapezoidal mf used for the modeling. The bdv got from the modeling section is used to get the weibull parameters using MLE. The shape parameters are used for the life estimation of the dielectric. DESCRIPTION Fuzzy logic modeling is widely used in those fields where the boundary between having a property and not having it is not sharp. The construction of this model can be viewed as a process in which a collection of objects called variables and parameters of the model are related by some other objects called the operators of the model. In the present case it is tried to estimate the bdv of dielectrics depending upon various input conditions. The most important source of partial discharge and breakdown in dielectrics is the voids. Voids are produced due to process control errors at the time of production of most of the solid dielectrics. This is a gas discharged event. The test dielectric is taken as leatherite paper and the estimation is based on data experimentally generated in the laboratory using a CIGRE-2 electrode. The choice of test procedure to know the breakdown voltage of a typical insulation material on insulation system is determined by the test objective. Constant voltage tests provide reliable comprehensive data for the distribution function of the breakdown time but is very time consuming. An accelerated test with increase in voltage stress in discrete steps is quite often used for an electrical insulation study and is widely accepted by the insulation designers. With this method the stress at which the insulation breaks down and time to failure is taken as 6 observed variable The effect of void dimensions on the output is studied and implemented in MATLAB environment. The various steps in modeling include study of the range variation, grouping, rule list generation and simulation. Present system is a MISO system having three inputs (thickness of dielectric, depth and diameter of void) and one output (bdv). The min max algorithm is used as t-norm and s-norm operator. Coa is used for difuzzification. Programming approach is adopted for estimation. The surface plot is plotted to study the variation. Weibull probability has gained wide acceptance in the statistical treatment of time to electrical breakdown of solid dielectrics. It seems to fit experimental data well. MLE is used for parameter estimation. Confidence interval is chosen to get lower and upper limits of the parameters within which the estimation lie for a surety. Throughout the experiment the step stress test is considered. The inverse power law is applied to life estimation. From the slope of the graph the slope is to be found out and used for estimating the life. RESULTS In the mamdani fuzzy logic modeling using the triangular and trapezoidal mf the Mae is found out to be 1.4% and 1.324% respectively. The weibull parameters and life estimation values have close resemblance with the experimentally generated value. CONCLUSION Fuzzy logic provides an easier and a better computation technique based on the fuzzyness of rules. By accurately choosing the parameters and deciding the rule bases the error can be significantly reduced. The weibull parameter calculation using MLE and lifetime also found to be in good agreement. Thus the results indicates that the modeling can be well implemented for such kind of estimation

Healthy And Unhealthy Statistics: Examining The Impact Of Erroneous Statistical Analyses In Health-Related Research

Sound statistical analyses are essential to the advancement of medicine. Although certainly not always the case, far too many publications are based on weak or inappropriate statistical methodology, leading to questionable results. Statistical reporting guidelines and standards for research are being introduced which should help curb this problem. Wide recognition of the need for statistical methodologies aligned with research questions and study designs, and the impact when this is not the case, would help prevent this problem. In this thesis, I illustrate the consequences of erroneous statistical analyses on data from an observational study on Multiple Sclerosis and I investigate the impact of inappropriate survival analyses through a simulation study