Frank M. Guess

Bayesian Inference for Masked System Lifetime Data

Estimating component and system reliabilities frequently requires using data from the system level. Because of cost and time constraints, however, the exact cause of system failure may be unknown. Instead, it may only be ascertained that the cause of system failure is due to a component in a subset of components. This paper develops methods for analysing such masked data from a Bayesian perspective. This work was motivated by a data set on a system unit of a particular type of IBM PS/2 computer. This data set is discussed and our methods are applied to it

Estimating system and component reliabilities under partial information on cause of failure

Estimating component reliabilities along with system reliability frequently requires using lifetimes from the system level. Due to cost and time constraints, however, the exact cause of system failure may be unknown. Instead it may only be ascertained that the cause of system failure is due to one component in a subset of components, e.g. the subset forms a subsystem. Confronted with such data, this article discusses how to fully exploit all of the available information using a maximum likelihood approach. We extend and clarify the useful work of Miyakawa (1984). A small Monte Carlo simulation study indicates the helpfulness of this approach.

Exact maximum likelihood estimation using masked system data

This work estimates component reliability from masked series-system life data, viz, data where the exact component causing system failure might be unknown. The authors extend the results of Usher and Hodgson (1988) by deriving exact maximum likelihood estimators (MLE) for the general case of a series system of three exponential components with independent masking. Their previous work shows that closed-form MLE are intractable, and they propose an iterative method for the solution of a system of three nonlinear likelihood equations. >

Bayes estimation of component-reliability from masked system-life data

This paper estimates component reliability from masked series-system life data, viz, data where the exact component causing system failure might be unknown. It focuses on a Bayes approach which considers prior information on the component reliabilities. In most practical settings, prior engineering knowledge on component reliabilities is extensive. Engineers routinely use prior knowledge and judgment in a variety of ways. The Bayes methodology proposed here provides a formal, realistic means of incorporating such subjective knowledge into the estimation process. In the event that little prior knowledge is available, conservative or even noninformative priors, can be selected. The model is illustrated for a 2-component series system of exponential components. In particular it uses discrete-step priors because of their ease of development and interpretation. By taking advantage of the prior information, the Bayes point-estimates consistently perform well, i.e., are close to the MLE. While the approach is computationally intensive, the calculations can be easily computerized.

System life data analysis with dependent partial knowledge on the exact cause of system failure

Abstract Because of cost and time factors the exact cause of system failure may be known only partially. For example, the cause is narrowed down to a component in a subsystem or a smaller set of components. This is called “masking” of the exact failure mode. Our paper focuses on reliability estimation when the masking probability is dependent on the particular cause of failure.

Estimators for Reliability Measures in Geometric Distribution Model Using Dependent Masked System Life Test Data

Masked system life test data arises when the exact component which causes the system failure is unknown. Instead, it is assumed that there are two observable quantities for each system on the life test. These quantities are the system life time, and the set of components that contains the component leading to the system failure. The component leading to the system failure may be either completely unknown (general masking), isolated to a subset of system components (partial masking), or exactly known (no masking). In the dependent masked system life test data, it is assumed that the probability of masking may depend on the true cause of system failure. Masking is usually due to limited resources for diagnosing the cause of system failures, as well as the modular nature of the system. In this paper, we present point, and interval maximum likelihood, and Bayes estimators for the reliability measures of the individual components in a multi-component system in the presence of dependent masked system life test data. The life time distributions of the system components are assumed to be geometric with different parameters. Simulation study will be given in order to 1) compare the two procedures used to derive the estimators for the reliability measures of system components, 2) study the influence of the masking level on the accuracy of the estimators obtained, and 3) study the influence of the masking probability ratio on the accuracy of the estimators obtained

Effect of Not Having Homogeneous Test Units in Accelerated Life Tests

In accelerated life tests (ALTs), test units are run at higher stress levels in order to experience more failures. A Weibull regression model can, in this case, be used to infer failure behavior at the normal stress level. In practice, statistical analyses usually do not take batch differences into account even when they are present. To correctly include batch differences in the analysis, one needs to use a regression model with random effects. In this paper, we use such a model to show that ignoring batch differences in modeling can result in overly precise estimates of quantiles and probabilities of failure at the normal stress level, as well as overly precise predictions of the failure time for a new unit at the normal stress level.

Burn-in to improve which measure of reliability?

Abstract Burn-in plans or screens are often used to improve the “reliability” of systems, subassemblies, and components. There are, however, different ways of measuring reliability. Sometimes contradictory results are obtained when different measures of reliability are used. This problem stems from the fact that each one of these measures is really assessing reliability from a different point of view. These differences are crucial for designing in reliability and for devising burn-in plans. It is known, for example, that a burn-in plan that optimizes (or improves) one reliability measure does not necessarily yield an optimal (or improvement) for another measure. After introducing and discussing several reliability measures, examples are presented to illustrate the behavior of different reliability measures. We stress the importance of understanding what the end user of a product needs in terms of “reliability” before the design stage, through all the developmental stages, and for burn-in plans.

Understanding the Characteristics of Non-industrial Private Forest Landowners Who Harvest Trees

Abstract Achieving regional and national goals of renewable energy production will depend on sufficient supply of biomass from private forests, the majority of which are controlled by non-industrial private forest landowners (NIPF). Considering the diversity in management objectives and changing demographic dynamics in this ownership group, it is important to understand the characteristics of landowners that may supply woody biomass. This study developed linear discriminant analysis (LDA) and classification tree (CT) models to examine the characteristics and motivation of such NIPF landowners. Thirteen combinations of CT variable selection and split-point selection models were used in conjunction with LDA. The “importance of income” from a woody biomass harvest was the most important factor influencing NIPF landowners’ decisions in supplying woody biomass. Another significant interrelated variable was “farmer or non-farmer” forestland ownership, which was also related with “years of residency”, “availability of a multi-management plan,” and “ownership of multi-tracts of land.” CT models provided higher-level explanatory information when compared with LDA models. Study findings provide useful insight for land managers, wood procurement managers, and policy-makers in identifying the landowner groups with interest in biomass supply, and in understanding the factors influencing their decisions.

Improved estimation of the lower percentiles of material properties

Estimating lower percentiles in reliability for medium-density fiberboard is an important issue for manufacturers for better assessing and improving manufacturing processes, plus for guiding better product warranties while seeking lower costs. Since data may be sparse or costly in the lower tails, estimation of these percentiles may be difficult. Bootstrapping provides a helpful solution for interval estimation of lower percentiles when other approaches fail or are not as realistic. This computer intensive resampling technique estimates more accurately the true standard error of any population parameter, not just percentiles. Bootstrapping can be used for parametric models or indeed nonparametric settings when parametric models are not appropriate. This paper shows the usefulness of bootstrap methods to better assess the key quality metric of internal bond (IB or tensile strength) of medium-density fiberboard (MDF) in the critical lower percentiles when data are limited.