A bayesian approach to environmental stress screening

Journal of Applied Probability, 2014

Environmental stress screening (ESS) of manufactured items is used to reduce the occurrence of future failures that are caused by latent defects by eliminating the items with these defects. Some practical descriptions of the relevant ESS procedures can be found in the literature; however, the appropriate stochastic modeling and the corresponding thorough analysis have not been reported. In this paper we develop a stochastic model for the ESS, analyze the effect of this operation on the population characteristics of the screened items, and also consider the relevant optimization issues.

1994

Glossary of ESS Terms Axes of Excitation-The number of axes of vibration applied during vibration screening. Classical ESS-ESS where screening levels are not determined and continuously modified through quantitative means such as those found in Mil-Hdbk-344. Defect: Latent Defect-An inherent or induced weakness, not detectable by ordinary means, which will either be precipitated to early failure under environmental stress screening conditions or eventually fail in the intended use environment. Patent Defect-An inherent or induced weakness which can be detected by inspection, functional test, or other defined means. Defect Density-The average number of defects per item. Detection Efficiency-A measure of the capability of detecting a patent defect. Environmental Stress Screening (ESS)-A process or series of processes in which environmental stimuli, such as rapid thermal cycling and random vibration, are applied to electronic items in order to precipitate latent defects to early failure. Failure-Free Period-A contiguous period of time during which an item is to operate without the occurrence of a failure while under environmental stress. Fallout-Failures observed during, or immediately after, and attributed to stress screens. Fallout Analysis-The study of fallout failures for the purpose of modifying screens. Fault Replication Test Method-A method used to generate a satisfactory initial vibration screening level by gradually increasing the stress level until previously known faults are precipitated. Final Acceptance Test-The environmental test used to validate that customer mean time between failure or failure-free requirements have been achieved. Final acceptance test is usually conducted after ESS. Fixture-The apparatus used to mount the electronic equipment on the vibrator/shaker machine. Flaw Precipitation Threshold Method-A method used to generate a satisfactory initial vibration screening level by performing a vibration survey and then performing detailed computations on the global responses within the test specimen. This method is also referred to as the "Tailored Spectral Response" method. Functional Test Program-Procedures associated with testing the functionality of electronic equipment.

Microelectronics and Reliability, 1995

Reviews in Chemical Engineering, 2014

Chemical process industries (CPI) are usually home to a large number of complex systems and components required for various operations involving hazardous chemicals. The intense operating conditions and complex interactions between the systems make the chemical plants vulnerable to accidents. Quotidian incidents and mishaps can lead to catastrophic incidents. Thus, the area of risk assessment and reliability analysis in CPI has been of much interest to the research community. The complexity of processes in CPI demands a risk assessment tool that can adapt itself to the dynamic environment and can efficiently model the functional and sequential dependencies between the components and the effects of external factors, component degradation, and variation in operating conditions. The risk assessment tool must have applicability during the operational lifetime of the system to serve as a platform for decision making and risk management. The unavailability of empirical data for some variables is another pertinent issue in risk analysis and reliability assessment in CPI. Analysts often have to work with subjective information such as expert opinion. Bayesian statistical methods based on the Bayes theorem are considered by many to be an effective tool to address the above-mentioned issues. These methods are based on the subjective interpretation of probability that helps to model the epistemic uncertainties and easily propagates them through complex system models. The methods provide a formal systematic way to incorporate subjective information into calculations. The inherent updating property accoutres these methods with the ability to deal with real-time changes. The opponents, however, point out that the methods produce high overconfidence and randomness in computed answers. In the last two decades, an increased interest can be seen in the research community toward the use of Bayesian methods in risk assessment. This paper presents a comprehensive literature review of the application of Bayesian methods through Bayesian parameter estimation techniques and Bayesian updating procedures in process industries. Both these techniques have been extensively used in various aspects of risk analysis, which are very pertinent in CPI. The purpose of the study is to produce an effective reference guide for scholars interested in applying Bayesian techniques to risk and reliability assessment in CPI.

A model is presented for applying Bayesian statistical techniques to the problem of determining, from the usual limited number of exposure measurements, whether the exposure profile for a similar exposure group can be considered a Category 0, 1, 2, 3, or 4 exposure. The categories were adapted from the AIHA exposure category scheme and refer to (0) negligible or trivial exposure (i.e., the true X 0.95 ≤1%OEL), (1) highly controlled (i.e., X 0.95 ≤10%OEL), (2) well controlled (i.e., X 0.95 ≤50%OEL), (3) controlled (i.e., X 0.95 ≤100%OEL), or (4) poorly controlled (i.e., X 0.95 >100%OEL) exposures. Unlike conventional statistical methods applied to exposure data, Bayesian statistical techniques can be adapted to explicitly take into account professional judgment or other sources of information. The analysis output consists of a distribution (i.e., set) of decision probabilities: e.g., 1%, 80%, 12%, 5%, and 2% probability that the exposure profile is a Category 0, 1, 2, 3, or 4 exposure. By inspection of these decision probabilities, rather than the often difficult to interpret point estimates (e.g., the sample 95th percentile exposure) and confidence intervals, a risk manager can be better positioned to arrive at an effective (i.e., correct) and efficient decision. Bayesian decision methods are based on the concepts of prior, likelihood, and posterior distributions of decision probabilities. The prior decision distribution represents what an industrial hygienist knows about this type of operation, using professional judgment ; company, industry, or trade organization experience; historical or surrogate exposure data; or exposure modeling predictions. The likelihood decision distribution represents the decision probabilities based on an analysis of only the current data. The posterior decision distribution is derived by mathematically combining the functions underlying the prior and likelihood decision distributions, and represents the final decision probabilities. Advantages of Bayesian decision analysis include: (a) decision probabilities are easier to understand by risk managers and employees; (b) prior data, professional judgment, or modeling information can be objectively incorporated into the decision-making process; (c) decisions can be made with greater certainty; (d) the decision analysis can be constrained to a more realistic " parameter space " (i.e., the range of plausible values for the true geometric mean and geometric standard deviation); and (e) fewer measurements are necessary whenever the prior distribution is well defined and the process is fairly stable. Furthermore, Bayesian decision analysis provides an obvious feedback mechanism that can be used by an industrial hygienist to improve professional judgment. For example, if the likelihood decision distribution is inconsistent with the prior decision distribution then it is likely that either a significant process change has occurred or the industrial hygienist's initial judgment was incorrect. In either case, the industrial hygienist should readjust his judgment regarding this operation.

Reliability and Maintainability …, 1995

IEEE Transactions on Reliability, 1996

& Conclusions  This article develops a Bayes model for step-stress accelerated life testing. The failure times at each stress level are exponentially distributed, but the specification of strict adherence to a time transformation function is not required. Rather, prior information is used to define indirectly a multivariate prior distribution for the failure rates at the various stress levels. Our prior distribution preserves the natural ordering of the failure rates in both the prior and posterior estimates. Methods are developed for Bayes point estimates as well as for making probability statements for usestress life parameters. The approach is illustrated with an example.

Quality and Reliability Engineering International, 2011

We develop a model for the economic design of a Bayesian control chart for monitoring a process mean. The process may randomly suffer failures that result in a non-operating state, and thus call for an immediate corrective maintenance action, as well as assignable causes that shift the process mean to an undesirable level. Quality shifts, apart from poorer quality outcome and higher operational cost, also result in higher failure rate. Consequently, their removal, besides improving the outcome quality and reducing the quality-related cost, is also a preventive maintenance action since it reduces the probability of a failure. The proposed Bayesian model allows the determination of the design parameters that minimize the total expected quality and maintenance cost per time unit. The effectiveness of the proposed model is evaluated through the comparison of its expected cost against the optimum expected cost of the simpler variable-parameter Shewhart chart.

International Journal of Statistics and Probability, 2017

In this article, we present a Bayesian analysis with convex tent priors for step-stress accelerated life testing (SSALT) using a proportional hazard (PH) model. As flexible as the cumulative exposure (CE) model in fitting step-stress data and its attractive mathematical properties, the PH model makes Bayesian inference much more accessible than the CE model. Two sampling methods through Markov chain Monte Carlo algorithms are employed for posterior inference of parameters. The performance of the methodology is investigated using both simulated and real data sets.

The main objective of this paper is to develop the Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under time censoring scheme of the Generalized Logistic (GL) Failure times. The power law function is used to represent the relationship between the stress and the scale parameters of a test unit. Bayes estimates are obtained using Markov Chain Monte Carlo (MCMC), simulation algorithm based on Gibbs sampling. Then, Monte Carlo error (MC error), credible intervals, and predicted values of the two scale parameters and the reliability function under design stress are obtained. Numerical illustration is addressed for illustrating the theoretical results. Win-Bugs software package is used for implementing Markov Chain Monte Carlo (MCMC) simulation and Gibbs sampling.