System Reliability Theory-Models and Statistical Methods.

Bayesian reliability analysis (BRA) technique has been actively used in reliability assessment for engineered systems. However, there are two key controversies surrounding the BRA: the reasonableness of the prior and the consistency among all data sets. These issues have been debated in Bayesian analysis for many years. As we observed, they have not been resolved satisfactorily. These controversies have seriously hindered the applications of BRA as a useful reliability analysis tool to support engineering design. In this paper, a Bayesian reliability analysis methodology with a prior and data validation and adjustment scheme (PDVAS) is developed to address these issues. As the part of the PDVAS development, a consistency measure is first defined that judges the level of consistency among all data sets including the prior. The consistency measure is then used to adjust either the prior or the data or both to the extent that the prior and the data are statistically consistent. This prior and data validation and adjustment scheme is developed for Binomial sampling with Beta prior, called Beta-Binomial Bayesian model. The properties of the scheme are presented and discussed that provides some insights of PDVAS. Various forms of the adjustment formulas are shown, and a selection framework of a specific formula, based on engineering design and analysis knowledge, is established. Several illustrative examples are presented, which show the reasonableness, effectiveness, and usefulness of PDVAS. General discussion of the scheme is offered to enhance the Bayesian reliability analysis in engineering design for reliability assessment.

Bayesian approaches have been demonstrated as effective methods for reliability analysis of complex systems with small-amount data, which integrate prior information and sample data using Bayes’ theorem. However, there is an assumption that precise prior probability distributions are available for unknown parameters, yet these prior distributions are sometimes unavailable in practical engineering. A possible way to avoiding this assumption is to generalize Bayesian reliability analysis approach by using imprecise probability theory. In this paper, we adopt a set of imprecise Dirichlet distributions as priors to quantify uncertainty of unknown parameters and extend traditional Bayesian reliability analysis approach by introducing an imprecise Dirichlet model (IDM). When the prior information is rare, the result of imprecise Bayesian analysis method is too rough to support engineering decision-making, so we proposed an optimization model to reduce the imprecision of the new method. Spindles are crucial for machine tools and reliability data related to spindles of new-developed machine tools are often rare. We can then use the imprecise Bayesian reliability analysis method to assess its reliability. In this paper, we mainly investigate the reliability assessment of a motorized spindle to illustrate the effectiveness of the proposed method.

This book presents the state-of-the-art in quality and reliability engineering from a product life cycle standpoint. Topics in reliability include reliability models, life data analysis and modeling, design for reliability and accelerated life testing, while topics in quality include design for quality, acceptance sampling and supplier selection, statistical process control, production tests such as screening and burn-in, warranty and maintenance. The book provides comprehensive insights into two closely related subjects, and includes a wealth of examples and problems to enhance reader comprehension and link theory and practice. All numerical examples can be easily solved using Microsoft Excel. The book is intended for senior undergraduate and post-graduate students in related engineering and management programs such as mechanical engineering, manufacturing engineering, industrial engineering and engineering management programs, as well as for researchers and engineers in the quality and reliability fields. Dr. Renyan Jiang is a Professor at the School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, China

This paper discusses educational tools, resources and experience in teaching physics-of-failure (PoF) modeling and data analysis methods used in accelerated life testing (ALT) and accelerated degradation testing (ADT). The concepts introduced in this paper include several probabilistic and highly technical approaches such as the PoF and mechanistic approaches to reliability prediction and assessments as well as advanced Bayesian analysis methods used in ALT and ADT to analyze life data obtained through various methods of constant and variable stress testing efforts. Other resources include codes and algorithms from the readily available computational tools R, MATLAB, and WinBUGS for solving advanced model and life estimation methods related to PoF, ALT and ADT analyses. This paper provides an overview of these resources and several example problems.

Advent of VLSI technology has paved the way for Programmable Logic Devices (PLD), which are widely used as the basic building blocks in high integrity electronic systems. PLDs are considered for their robust features such as high gate density, performance, speed etc. For PFBR Instrumentation and Control systems, PLDs are extensively used to implement digital designs such as VME bus interface logic, control logic and sequencing logic etc. Types of PLDs, such as Field Programmable Gate Arrays, Complex Programmable Logic Devices and Gate Array Logic devices are used in Core Temperature Monitoring System and Safety logics of shutdown systems. Since these devices are reliable as per the manufacturer's specification, they were used in R & D facilities like Fast Breeder Test Reactor and Augmented Boron Enrichment Plant as test beds. However, in order to use PLDs in commercial Nuclear Power Plant (in PFBR), it is vital to know about their performance in other critical applications. The availability of required data is limited, other than for space applications. So, it is proposed to conduct Quantitative Accelerated Life Tests (QALT) for the PLDs. QALT is designed to produce the data required for accelerated life data analysis. This analysis method uses life data obtained under accelerated conditions to extrapolate an estimated probability density function for the product under normal use conditions. Accelerated life tests are conducted on products to understand their failure modes and life characteristics. The products are subjected to enhanced stresses in order to force the products to fail early than they would normally, under use conditions. This process reduces test time. This paper discusses the methodology adapted to perform the Accelerated Life Test for the above mentioned PLDs.

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.

Qualitative system analysis as a means for sustainable governance of emerging technologies: the case of nanotechnology

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

Prior information and elicitation are the prerequisite in Bayesian reliability inference. Multiple sources for priors such as probability fitting based on historical data and expert judgment are often available when estimating the reliability of complex systems. This paper investigates the integration of multiple priors in Bayesian reliability analysis. Specifically, methods for multiple priors' integration based on Bayesian Melding are investigated. The performance of the studied methods with different prior information integration algorithms such as the arithmetic and geometric averaging is investigated. The impacts of the prior misspecification and the pooling parameter selection for prior integration algorithms are also studied. In numerical examples, simulation methods are applied for posterior reliability inference under the proposed prior integration methods and the performance of the two methods are compared.

Hardware systems are present in many fields of human activity. Markov models are sometimes used in hardware reliability, availability, and maintainability (RAM) modeling. They are especially useful in situations in which the system we want to analyze may be modeled with several states through which the system evolves, some of them corresponding to ON states, the rest to OFF states. We provide here RAM analyses of such systems within a Bayesian framework, addressing both short-term and long-term performance.

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.

In Malaysia, PILC cable has been used for more than 25 years. Based on the cable manufacturers' recommendation, the chronological lifetime of PILC is 40 years. However, the physical age of the cable may be lower due to various stresses experienced by the cables. Since there are 41,911 km of PILC cables in the system (more than 50% population), there must be a strategy to prioritize the replacement of PILC cables. Therefore the aim of this study is to determine the remaining life of the existing PILC in Malaysia. Based on the literature review, a well-known method to estimate remaining life is to use Accelerated Life Testing (ALT). ALT is a method used in this project to accelerate the aging of the samples to fail faster than normal aging. The data collected from the ALT are analyzed using Weibull Distribution and Inverse Power Law formula to predict remaining life of the PILC cables.

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.

This paper presents a novel methodology to evaluate robotic system reliability and Remaining Useful Life (RUL) integrating FMECA (Failure Modes, Effects and Criticality Analysis), life data analysis and data-driven & model-based methods. Starting from the FMECA analysis, the methodology proposes to identify the main critical components of new parts or systems, using life data analysis. A database collects and shares data directly from the field on similar systems and applications. Data are stored and managed via a web-based interface, the user may obtain them in real time as needed, when a modification in the robot or production cells occurs. Information are captured through a set of appropriate sensors, selected and located studying historical life data. From this dataset, RUL of components may be estimated using data-driven methods and model-based approaches. Then, the RUL results are shared with ERP systems to optimize production resources and maintenance activities and with FMECA again, to improve new projects in a closed loop. A preliminary application of the methodology is proposed on an anthropomorphic robot integrated in a production cell. This research is a part of PROGRAMs: PROGnostics based Reliability Analysis for Maintenance Scheduling, H2020-FOF-09-2017-767287.

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.