Fast Semiconductor Reliability Assessments Using SPRT

A method to solve multi-target classification problems with unknown clutter parameters is proposed in this paper. The unknown parameter is estimated and synthesized at each observation, and probability of each hypothesis is updated. Subsequently, the optimal waveform for the next illumination is designed based on NP criteria, and the final decision is made based on the sequential probability ratio testing. Simulated results are presented based on our method and show that the optimal waveform-based sequential testing can be decided through reduction of the average illumination number. Furthermore, results indicate a significant improvement over the non-optimal waveforms.

Lindley's concept of the information in an experiment is used to study alternate-hypothesis statistical tests. A test is considered to be a combination of a sampling rule and a decision rule which is based on the samples taken. Two information functions are formed: the information about the unknown parameter contained in the samples taken and the information contained in the decision to which these samples lead. The former quantity is at least as great as the latter, with equality if, and only if, the test is an SPRT (sequential probability ratio test) neglecting the excess over the boundary.

A novel fault detection system taking into account uncertainties in the reconstructed signals

Statistical data analysis includes several phases. First, there is the phase of data collection. Second, there is the phase of analysis and inference. The two phases are interconnected. There are two types of data analysis. One type is called parametric and the other type is nonparametric. In the present paper, we discuss parametric inference. In parametric inference, we model the results of a given experiment as realization of random variables having a particular distribution, which is specified by its parameters. A random sample is a sequence of independent and identically distributed (i.i.d.) random variables. Statistics are functions of the data in the sample, which do not involve unknown parameters. A statistical inference is based on statistics of a given sample. We discuss two kinds of parametric inference. Estimating the values of parameters, or testing hypotheses concerning the parameters in either kind of inference, we are concerned with the accuracy and precision of the results. In estimation of parameters, the results are precise if, with high probability, they belong to a specified neighborhoods of the parameters. In testing hypotheses, one has to decide which one of two or several hypotheses should be accepted. Hypotheses which are not accepted are rejected. We distinguish between two types of errors. Type I error is the one committed by rejecting a correct hypothesis. Type II is that of accepting a wrong hypothesis. It is desired that both types of errors will occur simultaneously with small probabilities. Both precision in estimation or small error probabilities in testing depend on the statistics used (estimators or test functions) and on the sample size. In this paper, we present sampling procedures that attain the desired objectives. In Sec. 2, we discuss estimation of the parameters of a binomial distribution. In Sec. 3, more general results about estimation of expected values are presented. In Sec. 4, we discuss the Wald Sequential Probability Ratio Test (SPRT), which has optimal properties for testing two simple hypotheses.

The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be estimated by least-squares estimation. Finally, the satellite clock can be estimated and predicted with the estimated noise parameters. In the new method, no prior information about the noise parameters is needed. Even with some extreme prior noise parameters, the new method can also work very well and has good convergence properties. For comparison, we conduct two experiments using the new method and the adaptively robust Kalman filter with classified adaptive factors based on opening windows separately, both results are consistent with each other very well, which verifies the correctness and effectiveness of this new method.

A new research project is developing a simple reliability prediction methodology for random failure rate and the time to intrinsic wearout. The models to be incorporated account for the latest advancement of the semiconductor technology and take into consideration the latest research in reliability assessment. Using common physics of failure (PoF) models for both intrinsic wearout and random failures, the project will seek data and analysis from semiconductor manufacturers, leaving most of the proprietary details to them, and only use the models to scale results between use conditions. This paper describes a methodology that is currently in development and not yet produced. Development of the models is based on aerospace industry collaboration and data from semiconductor manufacturers and foundries.

In order to enable higher electrical performance for the application of networking, larger FCBGA package was been demanded to meet the electrical target. According to that, the package size usually has been kept to be large around 60mm x 60mm and die size has been larger than 20mm x 20mm in advance networking application. Normally, larger FCBGA package would result in increased semiconductor assembly processes and reliability challenges, such as die corner delam, solder mask crack, Cu post side wall delam, TIM coverage loss and warpage issue. Molded type FCBGA package would be a solution to reduce processes and reliability risk. Several Molded type FCBGA packages were proposed in this paper to check the level of stress and warpage performance compared to traditional EHS-FCBGA package. Regarding solder mask crack, ABF substrate structure will be the suggestion to avoid solder mask crack issue. According lots fundamental work, molded type FCBGA package combined ABF substrate could reduce package stress effectively and perform similar warpage with traditional EHS-FCBGA to be a solution to solve current larger FCBGA package processes and reliability issue.

Since several years ago, many semiconductors companies have invested a lot of efforts and resources in the wire bonding conversion from gold (Au) wire to copper (Cu) wire in order to achieve the most competitive cost. Meanwhile, the fast growing mobile application and industry continues to leap forwards with miniaturization especially in the most popular QFN (Quad Flat No-lead) packages. From multiple analysis, it looks like breakthrough competitive edge will depend on the success of running wire bonding process of both wire types (Au & Cu) with the ultimate ultra-fine pitch (UUFP) process on the flimsy QFN leadframes. This new process can aim for targeted pitch size of 20um which is the smallest possible in the industry, and most likely it will become the ultimate pitch size for now and future. There are many challenges in the development of such process with major considerations and evaluations focusing on various designs, hardware, machine capability, process constraints, process control and amplification of respective Au and Cu wire process issues. The UUFP process is firstly started with design considerations on both direct and indirect material. From the discussions with major bonding wire suppliers, current feasible wire size of Au wire is 0.4 mils and Cu wire size is 0.5 mils. With both wires selected, next design consideration is the capillary design. The capillary tip needs to be the smallest possible together with the tightest tolerance of every major dimension. These requirements resulted in extremely tedious fabrication process which requires new molding tool and process enhancement. Furthermore, such small capillary can also encounter robustness issue due to the thin capillary wall and dimension tolerances. Upon receiving the wire and capillary, the subsequent challenge is the machine capability. There are two important considerations, resolution of process parameters (ultrasonic power and force) and bonding placement accuracy. In the previous development of 30/35 um pitch, whereby it was found that bond force requirement already hitting only several grams. It is expecting that the UUFP process will require even more stringent process window. It is expected few 0.1 gram force may result in significant change in the wire bonding responses. Despite that, the conventional process issues will get worse, which include resonance effect of QFN wire bonding, Au wire challenges (IMC growth, reliability risk) and Cu wire challenges (lifted ball, crater, short-tail). Therefore, the process window development can be extremely difficult. In order to obtain better success rate, comprehensive six sigma method is highly recommended. Upon completion of process window development, a series of robustness tests should be performed. There are some unique robustness tests which can disclose any potential issue or risk. Upon completion of bonding success, the bonded units will be loaded into reliability test for standard tests and extended tests. Sometimes, the entire development process may need to be repeated from the beginning design phase if there is any stubborn quality issue. With the utilization of comprehensive methodology, the new UUFP process is applicable to full production mode in near future. This process is believed to be the ultimate process for wire bonding pitch, for both Au & Cu wire types.

Reliability of reactor components and systems subject to fatigue and creep

Reliability analysis and risk assessment of a landfill slope failure in spatially variable municipal solid waste

The performance of manufacturing systems or equipment is, to a great extent, dependent upon the condition of their components. Closely monitoring the condition of the critical components and carrying out timely system diagnosis whenever a fault symptom is detected would help to reduce system downtime and improve overall productivity. Fault tree analysis (FTA) is a powerful tool for reliability studies and risk assessment. However, most research on FTA focuses on the generation of minimum cut sets and how to calculate the probability of main events. As a result, the issue concerning the ordering of basic events in a fault tree has been largely neglected. In this paper, a novel approach based on rough set theory and a pairwise comparison table for fault diagnosis is proposed. The approach attempts to learn from the pattern of decision-making by domain experts from past experience and uses the knowledge acquired, which is in the form of a minimum decision rule set, to determine the ordering of basic events in a fault tree. The details of the approach, together with the basic concepts of rough set theory, are presented. A case study is used to illustrate the application of the proposed approach. Results show that a reasonable ordering of basic events in a fault tree can be generated easily. With the ordering of basic events determined, a maintenance engineer in a manufacturing plant can then carry out fault diagnosis in an efficient and orderly manner.

In remanufacturing practices, understanding and communicating the failure risk and reliability of a critical part, component or subsystem plays a crucial role as it has a significant impact on the lifecycle management of the product and thus determines the success of the remanufacturing process. In this respect, statistical time-to-failure analysis provides a very powerful and versatile analytical tool for reliability analysis and risk assessment. Among various statistical tools available, Weibull model which uses time series data on records of failure incidents of a product for the fitting of a parametric distribution, is a powerful approach to characterizing the time-to-failure probability function of the product. It is able to provide valuable information for optimized lifecycle management and remanufacturing process. This paper demonstrates successful applications of Weibull model for time-to-failure analysis using case studies in remanufacturing practices and proposes a statistical approach to assess the reliability of critical parts and components for remanufacturing in the product’s lifecycle management. It is envisaged that the research results are able to benefit remanufacturing practices in many ways such as reducing warranty loss by minimizing probability of failure of remanufactured critical parts and components.

Abstract. Non-parametric Bayesian networks (NPBNs) are graphical tools for statistical inference widely used for reliability analysis and risk assessment and present several advantages, such as the embedded uncertainty quantification and limited computational time for the inference process. However, their implementation in hydrological studies is still scarce. Hence, to increase our understanding of their applicability and extend their use in hydrology, we explore the potential of NPBNs to reproduce catchment-scale hydrological dynamics. Long-term data from 240 river catchments with contrasting climates across the United States from the Catchment Attributes and Meteorology for Large-sample Studies (CAMELS) data set will be used as actual means to test the utility of NPBNs as descriptive models and to evaluate them as predictive models for maximum daily river discharge in any given month. We analyse the performance of three networks, one unsaturated (hereafter UN-1), one saturated (hereafter SN-1), both defined only by hydro-meteorological variables and their bivariate correlations, and one saturated network (hereafter SN-C), consisting of the SN-1 network and including physical catchments' attributes. The results indicate that the UN-1 network is suitable for catchments with a positive dependence between precipitation and discharge, while the SN-1 network can also reproduce discharge in catchments with negative dependence. The latter can reproduce statistical characteristics of discharge (tested via the Kolmogorov–Smirnov statistic) and have a Nash–Sutcliffe efficiency (NSE) ≥0.5 in ∼40 % of the catchments analysed, receiving precipitation mainly in winter and located in energy-limited regions at low to moderate elevation. Further, the SN-C network, based on similarity of the catchments, can reproduce discharge statistics in ∼10 % of the catchments analysed. We show that once a NPBN is defined, it is straightforward to infer discharge and to extend the network itself with additional variables, i.e. going from the SN-1 network to the SN-C network. However, the results also suggest considerable challenges in defining a suitable NPBN, particularly for predictions in ungauged basins. These are mainly due to the discrepancies in the timescale of the different physical processes generating discharge, the presence of a “memory” in the system, and the Gaussian-copula assumption used for modelling multivariate dependence.

In general, distribution theory plays a crucial role in modeling various real-life phenomena, making it a fundamental tool in statistical analysis and decision-making. Over the years, extensive research has been conducted on different statistical distributions and estimation techniques. While the literature abounds with information regarding well-known distributions, there is always room for exploring new variants that can better capture the characteristics of complex phenomena. In this paper, we contribute to the field of distribution theory by introducing novel probability distribution called the Weibull-Weibull distribution. The Weibull-Weibull distribution is derived by compounding two Weibull distributions, and it offers a flexible framework for modeling phenomena that exhibits a complex interplay of factors. By combining the strength of the Weibull distribution with itself, we are able to capture a wider range of shapes and behaviour, providing more accurate representations of real-world occurrences. To facilitate the practical application of the Weibull-Weibull distribution, we employ the maximum likelihood estimation (MLE) approach to estimate its shape and scale parameters. The MLE method is a widely used statistical technique that allows us to determine the most likely values of the parameters based on observed data. By applying this estimation method to the Weibull-Weibull distribution, we enable researchers and practitioners to effectively utilize this new distribution in their analyses and modeling efforts. Furthermore, we delved into a comprehensive study of statistical theory and properties of the Weibull-Weibull distribution. We investigate its moments, cumulative distribution function, probability density function, and other key measures. Through rigorous analysis, we establish the theoretical foundations of the Weibull-Weibull distribution and provide insights into its behaviour and characteristics. This comprehensive examination equips researchers with a solid understanding of the distribution, enabling them make informed decisions and interpretations when working with real-life data. In conclusion, our research introduces the Weibull-Weibull distribution as a valuable addition to the existing repertoire of statistical distributions. By leveraging the power of compounding two Weibull distributions, we provide a flexible and robust framework of modeling complex phenomena. With the use of maximum likelihood estimation and the given Chernoff bound, practitioners are able to estimate the distribution's parameters as well as analyze its tails accurately. Our extensive statistical analysis further enhances the understanding of the Weibull-Weibull distribution, facilitating its practical application in a wide range of fields, including reliability analysis, survival analysis, and risk assessment.

Modeling asymmetrically dependent multivariate ocean data using truncated copulas