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Front Matter |
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Some Recent Studies in Statistical Process Control |
Peihua Qiu |
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Abstract
Statistical process control (SPC) charts are widely used in manufacturing industries for quality control and management. They are used in more and more other applications, such as internet traffic monitoring, disease surveillance, and environmental protection. Traditional SPC charts designed for monitoring production lines in manufacturing industries are based on the assumptions that observed data are independent and identically distributed with a parametric in-control distribution. These assumptions, however, are rarely valid in practice. Therefore, recent SPC research focuses mainly on development of new control charts that are appropriate to use without these assumptions. In this article, we briefly introduce some recent studies on nonparametric SPC, control charts for monitoring dynamic processes, and spatio-temporal process monitoring. Control charts developed in these directions have found broad applications in practice.
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Statistical Quality Control and Reliability Analysis Using the Birnbaum-Saunders Distribution with I |
Víctor Leiva,Carolina Marchant,Fabrizio Ruggeri,Helton Saulo |
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Abstract
Quality improvement has been an important aspect considered by companies since the last century. However, today it is even more relevant in business and industry, particularly for production and service companies. Statistical quality control is the quantitative tool for quality improvement. The Gaussian distribution was the main ingredient of this quantitative tool, but nowadays new distributions are being considered, some of them taking into account asymmetry. The Birnbaum-Saunders model is one of these distributions and has recently received considerable attention because of its interesting properties and its relationship with the Gaussian distribution. Since its origins and applications in material science, the Birnbaum-Saunders distribution has found widespread uses in several areas, including quality control, with now well-developed methods that allow in-depth analyses. In this work, statistical quality control and reliability tools based on the Birnbaum-Saunders distribution are introduced. Implementation of those tools is presented using the . software. For the internal quality of companies, control charts for attributes and variables, as well as their multivariate versions
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Statistical System Monitoring (SSM) for Enterprise-Level Quality Control |
Siim Koppel,Shing I Chang |
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Abstract
The rapid development and adoption of sensors and data storage solutions such as IOT (Internet of Things) has enabled the collection of a large amount of data in production facilities. The data may come from different sources such as process parameters and quality characteristics. However, traditional statistical process control (SPC) tools were not built to take the full advantages of the data provided. Traditional SPC tools such as control charts are often applied to critical quality characteristics (QCs) on a product rather than incorporating process parameters associated with the critical QCs. This chapter proposes a method that is capable of monitoring all process and quality data simultaneously. The proposed method adopts precontrol and group control chart ideas to pinpoint change location and timeframe in a production system. After the change location and timeframe have been identified, more elaborate models or data analytics methods can be used to identify potential assignable causes. Simulation studies are conducted to establish the properties of the proposed method. Guidelines are provided to help users how to implement the proposed method in any production facility inclu
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Enhanced Cumulative Sum Charts Based on Ranked Set Sampling |
Mu’azu Ramat Abujiya,Muhammad Hisyam Lee |
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Abstract
The cumulative sum (CUSUM) control charts are widely used for the monitoring of normal processes for changes in the location and dispersion parameters. This study presents several CUSUM charts designed structures based on the ranked set sampling (RSS) data for overall efficient detection of changes in the process mean and variance. The run-length properties of these charts are examined and compared to the classical CUSUM location and dispersion charts. Results show that the application of RSS technique has significantly improved upon the standard CUSUM chart. Using real RSS data set, we present a practical example of the implementation of the CUSUM schemes.
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A Survey of Control Charts for Simple Linear Profile Processes with Autocorrelation |
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Sequential Monitoring of Circular Processes Related to the von Mises Distribution |
Cornelis J. Potgieter |
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The sequential monitoring of circular processes related to the von Mises distribution are considered. More specifically, methods for detecting changes in location and/or scale are considered when a process has in-control and out-of-control behavior following a von Mises distribution. Results on existing cumulative sum (cusum) charts are reviewed, and new sequential changepoint methods are developed. These are compared using Monte Carlo simulations. Finally, the sequential monitoring of a process with in-control distribution that is circular uniform is considered. An existing nonparametric cusum is reviewed and is compared to a new sequential changepoint method designed for a von Mises alternative.
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Abstract
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Time Truncated Life Tests Using the Generalized Multiple Dependent State Sampling Plans for Various |
Muhammad Aslam,Gadde Srinivasa Rao,Mohammed Albassam |
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Abstract
This chapter presents the designing of the generalized multiple dependent state sampling (GMDSS) plans for the various statistical distributions. We will present the design of GMDSS sampling when the failure time follows the gamma distribution, Burr type XII distribution and the Birnbaum-Saunders (BS) distribution. The necessary measures including the operating characteristics (OC) function are derived. The plan parameters of the proposed test plans are determined through the non-linear optimization solution. The proposed sampling plan is studied for a minimal sample size subject to specified requirements of the consumer and producer’ risks. The efficiency of the proposed plans in terms of sample sizes are discussed over the existing sampling plans using the same level of all parameters. The advantages of the proposed plans are discussed through simulated data and real data from the industry.
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Decision Theoretic Sampling Plan for One-Parameter Exponential Distribution Under Type-I and Type-I |
Deepak Prajapati,Sharmistha Mitra,Debasis Kundu |
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Abstract
In this paper, we design a decision theoretic sampling plan (DSP) based on Type-I and Type-I hybrid censored lifetime data from a one-parameter exponential distribution. The Bayes estimator of the mean lifetime is used to define a decision function. A suitable loss function is considered to derive the Bayes risk of this DSP. A finite algorithm is provided to obtain the optimum DSP and the corresponding Bayes risk. It has been observed numerically that the optimum DSP is better than the sampling plan proposed by Lam (Ann Stat 22:696–711, 1994) and Lin et al. (Commun Stat Simul Comput 37:1101–1116, 2008; Commun Stat Simul Comput 39:1499–1505, 2010) and it is as good as the Bayesian sampling plan (BSP) of Lin et al. (Ann Inst Stat Math 54:100–113, 2002) and Liang and Yang (J Stat Comput Simul 83: 922–940, 2013). It is observed that the Bayes risk of the optimum DSP is approximately equal to the Bayes risk of the BSP. In case of higher degree polynomials and for a non-polynomial loss function the DSP can be obtained without any additional effort as compared to BSP.
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Economical Sampling Plans with Warranty |
Jyun-You Chiang,Hon Keung Tony Ng,Tzong-Ru Tsai,Yuhlong Lio,Ding-Geng Chen |
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Abstract
Designing a proper life test plan to evaluate the quality of a lot of products in order to decide on accepting or rejecting the lot between the manufacturer and customers is an important objective in quality control studies. Most existing life test plans are developed based on the mean time to failure (MTTF) of the products in which a lot is acceptable if the MTTF of products is higher than a given threshold and is rejected otherwise. To save the time and cost of a life test, truncated life test with a prefixed upper limit of the test time can be used in acceptance sampling plan. Instead of life test plans based on MTTF, we consider here life test plans simply based on the number of product failures. Nowadays, to make products more competitive in the market, providing product warranty is a common strategy for manufacturers. Therefore, the development of acceptance sampling plans with warranty considerations is desired. In this chapter, the general structure of an economical design of acceptance sampling plan with warranty using truncated life test is studied. To take into account the uncertainty of the underlying model of the product lifetimes, Bayesian approach using prior informa
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Design of Reliability Acceptance Sampling Plans Under Partially Accelerated Life Test |
M. Kumar |
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Abstract
In this chapter, constant-stress Partially Accelerated Life Tests (PALT) are considered for products with the assumption that the lifetimes of products follow Weibull distribution with known shape parameter and unknown scale parameter. Based on data obtained using Type-II censoring, the maximum likelihood estimates (MLEs) of the Weibull parameters and acceleration factor are obtained assuming linear and Arrhenius relationships with the lifetime characteristics and stress. Exact distributions of the MLEs of the parameters of Weibull distribution are also obtained. Optimal acceptance sampling plans are developed using both linear and Arrhenius relationships. Some numerical results are also presented to illustrate the resulted test plans.
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Bayesian Sequential Design Based on Dual Objectives for Accelerated Life Tests |
Lu Lu,I-Chen Lee,Yili Hong |
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Abstract
Traditional accelerated life test plans are typically based on optimizing the C-optimality for minimizing the variance of an interested quantile of the lifetime distribution. These methods often rely on some specified planning values for the model parameters, which are usually unknown prior to the actual tests. The ambiguity of the specified parameters can lead to suboptimal designs for optimizing the reliability performance of interest. In this paper, we propose a sequential design strategy for life test plans based on considering dual objectives. In the early stage of the sequential experiment, we suggest allocating more design locations based on optimizing the D-optimality to quickly gain precision in the estimated model parameters. In the later stage of the experiment, we can allocate more observations based on optimizing the C-optimality to maximize the precision of the estimated quantile of the lifetime distribution. We compare the proposed sequential design strategy with existing test plans considering only a single criterion and illustrate the new method with an example on the fatigue testing of polymer composites.
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The Stress-Strength Models for the Proportional Hazards Family and Proportional Reverse Hazards Fami |
Bing Xing Wang,Pei Hua Jiang,Xiaofei Wang |
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Abstract
The stress-strength model has been widely used for reliability design of systems. The reliability of the model is defined as the probability that the strength is larger than the stress. This chapter considers the stress-strength model when both the stress and the strength variables follow the two-parameter proportional hazards family or the proportional reverse hazards family. These two distribution families include many commonly-used distributions, such as the Weibull distribution, the Gompertz distribution, the Kumaraswamy distribution and the generalized exponential distribution, etc. Based on complete samples and record values, we derive the maximum likelihood estimation for the these stress-strength reliability. We also present the generalized confidence intervals for these stress-strength reliability. The simulation results show that the proposed generalized confidence intervals work well.
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A Degradation Model Based on the Wiener Process Assuming Non-Normal Distributed Measurement Errors |
Yan Shen,Li-Juan Shen,Wang-Tu Xu |
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Abstract
For highly reliable products whose failure times are scarce, traditional methods for lifetime time analysis are no longer effective and efficient. Instead, degradation data analysis that investigates degradation processes of products becomes a useful tool in evaluating reliability. It focuses on the inherent randomness of products, and investigates the lifetime properties by developing degradation models and extrapolating to lifetime variables. But degradation data are often subject to measurement errors, which may have tails and better be described by non-normal distribution. In this chapter, we consider a Wiener-based model and assume logistic distributed measurement errors. For parameter estimation of the model, the Monte-Carlo expectation-maximization method is adopted together with the Gibbs sampling. Also an efficient algorithm is proposed for a quick approximation of maximum likelihood value. Moreover the remaining useful lifetime is estimated and discussed. From the simulation results, we find that the proposed model is more robust than the model based on the Wiener process assuming normal-distributed errors. Finally, an example is given to illustrate the application of the
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An Introduction of Generalized Linear Model Approach to Accelerated Life Test Planning with Type-I C |
Rong Pan,Kangwon Seo |
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Abstract
Accelerated life tests are often expensive and difficult to conduct. Failure time censoring is anticipated because some test units do not fail over the testing period even under the accelerated stress condition. Therefore, a test plan must be carefully designed to maximize its statistical efficiency. This chapter presents an approach to optimal test planning based on the proportional hazard model of accelerated life test data. It is shown that this approach can accommodate multiple stress factors and is applicable to any failure time distribution.
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Robust Design in the Case of Data Contamination and Model Departure |
Linhan Ouyang,Chanseok Park,Jai-Hyun Byun,Mark Leeds |
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In robust design, it is usually assumed that the experimental data are normally distributed and uncontaminated. However, in many practical applications, these assumptions can be easily violated. It is well known that normal model departure or data contamination can result in biased estimation of the optimal operating conditions of the control factors in the robust design framework. In this chapter, we investigate this possibility by examining these estimation effects on the optimal operating condition estimates in robust design. Proposed estimation methodologies for remedying the difficulties associated with data contamination and model departure are provided. Through the use of simulation, we show that the proposed methods are quite efficient when the standard assumptions hold and outperform the existing methods when the standard assumptions are violated.
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Defects Driven Yield and Reliability Modeling for Semiconductor Manufacturing |
Tao Yuan,Suk Joo Bae,Yue Kuo |
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Abstract
Manufacturing processes of modern ultra-large-scale integrated circuits are highly complex and costly. Defects generated in the manufacturing processes are unavoidable and affect not only manufacturing yield but also device reliability. In this reason, accurate modeling of the spatial defects distribution is imperatively important for yield and reliability estimation as well as process improvement. Defects on semiconductor wafers tend to cluster, which introduces excessive zeros, causing over-dispersion in defect count data. This chapter discusses some latest development in modeling the non-homogeneously distributed spatial defect counts, focusing on Bayesian spatial regression approaches based on Poisson models, negative binomial models, and zero-inflated models. Real wafer map data are used to evaluate the performance of these models. In addition, the yield models are extended to build extrinsic reliability models based on a defect-growth concept.
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发表于 2025-3-21 19:40:57
