An Effective Double Sampling Scheme for the c Control Chart

In the present paper is developed a statistical process control inspection procedure based on a new simple‐to‐implement and effective double sampling scheme for the c control chart, aimed at the minimization of the number of inspected observation units and warranting fixed levels for the type I and II error risks. In particular, the formulations of the false alarm risk α, the power P of the chart, and the expected number of inspected observation units for the developed inspection procedure are given, whereas a macro of Microsoft Excel is adopted to solve the tackled problem. In order to illustrate the application of the developed approach and to investigate on the influence of several operating parameters, numerical examples are carried out and the related considerations are given. Finally, by comparing the performance of the developed inspection procedure with that of the related classic c chart scheme, meaningful reduction of the number of the inspected observation units can be achieved by adopting the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

An AR‐Sieve Bootstrap Control Chart for Autocorrelated Process Data

There are two major approaches in dealing with autocorrelated process data in process control, that is, residual‐based approaches and methods that modify control limits to adjust for autocorrelation. We proposed a methodology for constructing control charts for autocorrelated process data using the AR‐sieve bootstrap. The simulation study illustrates the relative advantage of the AR‐sieve bootstrap control chart with respect to the in‐control and out‐of‐control run length and false alarm rate. The proposed methodology works even for small sample sizes and conditions of the near nonstationarity of the generating process. The proposed AR‐sieve bootstrap control chart presents the advantage of being distribution‐free for certain class of linear models as well as the tracking of actual process observations instead of model residuals, thus facilitating the implementation during actual plant operations. Copyright © 2011 John Wiley & Sons, Ltd.     

A Moving Average Control Chart for Monitoring the Fraction Non‐conforming

The p chart is often used to monitor the fraction of non‐conforming products. However, the p chart is slow in detecting sustaining shifts of small magnitude in the level of fraction non‐conforming. This paper discusses a more efficient alternative to the standard p chart approach, i.e. the construction of a moving average control chart for fraction non‐conforming, p. Approximations by means of mathematical calculations and the corresponding simulation results for the average run length profiles show that the performance of the new approach is superior to that of the standard approach. The new approach is easy to implement and hence might be attractive and useful to practitioners. Examples are also given to show how the proposed procedure is put to work in real situations. Copyright © 2004 John Wiley & Sons, Ltd.     

A Bootstrap Control Chart for Weibull Percentiles

The problem of detecting a shift of a percentile of a Weibull population in a process monitoring situation is considered. The parametric bootstrap method is used to establish lower and upper control limits for monitoring percentiles when process measurements have a Weibull distribution. Small percentiles are of importance when observing tensile strength and it is desirable to detect their downward shift. The performance of the proposed bootstrap percentile charts is considered based on computer simulations, and some comparisons are made with an existing Weibull percentile chart. The new bootstrap chart indicates a shift in the process percentile substantially quicker than the previously existing chart, while maintaining comparable average run lengths when the process is in control. An illustrative example concerning the tensile strength of carbon fibers is presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust Individuals Control Chart for Exploratory Analysis

Apart from their uses in the context of statistical process control, control charts are also used as an exploratory tool in the context of exploratory data analysis. These two application situations are not similar and, as a consequence, control charting methodology should be adjusted to the exploratory context. In this article we make an inventory of the requirements for control charts that are used for exploratory analysis and we propose a procedure that meets these requirements. Robustness against assignable causes of variation appears to be important. The proposed methodology is illustrated from two real-life examples.     

Calculating the (Almost) Exact Control Limits for a C-Chart

A power transformation using an exponent of 2/3 for Poisson-distributed data, with a small constant added, achieves symmetry for improved statistical process control (SPC) applications whether it is for an individual, a cumulative sum, or an exponentially weighted moving average chart. Two simple equations are proposed for calculating the lower control limit (LCL) and the upper control limit (UCL) for Poisson type data. Agreement between the exact LCL and UCL, as determined by the lower and upper tail area, is excellent. The square-root transformation that stabilizes the variance produces a negatively skewed distribution and tends to give false SPC signals.     

扩散先验分布下Bayes线性假设检验方法的构造

首先讨论了扩散先验分布下多元线性回归模型Y=Xβ e，e～N(0，σ^2In)中参数β的边缘后验分布，然后根据该分布构造了R^m 1与其子集上的最大后验密度之比，据此检验回归系数β的线性假设，最后研究了部分系数同时为零这一特殊情况的Bayes检验方法。     

利用聚能原理销毁危险弹药的试验方法

传统的爆破方法处理射击未爆弹、事故弹药、地雷等危险弹药存在操作安全隐患,文章分析了锥形装药爆破作用原理和效能,通过试验验证了锥形装药能够可靠穿透并引爆榴弹弹丸,设计出聚能引爆器装置,从而避免了作业人员处理弹药过程中与危险弹药的直接接触,提高了操作的安全性.     

Nonparametric Progressive Mean Control Chart for Monitoring Process Target

Nonparametric control charts are widely used when the parametric distribution of the quality characteristic of interest is questionable. In this study, we proposed a nonparametric progressive mean control chart, namely the nonparametric progressive mean chart, for efficient detection of disturbances in process location or target. The proposed chart is compared with the recently proposed nonparametric exponentially weighted moving average and nonparametric cumulative sum charts using different run length characteristics such as the average run length, standard deviation of the run length, and the percentile points of the run length distribution. The comparisons revealed that the proposed chart outperformed recent nonparametric exponentially weighted moving average and nonparametric cumulative sum charts, in terms of detecting the shifts in process target. A real life example concerning the fill heights of soft drink beverage bottles is also provided to illustrate the application of the proposed nonparametric control chart. Copyright © 2012 John Wiley & Sons, Ltd.     

A EWMA Control Chart for Exponential Distributed Quality Based on Moving Average Statistics

We propose an exponentially weighted moving average (EWMA) control chart for monitoring exponential distributed quality characteristics. The proposed control chart first transforms the sample data to approximate normal variables, then calculates the moving average (MA) statistic for each subgroup, and finally constructs the EWMA statistic based on the current and the previous MA statistics. The upper and the lower control limits are derived using the mean and the variance of EWMA statistics. The in‐control and the out‐of‐control average run lengths are derived and tabularized according to process shift parameters and smoothing constants. It is shown that the proposed control chart outperforms the MA control chart for all shift parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Design of a Control Chart Using a Modified EWMA Statistic

In this paper, the design of a control chart is given using a modified exponentially weighted moving average statistic under the assumption that the quality characteristic of interest follows the normal distribution. The structure of the proposed control chart is developed, and the necessary measures are derived to find the average run length for in‐control and out‐of‐control processes. The efficiency of the proposed chart is compared with two existing control charts in terms of the average run length. The results are explained with the help of industrial example. Copyright © 2016 John Wiley & Sons, Ltd.     

A Comparison of Normal Approximation Rules for Attribute Control Charts

Control charts, known for more than 80 years, have been important tools for business and industrial manufactures. Among many different types of control charts, the attribute control chart (np‐chart or p‐chart) is one of the most popular methods to monitor the number of observed defects in products, such as semiconductor chips, automobile engines, and loan applications. The attribute control chart requires that the sample size n is sufficiently large and the defect rate p is not too small so that the normal approximation to the binomial works well. Some rules for the required values for n and p are available in the textbooks of quality control and mathematical statistics. However, these rules are considerably different, and hence, it is less clear which rule is most appropriate in practical applications. In this paper, we perform a comparison of five frequently used rules for n and p required for the normal approximation to the binomial. With this result, we also refine the existing rules to develop a new rule that has a reliable performance. Datasets are analyzed for illustration. Copyright © 2013 John Wiley & Sons, Ltd.     

Monitoring Process Variance Using an ARL‐unbiased EWMA‐p Control Chart

Control charts are effective tools for signal detection in manufacturing processes. As much of the data in industries come from processes having non‐normal or unknown distributions, the commonly used Shewhart variable control charts cannot be appropriately used, because they depend heavily on the normality assumption. The average run length (ARL) is generally used to measure the detection performance of a process when using a control chart, but it is biased for the monitoring statistic with an asymmetric distribution. That is, the ARL‐biased control chart leads to take longer to detect the shifts in parameter than to trigger a false alarm. To overcome this problem, we herein propose an ARL‐unbiased exponentially weighted moving average proportion (EWMA‐p) chart to monitor the process variance for process data with non‐normal or unknown distributions. We further explore the procedure to determine the control limits and to investigate the out‐of‐control variance detection performance of the ARL‐unbiased EWMA‐p chart. With a numerical example involving non‐normal service times from a bank branch in Taiwan, we illustrate the applications of the proposed ARL‐unbiased EWMA‐p chart and also compare the out‐of‐control detection performance of the ARL‐unbiased EWMA‐p chart, the arcsin transformed symmetric EWMA variance, and other existing variance charts. The proposed ARL‐unbiased EWMA‐p chart shows superior detection performance. Thus, we recommend the ARL‐unbiased EWMA‐p chart for process data with non‐normal or unknown distributions. Copyright © 2015 John Wiley & Sons, Ltd.     

A double exponentially weighted moving average control chart for monitoring COM‐Poisson attributes

The Conway‐Maxwell‐Poisson (COM‐Poisson) distribution is a two‐parameter generalization of the Poisson distribution, which can be used for overdispersed or underdispersed count data and also contains the geometric and Bernoulli distributions as special cases. This article presents a double exponentially weighted moving average control chart with steady‐state control limits to monitor COM‐Poisson attributes (regarded as CMP‐DEWMA chart). The performance of the proposed control chart has been evaluated in terms of the average, the median, and the standard deviation of the run‐length distribution. The CMP‐DEWMA control chart is studied not only to detect shifts in each parameter individually but also in both parameters simultaneously. The design parameters of the proposed chart are provided, and through a simulation study, it is shown that the CMP‐DEWMA chart is more effective than the EWMA chart at detecting downward shifts of the process mean. Finally, a real data set is presented to demonstrate the application of the proposed chart.     

An Improved R (Range) Control Chart for Monitoring the Process Variance

An R chart is often used to monitor shifts in the process variability. However, the range, , statistics from a sampling distribution are highly skewed. Hence, the classical R chart based on the control limits will not give an in‐control average run length of approximately 370, or equivalently a type I error, . In this paper, an approach is shown to obtain the control limits of an improved R chart based on a desired type I error from the density function of the R_i statistics. Copyright © 2004 John Wiley & Sons, Ltd.     

A Bayesian Analysis of the Linear Calibration Problem

As part of a Bayesian analysis of the linear calibration problem, a posterior distribution is derived that is mathematically identical to the structural distribution obtained by Kalotay (1971) but different from the Bayesian distribution obtained by Hoadley (1970). Useful approximations are given. Although this posterior distribution has infinite variance, no practical problems arise in using it. The controversy concerning infinite variances and the use of inverse regression is discussed.     

On Bayesian EWMA control charts under different loss functions

The motivation for this study is to analyze Bayesian exponentially weighted moving average (EWMA) control chart under 3 loss functions namely, SELF, LLF, and PLF. Informative priors (normal and mixture of normal) and non‐informative priors (Uniform and Jefferys) are considered for the analysis. The performance of Bayesian EWMA control chart using posterior and posterior predictive distribution scheme has been evaluated using average run length (ARL) and standard deviation run length (SDRL) as performance measures. Monte Carlo simulations are used to compute the performance measures for different values of smoothing constant. An illustrative example is also presented for practical considerations of Bayesian EWMA control chart.     

Monitoring of Time‐Between‐Events with a Generalized Group Runs Control Chart

Control charting methods for time between events (TBE) is important in both manufacturing and nonmanufacturing fields. With the aim to enhance the speed for detecting shifts in the mean TBE, this paper proposes a generalized group runs TBE chart to monitor the mean TBE of a homogenous Poisson failure process. The proposed chart combines a TBE subchart and a generalized group conforming run length subchart. The zero‐state and steady‐state performances of the proposed chart were evaluated by applying a Markov chain method. Overall, it is found that the proposed chart outperforms the existing TBE charts, such as the T, T_r, EWMA‐T, Synth‐T_r, and GR‐T_r charts. Copyright © 2015 John Wiley & Sons, Ltd.