Monitoring nonlinear profiles using a wavelet-based distribution-free CUSUM chart

WDFTC is a wavelet-based distribution-free CUSUM chart for detecting shifts in the mean of a profile with noisy components. Exploiting a discrete wavelet transform (DWT) of the mean in-control profile, WDFTC selects a reduced-dimension vector of the associated DWT components from which the mean in-control profile can be approximated with minimal weighted relative reconstruction error. Based on randomly sampled Phase I (in-control) profiles, the covariance matrix of the corresponding reduced-dimension DWT vectors is estimated using a matrix-regularisation method; then the DWT vectors are aggregated (batched) so that the non-overlapping batch means of the reduced-dimension DWT vectors have manageable covariances. To monitor shifts in the mean profile during Phase II operation, WDFTC computes a Hotelling's T ²-type statistic from successive non-overlapping batch means and applies a CUSUM procedure to those statistics, where the associated control limits are evaluated analytically from the Phase I data. Experimentation with several normal and non-normal test processes revealed that WDFTC was competitive with existing profile-monitoring schemes.     

联合监控均值和方差的累积和控制图优化设计

为了提高监测均值和方差微小偏移的敏感度,围绕生产过程质量控制,建立同时监控均值和方差的累积和控制图.模型考虑均值和方差的变化,针对生产过程中的微小偏差,提出了一个新的累积和控制图,并给出了基于马尔可夫链理论的新控制图的平均链长计算方法.编程求解后对比文献中各控制图的平均链长数据以及更换变量数值改进控制图,通过计算变动比率得出新控制图的检测力度在不同偏移力度下都明显优于其他控制图方法.     

Control charting methods for autocorrelated cyber vulnerability data

Control charting cyber vulnerabilities is challenging because the same vulnerabilities can remain from period to period. Also, hosts (personal computers, servers, printers, etc.) are often scanned infrequently and can be unavailable during scanning. To address these challenges, control charting of the period-to-period demerits per host using a hybrid moving centerline residual-based and adjusted demerit (MCRAD) chart is proposed. The intent is to direct limited administrator resources to unusual cases when automatic patching is insufficient. The proposed chart is shown to offer superior average run length performance compared with three alternative methods from the literature. The methods are illustrated using three datasets.     

Support Vector Regression control charts for multivariate nonlinear autocorrelated processes

Statistical process control charts are one of the most widely used techniques in industry and laboratories that allow monitoring of systems against faults. To control multivariate processes, most classical charts need to model process structure and assume that variables are linearly and independently distributed. This study proposes to use a nonparametric method named Support Vector Regression to construct several control charts that allow monitoring of multivariate nonlinear autocorrelated processes. Also although most statistical quality control techniques focused on detecting mean shifts, this research investigates detection of different parameter shifts. Based on simulation results, the study shows that, with a controlled robustness, the charts are able to detect the different applied disturbances. Moreover in comparison to Artificial Neural Networks control chart, the proposed charts are especially more effective in detecting faults affecting the process variance.     

Computing the Percentage Points of the Run-Length Distributions of Multivariate CUSUM Control Charts

Multivariate CUSUM control charts are often used instead of the standard Hotelling's control charts in many practical problems when detection of small shifts in the process mean is important. However, design of multivariate CUSUM control charts are usually based on the average run length (ARL). In this work, we will compute the percentage points of the run-length distributions of two multivariate CUSUM control charts. It will be shown that interpretations based on ARL can be misleading since the in-control run-length distribution of a multivariate CUSUM is highly skewed. On the other hand, the percentage points of the run-length distribution provide additional information such as the median run length, early false out-of-control signals, and the skewness of the run-length distribution for a particular scheme. These extra information might provide quality control engineers further knowledge of a particular multivariate CUSUM control chart scheme.     

A continuous sampling plan using sums of conforming run‐lengths

A continuous sampling plan, CSP‐SUM, is proposed based on the use of sums of run‐lengths of conforming items for deciding when to switch between the phases of sampling inspection and 100% inspection. The conventional measures of performance of CSPs such as the average outgoing quality, average fraction inspected, and the proportion passed under sampling inspection are evaluated for CSP‐SUM. Using these and other measures, comparisons with some standard CSPs are provided and indicate better performance for CSP‐SUM. Comparisons are also made with a recently‐proposed CSP utilizing CUSUMs, termed CSP‐CUSUM, and indicate that the performance of CSP‐SUM can be close to that of CSP‐CUSUM. A table is provided to aid the choice of parameters for the operation of CSP‐SUM. It is recommended that a conforming run‐length control chart be maintained in parallel with CSP‐SUM to detect significant upward shifts in the fraction defective of the process. Copyright © 2003 John Wiley & Sons, Ltd.     

Controlling autocorrelated data in multistage manufacturing processes with an application to textile industry

In recent years, much attention has been given to monitoring multistage processes in order to effectively improve the product reliability. To this end, the output of the process is investigated under special circumstances, and the values corresponding to reliability‐related quality characteristic are measured. However, analyzing reliability data is quite complicated because of their unique features such as being censored and obeying nonnormal distributions. A more sophisticated picture arises when the observations of the process are autocorrelated in some cases, which makes the application of previous control procedures futile. In this paper, the accelerated failure time (AFT) regression models have been modified in order to account for autocorrelated data. Then, a cumulative sum (CUSUM) control chart and an exponentially weighted moving average (EWMA) control chart based on conditional expected values have been proposed to monitor the quality variable with Weibull distribution while taking the effective covariates into consideration. Extensive simulation studies reveal that the CUSUM control chart outperforms its counterpart in detecting out‐of‐control conditions. Finally, a real case study in a textile industry has been provided to investigate the application of the CUSUM control scheme.     

A Neural Network Method for Modelling the Parameters of a CUSUM Chart

The cumulative sum (CUSUM) chart is widely employed in quality control to monitor a process or to evaluate historic data. CUSUM charts are designed to exhibit acceptable average run lengths both when the process is in and out of control. This paper introduces a functional technique for generating the parameters h and k for such a chart that will have specified average run lengths. It employs the method of artificial neural networks to derive the appropriate coefficients. An EXCEL spreadsheet to assist computing the parameters is presented.     

A Note on the Lower-Sided Synthetic Chart for Exponentials

The synthetic control chart for exponential data is discussed and an expression is derived for its average run length, as well as its design parameters. The synthetic control chart for exponentials is shown analytically to be a two-in-a-row rule. This chart is compared with the Shewhart chart for individuals and with the worst-case, lower-sided exponential EWMA and CUSUM charts. While the synthetic control chart for exponentials outperforms the Shewhart chart for individuals, the EWMA and CUSUM charts are shown to be far superior in detecting decreases in the exponential mean.