Fast Initial Response Feature Research Articles

Dynamic generalized fast initial response for EWMA control schemes for monitoring processes with startup and post‐startup problems

Dynamic generalized fast initial response for EWMA control schemes for monitoring processes with startup and post‐startup problems

Enhanced CUSUM and dual CUSUM mean charts

The CUSUM (C) and dual C (DC) charts are well-known because of their sensitive nature against small-to-moderate shifts that occur in the process parameter(s). In this study, we propose new auxiliary information based (AIB) control charts for monitoring the process mean, which include Brownian motion-based C (BC), new BC (NBC), NBC with Crosier C (NBCC), dual NBC (DNBC) and dual NBCC (DNBCC) charts. In addition, fast initial response feature is also added to the proposed charts. We use Monte Carlo simulations to compute the run length properties of the control charts. Based on detailed run length comparisons, it is found that the proposed AIB charts are uniformly better than the existing AIB charts in terms of expected weighted and relative average run length benchmarks. An important concern all around the world is the quality and safety of drinking water. Several water quality tests are available that provide required information about the health of the waterway. Here, a water quality test dataset is taken on two variables, namely pH and total solids, and the proposed AIB charts are used to monitor the mean level of pH in the water.

Design Tukey’s Control Chart and mix with CUSUM Control Chart

Statistical process control is a collection of valuable tools for detecting alteration in a process. It has wide application in many areas field and other fields where variation is being monitored. The variation may be a natural cause variation or a particular cause variation. Statistical process control deals with the monitoring process to detect disturbances in the process. These disturbances may be from the process mean or variance. This study proposes efficient charts for detecting early shifts in dispersion parameters by applying the Fast Initial Response feature. We propose and compare the performance of different cumulative sum (CUSUM)control charts for phase II monitoring of location based on mean and median. The (CUSUM) control chart, which is a method of data analysis based on John Tukey's principles control chart (TCC), is used to compare the proposed charts with their existing counterparts is used to evaluate new charts to existing charts using performance measures such as average run length, the standard deviation of run length, additional quadratic loss, relative average run length, and performance comparison . The proposed charts detect early shifts in the process dispersion faster and have better overall. This article is a similar effort to design an improved charting structure in the form of mixed or using Tukey -CUSUM chart together, to show the process control chart., and drawing the Average Run Length ARL value.

The use of fast initial response features on the homogeneously weighted moving average chart with estimated parameters under the effect of measurement errors

AbstractFast initial response (FIR) features are generally used to improve the sensitivity of memory‐type control charts by shrinking time‐varying control limits in the earlier stage of the monitoring regime. This paper incorporates FIR features to increase the sensitivity of the homogeneously weighted moving average (HWMA) monitoring schemes with and without measurement errors under constant as well as linearly increasing variance scenarios. The robustness and the performance of the HWMA monitoring schemes are investigated in terms of numerous run‐length properties assuming that the underlying process parameters are known and unknown. It is found that the FIR features improves the performance of the HWMA monitoring scheme as compared to the standard no FIR feature HWMA scheme, and at the same time, it is observed that the simultaneous use of a recently proposed FIR feature and multiple measurements significantly reduces the negative effect of measurement errors. An illustrative example on the volume of milk in bottles is used to demonstrate a real‐life application.

Directionally sensitive MCUSUM mean charts

AbstractIn the context of a disease outbreak detection, a prime interest is to only detect increases in the process mean. It is thus desirable to have a directionally sensitive multivariate chart that can effectively detect either increases or decreases in the process mean vector. In this paper, with a suitable transformation that truncates multivariate observations either above or below the process mean vector, we propose one‐sided and two one‐sided MCUSUM charts for monitoring the mean of a multivariate normal process. Among the proposed charts, the one‐sided MCUSUM charts are directionally sensitive, while the two one‐sided MCUSUM charts are directionally insensitive. In addition, the fast initial response feature is also incorporated into the proposed charts to enhance their sensitivities against initial process shifts. The run length characteristics of these control charts are computed with the Monte Carlo simulation. Based on the run length comparisons, it is found that the proposed charts are more sensitive than the existing charts when detecting moderate‐to‐large shifts in the process mean. The proposed charts are also applied on real datasets to support the theory.

Distribution‐free triple EWMA control chart for monitoring the process location using the Wilcoxon rank‐sum statistic with fast initial response feature

AbstractThe exponentially weighted moving average (EWMA) control chart is a memory‐type chart known to be more efficient in detecting small and moderate shifts in the process parameter. The double EWMA (DEWMA) chart is an extension of the EWMA chart that is more effective than the latter in the detection of small‐to‐moderate shifts. This paper proposes a new distribution‐free (or nonparametric) triple EWMA (TEWMA) control chart based on the Wilcoxon rank‐sum (W) statistic to improve the detection ability in the process location parameter. Moreover, a new fast initial response (FIR) feature is added to further improve the sensitivity of the new TEWMA chart. The performance of the proposed TEWMA chart with and without FIR features is compared to those of the existing EWMA and DEWMA W charts. It is observed that the TEWMA chart with and without FIR features is superior to the competing charts in most situations. A real‐life illustration is provided to show the application and implementation of the new chart.

New CUSUM and dual CUSUM mean charts

AbstractThe CUSUM (C) charts are well recognized as a potentially advanced process monitoring tools because of their sensitivity against small and moderate shifts. In this paper, we first improve the sensitivity of the Brownian motion–based C (BC) chart with an appropriate transformation, named new BC (NBC) chart, for monitoring moderate and large shifts in the mean of a normal process. Then, using the control charting structure of the Crosier C (CC) chart, we propose the NBCC (NBC with CC structure) chart. In addition, for efficiently detecting a mean shift within an interval, dual version of these control charts are also proposed, named the dual NBC (DNBC) and dual NBCC (DNBCC) charts. Moreover, the fast initial response feature is also incorporated into the proposed charts. Using the Monte Carlo simulation, the run length properties of the proposed charts are computed. The run length performances of the existing and proposed charts are compared using the extra quadratic loss and integral relative average run length as performance criterion. It turns out that the NBC and NBCC (DNBC and DNBCC) charts are uniformly more sensitive than the C, CC, and NBC (dual C and dual CC) charts when detecting the mean shifts in small, moderate, and large intervals, where the DNBCC chart outperforms all considered charts. The proposed charts are also applied on real data sets to support the proposed theory.

Enhanced EWMA charts for monitoring the process coefficient of variation

AbstractThe coefficient of variation (CV) is an important quality characteristic when the process variance is a function of the process mean for a production process. In this paper, we develop an auxiliary information–based (AIB) estimator for estimating the squared CV, along with its approximated mean and variance. This estimator is then used to devise new one‐sided EWMA charts for monitoring the increases or decreases in the squared CV of a normal process, named the AIB‐EWMA CV charts. In addition, the sensitivities of these control charts are also enhanced with the fast initial response feature. The Monte Carlo simulation method is used to compute the run length characteristics of the proposed CV charts. Based on detailed run length comparisons, it is found that the proposed AIB‐EWMA CV charts are uniformly and substantially better than the existing EWMA CV charts when detecting different kinds of upward/downward shifts in the squared CV. The proposed charts are also applied to a real dataset to support the proposed theory.

A new dual CUSUM mean chart

AbstractThe conventional cumulative sum (CUSUM) chart is usually designed based on a known shift size. In usual practice, shift size is often unknown and can be assumed to vary within an interval. With such a range of shift size, the dual CUSUM (DCUSUM) chart provides more sensitivity than the CUSUM chart. In this paper, we propose dual Crosier CUSUM (DCCUSUM) charts with and without fast initial response features to efficiently monitor the infrequent changes in the mean of a normally distributed process. Monte Carlo simulations are used to compute the run length characteristics of one‐sided and two‐sided DCCUSUM charts. These run length characteristics are compared with those of the CUSUM, Crosier CUSUM, Shewhart‐CUSUM, and DCUSUM charts in terms of the integral relative average run length. It turns out that the proposed chart shows better performance when detecting a range of mean shift sizes. A real dataset is considered to illustrate the implementation of existing and proposed charts.

An enhanced GWMA chart for process mean

Memory-type control charts are frequently used to monitor small-to-moderate disturbances in the process parameter(s). Recently, an auxiliary-information-based (AIB) exponentially weighted moving average (EWMA) chart has been proposed for efficiently monitoring the process mean, called the AIB-EWMA chart, that surpasses the classical EWMA chart. On similar lines, in order to further enhance the sensitivity of the AIB-EWMA chart, we propose an AIB generally weighted moving average (GWMA) chart for monitoring the process mean, named the AIB-GWMA chart. The existing AIB-Shewhart and AIB-EWMA charts are special cases of the AIB-GWMA chart. With the help of Monte Carlo simulation, the run length characteristics of the AIB-GWMA chart are computed. It turns out that the AIB-GWMA chart performs uniformly and substantially better than the classical GWMA chart. Moreover, the AIB-GWMA chart also outperforms the AIB-EWMA chart when detecting mean shifts within certain ranges. A similar trend is observed when the proposed and existing control charts are compared with the fast initial response features. An example is used to explain the working and implementation of the GWMA, AIB-EWMA and AIB-GWMA charts.

Improved CUSUM charts for monitoring process mean

In this paper, we propose new cumulative sum (CUSUM) and Shewhart-CUSUM (SCUSUM) control charts for monitoring the process mean using ranked-set sampling (RSS) and ordered RSS (ORSS) schemes. The proposed CUSUM charts include the Crosier's CUSUM (CCUSUM) and Shewhart-CCUSUM (SCCUSUM) charts using RSS, and the CUSUM, CCUSUM, SCUSUM and SCCUSUM charts using ORSS. Moreover, fast initial response features are also attached with these CUSUM charts to improve their sensitivities for an initial out-of-control situation. Monte Carlo simulations are used to compute the run length characteristics of the proposed CUSUM charts. Upon comparing the run length performances of the CUSUM charts, it turns out that the proposed CUSUM charts are more sensitive than their existing counterparts. A real dataset is used to explain the implementation of the proposed CUSUM charts.

Properties and enhancements of robust likelihood CUSUM control chart

The properties of RLCUSUM control schemes used to monitor contaminated normally distributed processes are evaluated.An optimal design procedure for RLCUSUM control schemes is given. And several enhancements to RLCUSUM are considered.Compare robust likelihood CUSUM control charts with conventional CUSUM and GCUSUM, and conclude their pros and cons.Fast initial response feature is included, that makes the RLCUSUM control schemes more sensitive to start-up cases.An application is used to illustrate the implementation of RLCUSUM control schemes. In practice, the robust-likelihood cumulative sum (RLCUSUM) control charts, using truncation of the log-likelihood underpinnings of the CUSUM to ensure robust performance, which perform well to detect small shifts in the mean of heavy-tailed processes and have the ability to discount outliers. In this article, we evaluate the properties of RLCUSUM control schemes used to monitor the mean of contaminated normally distributed processes. An optimal design procedure for RLCUSUM control schemes is given, in addition, several enhancements to RLCUSUM are considered. These include a fast initial response feature that makes the RLCUSUM control schemes more sensitive to start-up cases, three types of truncation of RLCUSUM, which are cut off by horizontal ray, horizontal segment and oblique line respectively against both large and small shifts in a non-normality process. An extensive comparison with the conventional CUSUM and generalized likelihood ratio CUSUM (GCUSUM) in terms of average run length (ARL), shows that the RLCUSUM is more robust than the conventional CUSUM and GCUSUM control charts for its ARLs are monotonous against the process mean. Especially, the oblique line truncated RLCUSUM control chart has the best overall performance in the various cases of shifts. A final application based on monitoring packing 250g containers is used to illustrate the implementation of RLCUSUM control schemes.

New cumulative sum control charts for monitoring process variability

ABSTRACTIn this article, we propose new cumulative sum (CUSUM) control charts using the ordered ranked set sampling (RSS) and ordered double RSS schemes, with the perfect and imperfect rankings, for monitoring the variability of a normally distributed process. The run length characteristics of the proposed CUSUM charts are computed using the Monte Carlo simulations. The proposed CUSUM charts are compared in terms of the average and standard deviation of run lengths with their existing competitor CUSUM charts based on simple random sampling. It turns out that the proposed CUSUM charts with the perfect and imperfect rankings are more sensitive than the existing CUSUM charts based on the sample range and standard deviation. A similar trend is present when these CUSUM charts are compared with the fast initial response features. An example is also used to demonstrate the implementation and working of the proposed CUSUM charts.

Using FIR to Improve CUSUM Charts for Monitoring Process Dispersion

Statistical process control deals with monitoring process to detect disturbances in the process. These disturbances may be from the process mean or variance. In this study, we propose some charts that are efficient for detecting early shifts in dispersion parameter, by applying the Fast Initial Response feature. Performance measures such as average run length, standard deviation of the run length, extra quadratic loss, relative average run length, and performance comparison index are used to compare the proposed charts with their existing counterparts, including the Shewhart R chart and the Shewhart S chart with and without warning lines. Others include the CUSUM R chart, the CUSUM S chart, the EWMA of ln S2, the CUSUM of ln S2, the Pσ CUSUM, the χ CUSUM, and the Change Point (CP) CUSUM charts. The proposed charts do not only detect early shifts in the process dispersion faster, but also have better overall performance than their existing counterparts. Copyright © 2016 John Wiley & Sons, Ltd.

CUSUM procedures with probability control limits for monitoring processes with variable sample sizes

ABSTRACTControl charts are usually designed with constant control limits. In this article, we consider the design of control charts with probability control limits aimed at controlling the conditional false alarm rate at the desired value at each time step. The resulting control limits are dynamic and thus are more general and capable of accommodating more complex situations in practice as compared with the use of a constant control limit. We consider the situation when the sample sizes are varying over time, with a primary focus on the CUmulative SUM (CUSUM)-type control charts. Unlike other methods, no assumptions about future sample sizes are required with our approach. An integral equation approach is developed to facilitate the design and analysis of the CUSUM control chart with probability control limits. The relationship between the CUSUM charts using probability control limits and the CUSUM charts with a fast initial response feature is investigated.

Applying fast initial response features on GWMA control charts for monitoring autocorrelation data

ABSTRACTA generally weighted moving average (GWMA) control chart with fast initial response (FIR) features is addressed to monitor an autoregressive process mean shift. Numerical simulations based on average run length (ARL) show that the GWMA control chart with additional FIR feature requires less time to detect small or moderate shifts than GWMA control chart at low level of autocorrelation; whereas these two control charts perform similarly at high level of autocorrelation. Regardless of any level of autocorrelation, GWMA control charts provided with additional FIR feature have a good performance in detecting large shifts during the initial stage.

Run length quantiles of EWMA control charts monitoring normal mean or/and variance

Exponentially weighted moving average (EWMA) control charts are well-established devices for monitoring process stability. Typically, control charts are evaluated by considering their Average Run Length (ARL), that is the expected number of observations or samples until the chart signals. Because of the limitations of an average, various papers also dealt with the run length distribution and quantiles. Going beyond these papers, we develop algorithms for and evaluate the quantile performance of EWMA control charts with variance adjusted control limits and with fast initial response features, of EWMA charts based on the sample variance, and of EWMA charts simultaneously monitoring mean and variance. Additionally, for the mean charts we consider medium, late and very late process changes and their impact on appropriately conditioned run length quantiles. It is demonstrated that considering run length quantiles can protect from constructing distorted EWMA designs while optimising their zero-state ARL performance. The implementation of all the considered measures in the R package ‘spc’ allows any control chart user to consider EWMA schemes from the run length quantile prospective in an easy way.

The Continuous Run Sum Chart

The run sum chart is an effective two-sided chart that can be used to monitor for process changes. It is known that it is more sensible than the Shewhart chart with runs rules and its performance improves as the number of regions increases. However, as the number of regions increses the resulting chart has more parameters to be defined and its design becomes more involved. In this article, we introduce a one-parameter run sum chart. This chart accumulates scores equal to the subgroup means and signals when the cummulative sum exceeds a limit value. A fast initial response feature is proposed and its run length distribution function is found by a set of recursive relations. We compare this chart with other charts suggested in the literature and find it competitive with the CUSUM, the FIR CUSUM, and the combined Shewhart FIR CUSUM schemes.

Improved Fast Initial Response Features for Exponentially Weighted Moving Average and Cumulative Sum Control Charts

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts have found extensive applications in industry. The sensitivity of these quality control schemes can be increased by using fast initial response (FIR) features. In this paper, we introduce some improved FIR features for EWMA and CUSUM control charts and evaluate their performance in terms of average run length. We compare the proposed FIR‐based EWMA and CUSUM control schemes with some existing control schemes, that is, EWMA, FIR‐EWMA, CUSUM, and FIR‐CUSUM. It is noteworthy that the proposed control schemes are uniformly better than the other schemes considered here. An illustrative example is also given to demonstrate the implementation of the proposed control schemes. Copyright © 2013 John Wiley & Sons, Ltd.

Extension of CV-GWMA Control Chart with Fast Initial Response Feature

Extension of CV-GWMA Control Chart with Fast Initial Response Feature