Use of ranked set sampling in nonparametric control charts

Exponentially Weighted Moving Average (EWMA) control charts yield insights into data in a way more comprehensible to the practitioners and researchers because of its capability in discovering small to moderate process mean shifts. EWMA control chart is incorporated with conforming run length (CRL) chart, named synthetic EWMA chart, to enhance the performance of the chart in detecting the out-of-control signal. Synthetic EWMA chart based on ranked set sampling (RSS) for monitoring process mean has been proposed as it advanced the detection of chart over a series of mean shifts. With the situation that normality assumption is scarcely attain in practice, we proposed synthetic EWMA median chart based on RSS. Rather than select average run length (ARL) as sole performance evaluating tool, the median and percentiles of run-length distribution are used to examine the performance of the proposed chart as it provides more information on the entire run-length distribution. Near-optimal parameters of the proposed chart will be acquired by setting the incontrol ARL at a designated value. The run length performances of the proposed chart are then compared with the existing charts such as EWMA median chart based on RSS.

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are used to detect smaller shifts in process parameters. The usual EWMA and CUSUM charts depend on the normality assumption for a better detection ability. This study proposes an efficient EWMA control chart based on the spirit of Tukey control chart, especially designed for skewed distributions. The performance of the proposed and the competing charts is measured using different length properties such as average run length (ARL), standard deviation of run length (SDRL), and median run length (MDRL). We have observed that the proposed chart is quite efficient at detecting process shifts of smaller magnitude, especially for skewed distributions. For practical considerations, the proposed chart is implemented at aerospace manufacturing data on industrial production index.

Exponentially weighted moving average (EWMA) control charts are consistently used for the detection of small shifts contrary to Shewhart charts, which are commonly used for the detection of large shifts in the process. There are many interesting features of EWMA charts that have been studied for complete data in the literature. The aim of present study is to introduce and compare the double exponentially weighted moving average (DEWMA) and EWMA control charts under type-I censoring for Poisson-exponential distribution. The monitoring of mean level shifts using censored data is of a great interest in many applied problems. Moreover, a new idea of conditional median is introduced and further compared with the existing conditional expected values approach for monitoring the small mean level shifts. The performance of the DEWMA and EWMA charts is evaluated using the average run length, expected quadratic loss, and performance comparison index measures. The optimum sample size comparisons for the specified and unspecified parameters are also part of this study. Two applications for practical considerations are also discussed. It is observed that different censoring rates and the size of shifts significantly affect the performance of the EWMA and DEWMA charts. Copyright © 2016 John Wiley & Sons, Ltd.

ABSTRACTThe process monitoring and construction of control charts involves the measurement of the quality characteristic under certain time and cost constraints. Ranked set sampling (RSS) is a very useful and inexpensive method of obtaining a more representative sample when the actual quantification of sampling units is expensive or destructive, while the ranking of the observations is easier. In this paper, RSS and its variation, extreme RSS, median RSS and neoteric RSS are employed to construct new memory type homogeneously weighted moving average (HWMA) control charts to monitor the process location. The HWMA chart assigns a particular weight to the most recent sample, while all the previous samples are assigned an equal proportion of the remaining weight. The run length properties of the proposed control charts are studied by using extensive Monte Carlo simulations. The performance of the proposed charts is compared with the simple random sampling-based exponentially weighted moving average (EWMA) and HWMA besides RSS-based EWMA counterparts. The comprehensive comparisons established the better shift detection ability of the proposed control charts. To demonstrate the practical implementation of the proposed charts, a real industrial dataset is used which also confirms the better mean shift detection ability of the proposed charts.

The exponentially weighted moving average (EWMA) control charts with variable sampling intervals (VSIs) have been shown to be substantially quicker than the fixed sampling intervals (FSI) EWMA control charts in detecting process mean shifts. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be true for some processes. In the present paper, the performances of the EWMA and combined X¯–EWMA control charts with VSIs are evaluated under non-normality. It is shown that adding the VSI feature to the EWMA control charts results in very substantial decreases in the expected time to detect shifts in process mean under both normality and non-normality. However, the combined X¯–EWMA chart has its false alarm rate and its detection ability is affected if the process data are not normally distributed.

Control chart is one of tools for quality control of production. control chart is one of tool that can be used to control the quality of production for variable data such as weight of product. However, there is a weakness of control chart, which is sensitivless in detecting small shift of the mean process. Exponentially Weighted Moving Average (EWMA) control chart is one of the quality control tool that can improve the weakness of control chart. EWMA control chart has a weight smoothing parameter (λ) which makes EWMA control chart more sensitive in detecting small shifts the process mean. Each production data will be weighted and past production data will be affected by present production data. EWMA control chart will be used to make a control chart by weight of cigarette data in Brak Megawon III PT Djarum Kudus. In this study, will be established to assist in the GUI Matlab computational EWMA methods chart controller to control the quality of production at PT Djarum Kudus.In this study showed that the most optimum weight refiner which is at a value of 0.6. Keyword : EWMA, Smoothing weight (λ), GUI, Weight of cigarette

Monitoring rare health events, as a significant public health subject, has been considered recently by different authors. In this regard, different statistical methods such as g-type control chart, Poisson CUSUM control chart, sets-based methods, and Bernoulli CUSUM chart have been developed. Zero-inflated binomial (ZIB) distribution, due to its structure, can also be considered to develop methods for monitoring rare health-related events. If zero inflation is considered in the sampling data, and the sampling subgroup size is mandatory greater than 1, then the data best fits the ZIB distribution and the aforementioned control charts cannot be applied. ZIB distribution assumes that random shocks, corresponding to rare health events, occur and then number of failures in each subgroup fits a binomial distribution. In this paper, an exponentially weighted moving average (EWMA) control chart is applied for ZIB data to develop a ZIB-EWMA chart. Since ZIB-EWMA statistic values are not independent, Markov chain approach is considered to evaluate the performance of the proposed control chart in terms of average run length (ARL). According to the ARL measure, this ZIB-EWMA chart has a better performance in comparison with the methods available in the literature. In addition, a real case study related to rare infections in a hospital is investigated to show the applicability of the proposed control chart.

Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are commonly used for monitoring the process mean. In this paper, a new hybrid EWMA (HEWMA) control chart is proposed by mixing two EWMA control charts. An interesting feature of the proposed control chart is that the traditional Shewhart and EWMA control charts are its special cases. Average run lengths are used to evaluate the performances of each of the control charts. It is worth mentioning that the proposed HEWMA control chart detects smaller shifts substantially quicker than the classical CUSUM, classical EWMA and mixed EWMA–CUSUM control charts. Copyright © 2012 John Wiley & Sons, Ltd.

The memory control charts, including cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts, are widely used to monitor small‐to‐moderate shifts in the process location and/or dispersion. The homogenously weighted moving average (HWMA) control chart is the advanced form of the EWMA control chart to monitor process location shifts. Besides, the auxiliary information‐based memory control charts efficiently monitor process location shifts. The objective of this study is to propose an auxiliary information based double HWMA, symbolized as control chart to further enhance the monitoring of process location shifts. The control chart is modeled by mixing the auxiliary information‐based HWMA plotting statistic features into the other HWMA control chart. For numerical results, Monte Carlo simulations are used as a computational technique. Famous performance measures including average run length (), extra quadratic loss, relative , and performance comparison index are used to compare the performance of proposed control chart against other control charts including classical CUSUM and EWMA, mixed ‐, auxiliary information based EWMA (), HWMA, auxiliary information based HWMA (), and double HWMA control charts. The comparisons revealed that the proposed control chart outperformed other control charts, especially for small‐to‐moderate process location shifts. An automobile braking system application is also provided for users and practitioners to demonstrate the importance of the proposed study from a practical perspective.

The adaptive exponentially weighted moving average (AEWMA) control charts are the advanced form of classical memory control charts used for efficiently monitoring small-to-large shifts in the process parameters (location and/or dispersion). These AEWMA control charts estimate the unknown shifts using exponentially weighted moving average (EWMA) or cumulative sum (CUSUM) control charts statistics. The hybrid EWMA (HEWMA) control chart is preferred over classical memory control charts to detect early shifts in process parameters. So, this study presents a new auxiliary information-based (AIB) AEWMA (IAEWMAAIB) control chart for process location that estimates the unknown location shift using HEWMA statistic. The objective is to develop an unbiased location shift estimator using HEWMA statistic and then adaptively update the smoothing constant. The shift estimation using HEWMA statistic instead of EWMA or CUSUM statistics boosts the performance of the proposed IAEWMAAIB control chart. The Monte Carlo simulation technique is used to get the numerical results. Famous performance evaluation measures like average run length, extra quadratic loss, relative average run length, and performance comparison index are used to evaluate the performance of the proposed chart with existing counterparts. The comparison reveals the superiority of the proposed control chart. Finally, two real-life applications from the glass manufacturing industry and physicochemical parameters of groundwater are considered to show the proposed control chart’s implementation procedure and dominance.

Statistical process control provides package of statistical tools applied for improving quality of manufacturing, production and services processes. Cumulative sum, exponentially weighted moving average (EWMA) and progressive mean charts belong to family of memory-type charts which effectively spot small and persistent shifts in the process parameter(s). EWMA chart requires normality and a proper choice of smoothing parameter to perform efficiently. Any deviation from these conditions affects its performance in terms of efficacy and robustness. For the said concerns, progressive exponentially weighted moving average (PEWMA) chart is developed to monitor the shifts in the process location. The performance of the proposed PEWMA chart is evaluated in terms of average run length and some other metrics of run length distribution. The assessment of the proposed chart has been made under standard normal, Student’s t, gamma, Laplace, logistic, exponential, contaminated normal and lognormal distributions. The performance of the proposed PEWMA chart is also compared with some existing competitors including the classical EWMA, classical CUSUM, HWMA, MEC, MCE and DEWMA charts. The analysis reveals that the proposal offers a design structure which has high sensitivity to small and persistent drifts in the process mean and has advantage of robustness under non-normal scenarios. An application from substrates manufacturing process (in which flow width of the resist is the key quality characteristic) is also provided for practical implementations.

Different control charts are proposed by many researchers for the aim of detecting process shifts in the mean and assuring quality of the product. Exponentially weighted moving average (EWMA) control charts is one of the famous charts which performs well in detecting small shifts in the process mean. In this paper, a new statistic based on different smoothing parameters is proposed to improve the performance of the exponentially weighted moving average (EWMA) control chart in detecting large shifts as well as small and medium shifts. The performance of the developed scheme based on the proposed smoothing parameter is evaluated in terms of average run length criterion in comparison with the traditional EWMA control chart. The results show the better performance of the proposed scheme rather than the traditional EWMA control charts in most cases.

Exponentially weighted moving average (EWMA) control chart can be designed to quickly detect small shifts in the mean of a sequence of independent normal observations. But this chart cannot perform well for skewed distribution. The main goal of this article is to suggest an EWMA control chart method that can be used to monitoring small shifts in a skewed distribution. Weighted variance method is introduced to construct a kind of EWMA chart for skewed distribution and the optimization design of this chart is given by using average run length as a performance assessment criteria. Pair of asymmetry control limits could be evaluated by sample dates in skewed distribution. The advantage of this method in detecting little drift for skewed distribution was illustrated by comparing with others control charts.

It is known that both the optimal exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are based on a given reference value $\delta$, which, for the CUSUM chart, is the magnitude of a shift in the mean to be detected quickly. In this paper a generalized EWMA control chart (GEWMA) which does not depend on $\delta$ is proposed for detecting the mean shift. We compare theoretically the GEWMA control chart with the optimal EWMA, CUSUM and the generalized likelihood ratio (GLR) control charts. The results of the comparison in which the in-control average run length approaches infinity show that the GEWMA control chart is better than the optimal EWMA control chart in detecting a mean shift of any size and is also better than the CUSUM control chart in detecting the mean shift which is not in the interval $(0.7842\delta ,1.3798\delta )$. Moreover, the GLR control chart has the best performance in detecting mean shift among the four control charts except when detecting a particular mean shift $\delta,$ when the in-control average run length approaches infinity.

Control charts applied to simulated sow herd datasets