Abdul Haq

A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean

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

Improved quality control charts for monitoring the process mean, using double-ranked set sampling methods

Statistical control charts are widely used in the manufacturing industry. The Shewhart-type control charts are developed to improve the monitoring process mean by using the double quartile-ranked set sampling, quartile double-ranked set sampling, and double extreme-ranked set sampling methods. In terms of the average run length, the performance of the proposed control charts are compared with the existing control charts based on simple random sampling, ranked set sampling and extreme-ranked set sampling methods. An application of real data is also considered to investigate the performance of the suggested process mean control charts. The findings of the study revealed that the newly suggested control charts are superior to the existing counterparts.

Improved Exponentially Weighted Moving Average Control Charts for Monitoring Process Mean and Dispersion

Exponentially weighted moving average (EWMA) control charts are mostly used to monitor the manufacturing processes. In this paper, we propose some improved EWMA control charts for detecting the random shifts in the process mean and process dispersion. These EWMA control charts are based on the best linear unbiased estimators obtained under ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS), named EWMA-ORSS and EWMA-OIRSS charts, respectively. Monte Carlo simulations are used to estimate the average run length, median run length and standard deviation of run length of the proposed EWMA control charts. It is observed that the EWMA-ORSS mean control chart is able to detect the random shifts in the process mean substantially quicker than the Shewhart-cumulative sum and the Shewhart-EWMA control charts based on the RSS scheme. Both EWMA-ORSS and EWMA-OIRSS location charts perform better than the classical EWMA, hybrid EWMA, Shewhart-EWMA and fast initial response-EWMA charts. The EWMA-ORSS dispersion control chart performs better than the simple random sampling based CS-EWMA and other EWMA control charts in efficient detection of the random shifts that occur in the process variability. An application to real data is also given to explain the implementation of the proposed EWMA control charts. Copyright

An improved mean deviation exponentially weighted moving average control chart to monitor process dispersion under ranked set sampling

Quality-control charts are widely used to monitor and detect shifts in the process mean and dispersion. Abbasi and Miller [MDEWMA chart: an efficient and robust alternative to monitor process dispersion, J Stat Comput Simul 2013;83:247–268] suggested a robust mean deviation exponentially weighted moving average (MDEWMA) control chart for monitoring process dispersion under simple random sampling. In this study, an improved MDEWMA (IMDEWMA) control chart is proposed under ranked set sampling to monitor process dispersion. Detailed Monte Carlo simulations are performed from symmetric and asymmetric populations to investigate the performances of the proposed and existing control charts in terms of average run length (ARL), median run length and standard deviation of run length. An application to real-life data is also presented to illustrate the use of the IMDEWMA control chart. It is observed that the IMDEWMA control chart indicates a shift in process dispersion substantially quicker than the MDEWMA control chart, while maintaining comparable ARLs when the process is in control.

Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes

Control charts are a powerful statistical process monitoring tool often used to monitor the stability of manufacturing processes. In quality control applications, measurement errors adversely affect the performance of control charts. In this paper, we study the effect of measurement error on the detection abilities of the exponentially weighted moving average (EWMA) control charts for monitoring process mean based on ranked set sampling (RSS), median RSS (MRSS), imperfect RSS (IRSS) and imperfect MRSS (IMRSS) schemes. We also study the effect of multiple measurements and non-constant error variance on the performances of the EWMA control charts. The EWMA control chart based on simple random sampling is compared with the EWMA control charts based on RSS, MRSS, IRSS and IMRSS schemes. The performances of the EWMA control charts are evaluated in terms of out-of-control average run length and standard deviation of run lengths. It turns out that the EWMA control charts based on MRSS and IMRSS schemes are better than their counterparts for all measurement error cases considered here.

New Synthetic EWMA and Synthetic CUSUM Control Charts for Monitoring the Process Mean

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are potentially powerful statistical process monitoring tools because of their excellent speed in detecting small to moderate persistent process shifts. Recently, synthetic EWMA (SynEWMA) and synthetic CUSUM (SynCUSUM) control charts have been proposed based on simple random sampling (SRS) by integrating the EWMA and CUSUM control charts with the conforming run length control chart, respectively. These synthetic control charts provide overall superior detection over a range of mean shift sizes. In this article, we propose new SynEWMA and SynCUSUM control charts based on ranked set sampling (RSS) and median RSS (MRSS) schemes, named SynEWMA-RSS and SynEWMA-MRSS charts, respectively, for monitoring the process mean. Extensive Monte Carlo simulations are used to estimate the run length characteristics of the proposed control charts. The run length performances of these control charts are compared with their existing powerful counterparts based on SRS, RSS and MRSS schemes. It turns out that the proposed charts perform uniformly better than the Shewhart, optimal synthetic, optimal EWMA, optimal CUSUM, near-optimal SynEWMA, near-optimal SynCUSUM control charts based on SRS, and combined Shewhart-EWMA control charts based on RSS and MRSS schemes. A similar trend is observed when constructing the proposed control charts based on imperfect RSS schemes. An application to a real data is also provided to demonstrate the implementations of the proposed SynEWMA and SynCUSUM control charts. Copyright

A New Maximum Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean and Dispersion

Maximum exponentially weighted moving average (MaxEWMA) control charts have attracted substantial interest because of their ability to simultaneously detect increases and decreases in both the process mean and the process variability. In this paper, we propose new MaxEWMA control charts based on ordered double ranked set sampling (ODRSS) and ordered imperfect double ranked set sampling (OIDRSS) schemes, named MaxEWMA-ODRSS and MaxEWMA-OIDRSS control charts, respectively. The proposed MaxEWMA control charts are based on the best linear unbiased estimators obtained under ODRSS and OIDRSS schemes. Extensive Monte Carlo simulations are used to estimate the average run length and standard deviation of the run length of the proposed MaxEWMA control charts. The run length performances and the diagnostic abilities of the proposed MaxEWMA control charts are compared with that of their counterparts based on simple random sampling (SRS), ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling schemes (OIRSS) schemes, that is, MaxEWMA-SRS, maximum generally weighted moving average (MaxGWMA-SRS), MaxEWMA-ORSS and MaxEWMA-OIRSS control charts. It turns out that the proposed MaxEWMA-ODRSS and MaxEWMA-OIDRSS control charts perform uniformly better than the MaxEWMA-SRS, MaxGWMA-SRS, MaxEWMA-ORSS and MaxEWMA-OIRSS control charts in simultaneous detection of shifts in the process mean and variability. An application to real data is also provided to illustrate the implementations of the proposed and existing MaxEWMA control charts. Copyright

New Synthetic Control Charts for Monitoring Process Mean and Process Dispersion

A statistical quality control chart is widely recognized as a potentially powerful tool that is frequently used in many manufacturing and service industries to monitor the quality of the product or manufacturing processes. In this paper, we propose new synthetic control charts for monitoring the process mean and the process dispersion. The proposed synthetic charts are based on ranked set sampling (RSS), median RSS (MRSS), and ordered RSS (ORSS) schemes, named synthetic-RSS, synthetic-MRSS, and synthetic-ORSS charts, respectively. Average run lengths are used to evaluate the performances of the control charts. It is found that the synthetic-RSS and synthetic-MRSS mean charts perform uniformly better than the Shewhart mean chart based on simple random sampling (Shewhart-SRS), synthetic-SRS, double sampling-SRS, Shewhart-RSS, and Shewhart-MRSS mean charts. The proposed synthetic charts generally outperform the exponentially weighted moving average (EWMA) chart based on SRS in the detection of large mean shifts. We also compare the performance of the synthetic-ORSS dispersion chart with the existing powerful dispersion charts. It turns out that the synthetic-ORSS chart also performs uniformly better than the Shewhart-R, Shewhart-S, synthetic-R, synthetic-S, synthetic-D, cumulative sum (CUSUM) ln S2, CUSUM-R, CUSUM-S, EWMA-ln S2, and change point CUSUM charts for detecting increases in the process dispersion. A similar trend is observed when the proposed synthetic charts are constructed under imperfect RSS schemes. Illustrative examples are used to demonstrate the implementation of the proposed synthetic charts. Copyright

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

An Improved Maximum Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean and Variability

Maximum exponentially weighted moving average (MaxEWMA) control charts have gained considerable attention for detecting changes in both process mean and process variability. In this paper, we propose an improved MaxEWMA control charts based on ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS) schemes for simultaneous detection of both increases and decreases in the process mean and/or variability, named MaxEWMA-ORSS and MaxEWMA-OIRSS control charts. These MaxEWMA control charts are based on the best linear unbiased estimators of location and scale parameters obtained under ORSS and OIRSS methods. Extensive Monte Carlo simulations have been used to estimate the average run length and standard deviation of run length of the proposed MaxEWMA control charts. These control charts are compared with their counterparts based on simple random sampling (SRS), that is, MaxEWMA-SRS and MaxGWMA-SRS control charts. The proposed MaxEWMA-ORSS and MaxEWMA-OIRSS control charts are able to perform better than the MaxEWMA-SRS and MaxGWMA-SRS control charts for detecting shifts in the process mean and dispersion. An application to real data is provided to illustrate the implementation of the proposed MaxEWMA control charts. Copyright