Mu'azu Ramat Abujiya

Quality Control Chart for the Mean using Double Ranked Set Sampling

In this paper, an attempt is made to develop Quality Control Charts for monitoring the process mean based on Double Ranked Set Sampling (DRSS) rather than the traditional Simple Random Sampling (SRS). Considering a normal population and several shift values, the performance of the Average Run Length (ARL) of these new charts was compared with the control charts based on Ranked Set Sampling (RSS) and SRS with the same number of observations. It is shown that the new charts do a better job of detecting changes in process mean compared with SRS and RSS.

Improving the Performance of Combined Shewhart–Cumulative Sum Control Charts

For an improved monitoring of process parameters, it is generally desirable to have efficient designs of control charting structures. The addition of Shewhart control limits to the cumulative sum (CUSUM) control chart is a simple monitoring scheme sensitive to wide range of mean shifts. To improve the detection ability of the combined Shewhart–CUSUM control chart to off-target processes, we developed the scheme using ranked set sampling instead of the traditional simple random sampling. We investigated the run length properties of the Shewhart–CUSUM with ranked set samples and compared their performance with certain established control charts. It is revealed that the proposed schemes offer better protection against different types of mean shifts than the existing counterparts including classical Shewhart, classical CUSUM, classical combined Shewhart–CUSUM, adaptive CUSUM, double CUSUM, three simultaneous CUSUM, combined Shewhart-weighted CUSUM, runs rules-based CUSUM and the mixed exponentially weighted moving average-CUSUM. Applications on real data sets are also given to demonstrate the implementation simplicity of the proposed schemes

Improving the Performance of Exponentially Weighted Moving Average Control Charts

A control chart is a graphical tool used for monitoring a production process and quality improvement. One such charting procedure is the Shewhart-type control chart, which is sensitive mainly to the large shifts. For small shifts, the cumulative sum (CUSUM) control charts and exponentially weighted moving average (EWMA) control charts were proposed. To further enhance the ability of the EWMA control chart to quickly detect wide range process changes, we have developed an EWMA control chart using the median ranked set sampling (RSS), median double RSS and the double median RSS. The findings show that the proposed median-ranked sampling procedures substantially increase the sensitivities of EWMA control charts. The newly developed control charts dominate most of their existing counterparts, in terms of the run-length properties, the Average Extra Quadratic Loss and the Performance Comparison Index. These include the classical EWMA, fast initial response EWMA, double and triple EWMA, runs-rules EWMA, the max EWMA with mean-squared deviation, the mixed EWMA-CUSUM, the hybrid EWMA and the combined Shewhart–EWMA based on ranks. An application of the proposed schemes on real data sets is also given to illustrate the implementation and procedural details of the proposed methodology. Copyright

Increasing the sensitivity of cumulative sum charts for location

The cumulative sum (CUSUM) chart is a very effective control charting procedure used for the quick detection of small-sized and moderate-sized changes. It can detect small process shifts missed by the Shewhart-type control chart, which is sensitive mainly to large shifts. To further enhance the sensitivity of the CUSUM control chart at detecting very small process disturbances, this article presents CUSUM control charts based on well-structured sampling procedures, double ranked set sampling, median-double ranked set sampling, and double-median ranked set sampling. These sampling techniques significantly improve the overall performance of the CUSUM chart over the entire process mean shift range, without increasing the false alarm rate. The newly developed control schemes do not only dominate most of the existing charts but are also easy to design and implement as illustrated through an application example of real datasets. The control schemes used for comparison in this study include the conventional CUSUM chart, a fast initial response CUSUM chart, a 2-CUSUM chart, a 3-CUSUM chart, a runs rules-based CUSUM chart, the enhanced adaptive CUSUM chart, the CUSUM chart based on ranked set sampling (RSS), and the single CUSUM and combined Shewhart-CUSUM charts based on median RSS

Combined Shewhart CUSUM charts using auxiliary variable

New Combined Shewhart CUSUM charts are proposed.The proposed scheme consists of mean estimator with one auxiliary variable.The study shows that the proposed charts outperform their existing counterparts.A real-life industrial example is provided. A control chart is an important statistical tool for monitoring disturbances in a statistical process, and it is richly applied in the industrial sector, the health sector and the agricultural sector, among others. The Shewhart chart and the Cumulative Sum (CUSUM) chart are traditionally used for detecting large shifts and small shifts, respectively, while the Combined Shewhart-CUSUM (CSC) monitors both small and large shifts. Using auxiliary information, we propose new CSC (MiCSC) charts with more efficient estimators (the Regression-type estimator, the Ratio estimator, the Singh and Tailor estimator, the power ratio-type estimator, and the Kadilar and Cingi estimators) for estimating the location parameter. We compare the charts using average run length, standard deviation of the run length and extra quadratic loss, with other existing charts of the same purpose and found out that some of the MiCSC charts outperform their existing counterparts. At last, a real-life industrial example is provided.

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

A New Combined Shewhart–Cumulative Sum S Chart for Monitoring Process Standard Deviation

The combined application of a Shewhart chart and cumulative sum (CUSUM) control chart is an effective tool for the detection of all sizes of process shifts as the scheme combines the advantages of a CUSUM at detecting small to moderate shifts and Shewhart for the quick detection of very large shifts. This article proposes new combined Shewhart-CUSUM S charts based on the extreme variations of ranked set sampling technique, for efficient monitoring of changes in the process dispersion. Using Monte Carlo simulations, the combined scheme is designed to minimize the average extra quadratic loss over the entire process shift domain. The results show that the combined Shewhart-CUSUM S charts uniformly outperform several other procedures for detecting increases and decreases in the process variability. Moreover, the proposed scheme can detect changes that are small enough to escape the Shewhart S chart or fairly large to escape detection by the CUSUM S chart. Numerical example is given to illustrate the practical application of the proposed scheme using real industrial data.

Combined application of Shewhart and cumulative sum R chart for monitoring process dispersion

This study analyzes the performance of combined applications of the Shewhart and cumulative sum (CUSUM) range R chart and proposes modifications based on well-structured sampling techniques, the extreme variations of ranked set sampling, for efficient monitoring of changes in the process dispersion. In this combined scheme, the Shewhart feature enables quick detection of large shifts from the target standard deviation while the CUSUM feature takes care of small to moderate shifts from the target value. We evaluate the numerical performance of the proposed scheme in terms of the average run length, standard deviation of run length, the average ratio average run length, and average extra quadratic loss. The results show that the combined scheme can detect changes in the process that were small or large enough to escape detection by the lone Shewhart R chart or CUSUM R chart, respectively. We present a comparison of the proposed schemes with several dispersion charts for monitoring changes in process variability. The practical application of the proposed scheme is demonstrated using real industrial data.

A New EWMA Control Chart for Monitoring Poisson Observations

Quality control charts based on exponentially weighted moving average (EWMA) has been widely used for monitoring continuous process data. However, many quality characteristics of interest are in the form of counts for nonconformities and are often monitored by a Poisson model. In this article, we introduce a new design structure for the Poisson EWMA charts for monitoring Poisson processes. The proposed scheme is based on a well-structured sampling technique, ranked set sampling instead of the traditional simple random sampling. Using Monte Carlo simulations, we compute the run length properties of the new Poisson EWMA chart and compare their relative performance with the existing schemes for monitoring increases and decreases at the Poisson rate. It is found that the new scheme significantly improves the classical procedures for detecting changes in the Poisson processes. Finally, we illustrate the practical application of the proposed scheme through numerical example. Copyright

The three statistical control charts using ranked set sampling

This article investigated the performance of the three common statistical control charts, the Shewhart x̅ chart, cumulative sum (CUSUM) chart, and exponentially weighted moving average (EWMA) chart for location using ranked set sampling (RSS) instead of the traditional simple random sampling (SRS). Considering a normal population, a Monte Carlo simulation is carried out for several shift values for each of the control chart. The average run length (ARL) showed that the control charts based on RSS data are superior to their corresponding SRS counterparts with no significant difference between CUSUM and EWMA charts. There is an interesting increase in the sensitivity of RSS based Shewhart x̅ chart relative to other charts.