Economic‐statistical design of 2‐of‐2 and 2‐of‐3 runs rule scheme

In this paper, we investigate the economic‐statistical design method for the 2‐of‐2 runs rule and the 2‐of‐3 runs rule. The Markov chain approach is used to obtain the average run length and the process cycle time. In addition, a simplified algorithm is presented to search the optimal setting of the design parameters. A numerical example and sensitivity analysis are also provided to compare the performances of the runs rules. The results show that the use of runs rule scheme can reduce operating cost comparing with the Shewhart control chart while maintaining a good statistical performance. Copyright © 2008 John Wiley & Sons, Ltd.     

One‐sided runs‐rules schemes to monitor autocorrelated time series data using a first‐order autoregressive model with skip sampling strategies

In some industrial or health‐related processes, it makes more practical sense to monitor either an increase only or a decrease only in the quality characteristic of interest. Consequently, in this paper, we propose four one‐sided Shewhart charts supplemented with runs‐rules to monitor the mean of autocorrelated normally distributed samples using a stationary first‐order autoregressive model. To counteract the negative effect of autocorrelation, we implement a sampling strategy which involves sampling of non‐neighboring observations to form rational subgroups. The Markov chain technique is used to derive zero‐state and steady‐state closed‐form expressions of the specific shift performance metric, ie, average run‐length (ARL). Moreover, we compute the expected ARL metric which evaluates each monitoring scheme based on all specified range of possible values of the shift parameter, or more specifically, from a global point of view and thus gives a different perspective from the specific shift ARL metric. We observed that the steady‐state improved w‐of‐w and the improved 2‐of‐(H + 1) schemes yield a better overall performance than their corresponding basic counterparts for all different levels of autocorrelation. A real‐life example is provided to illustrate the implementation of the monitoring schemes proposed here.     

Monitoring of Time‐Between‐Events with a Generalized Group Runs Control Chart

Control charting methods for time between events (TBE) is important in both manufacturing and nonmanufacturing fields. With the aim to enhance the speed for detecting shifts in the mean TBE, this paper proposes a generalized group runs TBE chart to monitor the mean TBE of a homogenous Poisson failure process. The proposed chart combines a TBE subchart and a generalized group conforming run length subchart. The zero‐state and steady‐state performances of the proposed chart were evaluated by applying a Markov chain method. Overall, it is found that the proposed chart outperforms the existing TBE charts, such as the T, T_r, EWMA‐T, Synth‐T_r, and GR‐T_r charts. Copyright © 2015 John Wiley & Sons, Ltd.     

A Shewhart‐type Control Scheme to Monitor Weibull Data without Subgrouping

This study proposes a Shewhart control scheme to simultaneously monitor the shape parameter and the scale parameter of Weibull data without subgrouping. The proposed control scheme comprises two charts: the X chart and the moving‐ratio (MRa) chart. The X chart plots individual observations to detect the shift of the scale parameter by assuming that the shape parameter is in‐control. In contrast, the MRa chart plots moving ratios, the minimum of two consecutive Weibull data divided by the maximum of them, to detect the shift of the shape parameter. This study models the transition process of the proposed control scheme as a Markov chain to calculate two performance measures: the average number of observations to signal and the average run length. Performance analysis shows that the proposed control scheme is effective in detecting the shift of parameters, especially for the downward shift of the shape parameter. Finally, the implementation of the proposed control scheme is illustrated in two skewed data sets. Copyright © 2013 John Wiley & Sons, Ltd.     

On the Performance of Shewhart‐type Synthetic and Runs‐rules Charts Combined with an Chart

A synthetic chart is a combination of a conforming run‐length chart and an chart, or equivalently, a 2‐of‐(H + 1) runs‐rules (RR) chart with a head‐start feature. However, a synthetic chart combined with an chart is called a Synthetic‐ chart. In this article, we build a framework for Shewhart Synthetic‐ and improved RR (i.e., 1‐of‐1 or 2‐of‐(H + 1) without head‐start) charts by conducting an in‐depth zero‐state and steady‐state study to gain insight into the design of different classes of these schemes and their average run‐length performance using the Markov chain imbedding technique. More importantly, we propose a modified side‐sensitive Synthetic‐ chart, and then using overall performance measures (i.e., the extra quadratic loss, average ratio of average run‐length, and performance comparison index), we show that this new chart has a uniformly better performance than its Shewhart competitors. We also provide easy‐to‐use tables for each of the chart's design parameters to aid practical implementation. Moreover, a performance comparison with their corresponding counterparts (i.e., synthetic and RR charts) is conducted. Copyright © 2015 John Wiley & Sons, Ltd.     

A New Distribution‐free Control Chart for Joint Monitoring of Unknown Location and Scale Parameters of Continuous Distributions

While the assumption of normality is required for the validity of most of the available control charts for joint monitoring of unknown location and scale parameters, we propose and study a distribution‐free Shewhart‐type chart based on the Cucconi 1 statistic, called the Shewhart‐Cucconi (SC) chart. We also propose a follow‐up diagnostic procedure useful to determine the type of shift the process may have undergone when the chart signals an out‐of‐control process. Control limits for the SC chart are tabulated for some typical nominal in‐control (IC) average run length (ARL) values; a large sample approximation to the control limit is provided which can be useful in practice. Performance of the SC chart is examined in a simulation study on the basis of the ARL, the standard deviation, the median and some percentiles of the run length distribution. Detailed comparisons with a competing distribution‐free chart, known as the Shewhart‐Lepage chart (see Mukherjee and Chakraborti 2 ) show that the SC chart performs just as well or better. The effect of estimation of parameters on the IC performance of the SC chart is studied by examining the influence of the size of the reference (Phase‐I) sample. A numerical example is given for illustration. Summary and conclusions are offered. Copyright © 2013 John Wiley & Sons, Ltd.     

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 Copyright © 2012 John Wiley & Sons, Ltd.     

Nonparametric Synthetic Control Charts for Process Variation

In this article, we propose nonparametric synthetic and side‐sensitive synthetic control charts for controlling fraction nonconforming due to increase in the process variation. Synthetic control chart is a combination of sign and conforming run length control charts. We compare performance of the proposed control charts with the Shewhart sign and S² charts. Our performance study shows that the proposed control charts have a higher power of detecting out‐of‐control signal. We also study the steady‐state behavior of a nonparametric synthetic control chart. We present a Markov chain model to evaluate the steady‐state average run length of the synthetic and side‐sensitive synthetic control charts. Copyright © 2011 John Wiley & Sons, Ltd.     

A t‐chart for Monitoring Multi‐variety and Small Batch Production Run

Statistical process control is an important tool to monitor and control a process. It is used to ensure that the manufacturing process operates in the in‐control state. Multi‐variety and small batch production runs are common in manufacturing environments like flexible manufacturing systems and Just‐in‐Time systems, which are characterized by a wide variety of mixed products with small volume for each kind of production. It is difficult to apply traditional control charts efficiently and effectively in such environments. The method that control charts are plotted for each individual part is not proper, since the successive state of the manufacturing process cannot be reflected. In this paper, a proper t‐chart is proposed for implementation in multi‐variety and small batch production runs to monitor the process mean, and its statistical properties are evaluated. The run length distribution of the proposed t‐chart has been obtained by modelling the multi‐variety process. The ARL performance for various shifts, number of product types, and subgroup sizes has also been obtained. The results show that the t‐chart can be successfully implemented to monitor a multi‐variety production run. Finally, illustrative examples show that the proposed t‐chart is effective in multi‐variety and small batch manufacturing environment. Copyright © 2013 John Wiley & Sons, Ltd.     

INDEX TO CONTENTS, 1983

This article gives a simple and efficient method, using Markov chains, to obtain the exact run-length properties of Shewhart control charts with supplementary runs rules. Average run-length comparisons are made among the Shewhart chart with supplementary runs rules, the basic Shewhart chart, and the cumulative sum (CUSUM) chart.     

Phase I control charts for independent Bernoulli data

Phase I Shewhart p, np and runs of conforming charts are investigated. The performance of these charts are assessed using the probability of a false alarm. As with other Phase I Shewhart charts, the probability of a false alarm increases as the number, m, of samples increases for a fixed sample size, n. For a fixed value of m, the probability of at least one signal decreases as the sample size n increases. The probability of a signal for a runs of conforming chart depends on the number of samples m. Like the p and np charts, as m increases the probability of a false alarm increases. Unlike the p and np charts, the false alarm rate for a runs of conforming chart does not depend on the in‐control value of p. Copyright © 2001 John Wiley & Sons, Ltd.     

Properties of the Markov‐Dependent Attribute Control Chart with Estimated Parameters

The performance of attribute control charts that monitor Markov‐dependent data is usually evaluated under the assumption of known process parameters, that is, known values of a the probability an item is nonconforming given the previous item is conforming and b the probability an item is conforming given the previous item is nonconforming. In practice, these parameters are usually not known and are calculated from an in‐control Phase I‐data set. In this paper, a comparison of the in‐control ARL (average run length) properties of the attribute chart for Markov‐dependent data with known and estimated parameters is presented. The probability distribution of the estimators is developed and used to calculate the in‐control ARL and standard deviation of the run length of the chart with estimated parameters. For particular values of a and b, the in‐control ARL values of the charts with estimated parameters may be very different than those with known parameters. The size of the Phase‐I data set needed for charts with estimated parameters to exhibit the same in‐control ARL properties as those with known parameters may vary widely depending on the parameters of the process, but in general, large samples are needed to obtain accurate estimates. As the Phase‐I sample size increases, the in‐control ARL values of the charts with estimated parameters approach that of the known parameter case but not in a monotonic fashion as in the case of the X‐bar chart. Copyright © 2015 John Wiley & Sons, Ltd.     

M‐ATTRIVAR: An attribute‐variable chart to monitor multivariate process means

In this paper, an attribute‐variable control chart, namely, M‐ATTRIVAR, is introduced to monitor possible shifts in a vector of means. The monitoring starts using an attribute chart (classifying the units as approved or not using a gauge) and continues in such a way until a warning signal is given, shifting the control to a variable chart for the next sampling. If the variable chart does not confirm the warning, the monitoring returns to an attribute control. Otherwise, the monitoring remains with the variable chart. Whenever any of the charts (attribute or variable) signals an alarm, the control scheme triggers an alarm. The main advantage of this new proposal is the possibility of judging the state of the process only by the attribute chart most of the time (normally more economical and faster). The performance of the M‐ATTRIVAR control chart is compared versus the main competitor (T² control chart) in terms of performance detection (out‐of‐control average run length) but also economically (average sampling cost). The M‐ATTRIVAR is always cheaper than T², and in many scenarios, it detects quicker process shifts than the T² control chart. A numerical example illustrates a practical situation.     

The economic performance of the Shewhart t chart

In the production of small batches of customized parts, high flexibility and frequent switching of production from one product variant to another could not allow for the implementation of a control chart to monitor the process. In fact, when a short‐run production should be started, the distribution parameters of the quality characteristics to be monitored are frequentlytextitunknown and the production run is too short to get sufficient Phase I samples. To overcome this problem, the statistical properties of Shewhart t charts monitoring a short production run have been recently discussed in literature. In this paper, we investigate their economic performance: the SPC inspection cost optimization is constrained by the manufacturing and the inspection activities configuration. The decision variables of the problem include the chart design parameters and the size of batches of parts to be worked and released to the local inspection area. A numerical analysis aimed at evaluating the economic performance of the Shewhart t chart vs the Shewhart chart with known parameters has been performed. The expected economic loss associated with the implementation of the Shewhart t chart is acceptable with respect to the ‘ideal’ condition of the control chart with known parameters when the cost optimization is achieved without a statistical constraint limiting the number of expected false alarms. Finally, the effect of an erroneous initial set‐up on the correctness of the inspection cost estimation has been investigated. Copyright © 2011 John Wiley & Sons, Ltd.     

An overview of synthetic‐type control charts: Techniques and methodology

In this paper, we provide an overview of a class of control charts called the synthetic charts. Synthetic charts are a combination of a traditional chart (such as a Shewhart, CUSUM, or EWMA chart) and a conforming run‐length (CRL) chart. These charts have been considered in order to maintain the simplicity and improve the performance of small and medium‐sized shift detection of the traditional Shewhart charts. We distinguish between different types of synthetic‐type charts currently available in the literature and highlight how each is designed and implemented in practice. More than 100 publications on univariate and multivariate synthetic‐type charts are reviewed here. We end with some concluding remarks and a list of some future research ideas.     

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. Copyright © 2014 John Wiley & Sons, Ltd.     

Mixed Exponentially Weighted Moving Average–Cumulative Sum Charts for Process Monitoring

The control chart is a very popular tool of statistical process control. It is used to determine the existence of special cause variation to remove it so that the process may be brought in statistical control. Shewhart‐type control charts are sensitive for large disturbances in the process, whereas cumulative sum (CUSUM)–type and exponentially weighted moving average (EWMA)–type control charts are intended to spot small and moderate disturbances. In this article, we proposed a mixed EWMA–CUSUM control chart for detecting a shift in the process mean and evaluated its average run lengths. Comparisons of the proposed control chart were made with some representative control charts including the classical CUSUM, classical EWMA, fast initial response CUSUM, fast initial response EWMA, adaptive CUSUM with EWMA‐based shift estimator, weighted CUSUM and runs rules–based CUSUM and EWMA. The comparisons revealed that mixing the two charts makes the proposed scheme even more sensitive to the small shifts in the process mean than the other schemes designed for detecting small shifts. Copyright © 2012 John Wiley & Sons, Ltd.     

Design of Runs Rules Schemes

Runs rules are often used to increase the sensitivity of a Shewhart control chart. In this work, plots of various runs rules schemes are given to simplify the determination of control limits based on a desired in-control average run length (ARL₀).     

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 © 2014 John Wiley & Sons, Ltd.     

On the effectiveness of the unit sample size for standard control charts: ARL VS. Aurl

In this paper we investigate the use of the average unit run length (AURL) as an important measure of the effectiveness of various quality control charting schemes. In particular we focus on its appropriateness for normally distributed processes that tend to produce units (or measurements) at slow rates. In our investigations with the standard Shewhart X? and R charts, as well as the CUSUM chart, AURL shows that a sample size of n=1 can yield the fastest means of detecting shifts.