Search results

This paper seeks to propose a univariate robust control chart for location and the necessary table of factors for computing the control limits and the central line as an alternative to the Shewhart X¯ control chart.

The proposed method is based on two robust estimators, namely, the sample median, MD, to estimate the process mean, μ, and the median absolute deviation from the sample median, MAD, to estimate the process standard deviation, σ. A numerical example was given and a simulation study was conducted in order to illustrate the performance of the proposed method and compare it with that of the traditional Shewhart X¯ control chart.

The proposed robust X¯_MDMAD control chart gives better performance than the traditional Shewhart X¯ control chart if the underlying distribution of chance causes is non‐normal. It has good properties for heavy‐tailed distribution functions and moderate sample sizes and it compares favorably with the traditional Shewhart X¯ control chart.

The most common statistical process control (SPC) tool is the traditional Shewhart X¯ control chart. The chart is used to monitor the process mean based on the assumption that the underlying distribution of the quality characteristic is normal and there is no major contamination due to outliers. The sample mean, X¯, and the sample standard deviation, S, are the most efficient location and scale estimators for the normal distribution often used to construct the X¯ control chart, but the sample mean, X¯, and the sample standard deviation, S, might not be the best choices when one or both assumptions are not met. Therefore, the need for alternatives to the X¯ control chart comes into play. The literature shows that the sample median, MD, and the median absolute deviation from the sample median, MAD, are indeed more resistant to departures from normality and the presence of outliers.

The concept of the proposed R chart is based on the sum of chi squares (χ²). The average run lengths (ARLs) of the proposed R chart are computed and compared with the ARLs of a standard R chart, Shewhart variance chart proposed by Chang and Gan, a CUSUM range chart (with and without FIR feature) proposed by Chang and Gan and also with an EWMA range chart proposed by Crowder and Hamilton for various chart parameters. This paper aims to show that only FIR CUSUM schemes perform better than the proposed R chart but other CUSUM and EWMA schemes are less efficient than the proposed R chart.

The concept of the proposed R chart is based on the sum of chi squares (χ²). The proposed R chart divides the plot area into three regions, namely: outright rejection region; outright acceptance region; and transition region. The NULL hypothesis is rejected if a point falls beyond the control limit, and accepted if it falls below the warning limit. However, when a point falls beyond the warning limit, but not beyond the control limit, the decision is taken on the basis of individual observations of the previous H samples, which are considered to evaluate statistic U, that is the sum of chi squares. The NULL hypothesis is rejected if U exceeds a predefined value (U*) and accepted otherwise.

The comparisons also show that the CUSUM, EWMA and proposed R charts outperform the Shewhart R chart by a substantial amount. It is concluded that only FIR CUSUM schemes perform better than the proposed R chart, as it is second in ranking. The other CUSUM and EWMA schemes are less efficient than the proposed R chart.

CUSUM and EWMA charts can catch a small shift in the process average but they are not efficient to catch a large shift. Many researchers have also pointed out that these charts' applicability is limited to the chemical industries. Another limitation of CUSUM and EWMA charts is that they can catch the shift only when there is a single and sustained shift in the process average. If the shift is not sustained, then they will not be effective.

Many difficulties related to the operation and design of CUSUM and EWMA control charts are greatly reduced by providing a simple and accurate proposed scheme. The performance characteristics (ARLs) of the proposed charts described in this paper are very much comparable with FIR CUSUM, CUSUM, EWMA and other charts. It can be concluded that, instead of considering many chart parameters used in CUSUM and EWMA charts, it is better to consider a simple and more effective scheme, because a control chart loses its simplicity with multiple parameters. Moreover, practitioners may also experience difficulty in using these charts in production processes.

It is a modification of the Shewhart Range Chart but it is more effective than the Shewhart Range chart, as shown in the research paper.

“Twin metric” control preserves the simple, intuitive graphical features of Shewhart control charts, while incorporating the much improved performance of CUSUM. Two metrics are plotted on the twin metric control chart at each sample interval; the Shewhart value and a simplified CUSUM value. The action limits for the two metrics are numerically identical. The name twin metric emphasizes this identity. Twin metric responsiveness, measured in terms of the average run length (ARL) curve, is several times better than Shewhart control, with or without runs rules to supplement the Shewhart chart. Twin metric enables substantially better response to real process shifts and substantially fewer false alarms compared to Shewhart charts. Discusses the conceptual framework, the arithmetic formulas, and the operational aspects, including estimation of the process standard deviation, estimation of the current process average after a twin metric signal, and monitoring process variability using twin metric control. Provides a table of ARLs for six twin metric options. Gives quantitative performance comparisons comparing twin metric to Shewhart and to combined Shewhart‐CUSUM.

The purpose of this paper is to introduce a new design of an R chart to catch smaller shifts in the process dispersion as well as maintaining the simplicity so that it may be applied at shopfloor level.

Here a new R chart has been proposed which can overcome the limitations of Shewhart, CUSUM and EWMA range charts. The concept of this R chart is based on chi‐square (χ²) distribution. Although CUSUM and EWMA charts are very useful for catching the small shifts in the mean or standard deviation, they can catch the process shift only when there is a single and sustained shift in process average or standard deviation.

It was found that the proposed chart performs significantly better than the conventional (Shewhart) R chart, CUSUM range schemes proposed by Chang and Gan for most of the process shifts in standard deviation. The ARLs of the proposed R chart is higher than ARLs of CUSUM schemes for only ten cases out of 40. The performance of the proposed R chart has also been compared with the variance chart proposed by Chang and Gan for various shifts in standard deviation. The ARLs of the proposed R chart are compared with Chang's R chart for sample sizes of 3 and it can be concluded from the comparisons that the proposed R chart is much better than Chang's variance chart for all shift ratios for sample size of three. Many difficulties related to the operation and design of CUSUM and EWMA control charts are greatly reduced by providing a simple and accurate proposed R chart scheme. The performance characteristics (ARLs) of the proposed charts are very comparable to a great degree with FIR CUSUM, simple CUSUM and other variance charts. It can be concluded that, instead of considering many parameters, it is better to consider single sample size and single control limits because a control chart loses its simplicity with a greater number of parameters. Moreover, practitioners may also find difficulty in applying it in production processes. On the other hand, CUSUM control charts are not effective when there is a single and sustained shift in the process dispersion.

A lot of effort has been done to develop the new range charts for monitoring the process dispersion. Various assumptions and factors affecting the performance of the R chart have been identified and taken into account. In the proposed design, the observations have been assumed independent of one another but the observations may also be assumed to be auto‐correlated with previous observations and the performance of the proposed R chart may be studied.

The research findings could be applied to various manufacturing and service industries as it is more effective than the conventional (Shewhart) R chart and simpler than CUSUM charts.

The purpose of this paper is to introduce a new design of the X¯ chart to catch smaller shifts in the process average as well as to maintain the simplicity like the Shewhart X¯ chart so that it may be applied at shopfloor level.

In this paper, a new X¯ chart with two strategies is proposed which can overcome the limitations of Shewhart, CUSUM and EWMA charts. The Shewhart chart uses only two control limits to arrive at a decision to accept the Null Hypothesis (H₀) or Alternative Hypothesis (H₁), but in the new X¯ chart, two more limits at “K” times sample standard deviation on both sides from center line have been introduced. These limits are termed warning limits. The first strategy is based on chi‐square distribution (CSQ), while the second strategy is based on the average of sample means (ASM).

The proposed X¯ chart with “strategy ASM” shows lower average run length (ARL) values than ARLs of variable parameter (VP) X¯ chart for most of the cases. The VP chart shows little better performance than the new chart; but at large sample sizes (n) of 12 and 16. The VSS X¯ chart also shows lower ARLs but at very large sample size, which should not be used because, as far as possible, samples should be taken from a lot produced under identical conditions. The inherent feature of the new chart is its simplicity, so that it can be used without difficulty at shopfloor level as it uses only a fixed sample size and fixed sampling interval but it is very difficult to set the various chart parameters in VP and VSS X¯ charts.

A lot of effort has been expended to develop the new strategies for monitoring the process mean. Various assumptions and factors affecting the performance of the X¯ chart have been identified and taken into account. In the proposed design, the observations have been assumed independent of one another but the observations may also be assumed to be auto‐correlated with previous observations and performance of the proposed chart may be studied.

The research findings could be applied to various manufacturing and service industries as it is more effective than the Shewhart chart and simpler than the VP, VSS and CUSUM charts.

A product or service usually has multiple measurable characteristics, and its performance on different measures may vary and may change over time. Multi-criterion and multi-period performance benchmarking presents a challenge for management to determine performance gaps among comparable products or services. The purpose of this paper is to propose a new performance benchmarking method to address this challenge.

The author develop this method by formulating two benchmarking functions: a differentiation function based on Shewhart average and standard deviation charts to distinguish the performance of products or services on a single measure, and a categorization function to classify each product’s or service’s overall performance across all measures. By systematically removing the lowest-performing products or services from comparison, the author use these functions iteratively to detect performance gaps.

Using this method, the author find performance gaps in each of three benchmarking applications of airports, hotels, and minivans, although a number of performance gaps are not obvious from the raw data.

This benchmarking study focuses on the quantifiable outcome performance of products and services.

This benchmarking method is generic and applicable to most products and services. It is robust not only for discovering performance gaps, but also for providing useful insights for managers to prioritize improvement efforts on individual performance measures.

The novelty of this benchmarking method lies in that it can not only find the “best overall” products or services for all performance measures, but can also pinpoint the “best-in-class” products or services as well as performance gaps for each performance measure. In addition, this paper presents several original ideas for performance benchmarking, including: using the control limits of Shewhart control charts to categorize performance gaps, systematically removing the lowest-performing products or services from comparison for the purpose of detecting hidden performance gaps, and using symbolic expressions to integrate benchmarking results from all measures and to show all performance gaps intuitively.

Combined Shewhart‐cumulative score (cuscore) quality control schemes are available for controlling the mean of a continuous production process. In many industrial applications, it is important to control the process variability as well. The proposed combined Shewhart‐cumulative‐score (cuscore) procedure for detecting shifts in process variability uses the procedures developed by Ncube and Woodall (1984) to monitor shifts in the process mean of continuous production processes. It is shown, in the one‐sided case, by average run length comparisons, that the proposed schemes perform significantly better than comparative Shewhart procedures and in some cases even better than cusum schemes when using some process variability quality characteristics.

This paper presents economic and economic–statistical designs of the adaptive exponentially weighted moving average (AEWMA) control chart for monitoring the process mean. It also aims to compare the effect of estimated process parameters on the economic performance of three charts, which are Shewhart, exponentially weighted moving average and AEWMA control charts with economic–statistical design.

The optimal parameters of the control charts are obtained by applying the Lorenzen and Vance’s (1986) cost function. Comparisons between the economic–statistical and economic designs of the AEWMA control chart in terms of expected cost and statistical measures are performed. Also, comparisons are made between the economic performance of the three competing charts in terms of the average expected cost and standard deviation of expected cost.

This paper concludes that taking into account the economic factors and statistical properties in designing the AEWMA control chart leads to a slight increase in cost but in return the improvement in the statistical performance is substantial. In addition, under the estimated parameters case, the comparisons reveal that from the economic point of view the AEWMA chart is the most efficient chart when detecting shifts of different sizes.

The importance of the study stems from designing the AEWMA chart from both economic and statistical points of view because it has not been tackled before. In addition, this paper contributes to the literature by studying the effect of the estimated parameters on the performance of control charts with economic–statistical design.

The traditional Shewhart control chart, the X-bar and R/S chart, cannot give support to decide when it is not economically feasible to stop the process in order to remove special causes. Therefore, the purpose of this paper is to propose a new control chart design – a modified acceptance control chart, which provides a supportive method for decision making in economic terms, especially when the process has high capability indices.

The authors made a modeling expectation average run length (ARL), which incorporates the probability density function of the sampling distribution of C_pk, to compare and analyze the efficiency of the proposed design.

This study suggested a new procedure to calculate the control limits (CL) of the X-bar chart, which allows economic decisions about the process to be made. By introducing a permissible average variation and defining three regions for statistical CL in the traditional X-bar control chart, a new design is proposed.

A framework is presented to help practitioners in the use of the proposed control chart. Two new parameters (C_p and C_pk) in addition to m and n were introduced in the expected ARL equation. The C_pk is a random variable and its probability function is known. Therefore, by using a preliminary sample of a process under control, the authors can test whether the process is capable or not.

The aim of this study is to present the economic‐statistical design of an EWMA control chart for monitoring the process dispersion.

The optimal economic‐statistical design of the S EWMA chart was determined for a wide benchmark of examples organized as a two level factorial design and was compared with the designs obtained for the S Shewhart chart. Both the two charts have been designed so that an equal number of false alarms (in‐control Average Run Length) is expected.

The S EWMA allows significant hourly cost savings to be achieved for the entire set of process scenarios with respect to the S Shewhart; a mean percentage cost saving of 6.77 per cent is obtained for processes characterized by a reduction in process dispersion (i.e. processes whose natural variability is reduced through an external technological intervention), whereas up to a 9.78 per cent saving is achieved for processes whose dispersion is increased by the occurrence of an undesired special cause.

The proposed S EWMA chart can be considered as an effective tool when statistical process control procedures should be implemented on a process with the aim of monitoring its data dispersion.

In literature the economic design of EWMA charts covers only the process cost evaluation when the sample mean is monitored; here, the study is extended to the sample standard deviation to investigate if the EWMA scheme still outperforms the Shewhart chart. An extensive analysis is proposed to evaluate the influence of the process operating parameters on the EWMA chart design variables.