X̄ Charts with Variable Parameters

Varying the parameters of the X̄ chart has been explored extensively in recent years. In this paper, we extend the study of the X̄ chart with variable parameters to include variable action limits. The action limits establish whether the control should be relaxed or not. When the X̄ falls near the target, the control is relaxed so that there will be more time before the next sample and/or the next sample will be smaller than usual. When the X̄ falls far from the target but not in the action region, the control is tightened so that there is less time before the next sample and/or the next sample will be larger than usual. The goal is to draw the action limits wider than usual when the control is relaxed and narrower than usual when the control is tightened. This new feature then makes the X̄ chart more powerful than the CUSUM scheme in detecting shifts in the process mean.

AATS for the X̄ Chart with Variable Parameters

A Fortran computer program is given for the computation of the adjusted average time to signal, or AATS, for adaptive X̄ charts with one, two, or all three design parameters variable: the sample size, n, the sampling interval, h, and the factor k used in determining the width of the action limits. The program calculates the threshold limit to switch the adaptive design parameters and also provides the in-control average time to signal, or ATS.

(X)over-bar charts with variable parameters

Varying the parameters of the (X) over bar chart has been explored extensively in recent years. In this paper, we extend the study of the (X) over bar chart with variable parameters to include variable action limits. The action limits establish whether the control should be relaxed or not. When the (X) over bar falls near the target, the control is relaxed so that there will be more time before the next sample and/or the next sample will be smaller than usual. When the (X) over bar falls far from the target but not in the action region, the control is tightened so that there is less time before the next sample and/or the next sample will be larger than usual. The goal is to draw the action limits wider than usual when the control is relaxed and narrower than usual when the control is tightened. This new feature then makes the (X) over bar chart more powerful than the CUSUM scheme in detecting shifts in the process mean.

Economic design of (X)over-bar charts with variable parameters: the Markov chain approach

This paper presents an economic design of (X) over bar control charts with variable sample sizes, variable sampling intervals, and variable control limits. The sample size n, the sampling interval h, and the control limit coefficient k vary between minimum and maximum values, tightening or relaxing the control. The control is relaxed when an (X) over bar value falls close to the target and is tightened when an (X) over bar value falls far from the target. A cost model is constructed that involves the cost of false alarms, the cost of finding and eliminating the assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A comprehensive study is performed to examine the economic advantages of varying the (X) over bar chart parameters.

Joint X̄ and R charts with variable parameters

Recent studies have shown that the X̄chart with variable parameters (Vp X̄ chart) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both, X̄ and R charts. Basically, the X̄ and R values establish if the control should or should not be relaxed. When the X̄ and R values fall in the central region the control is relaxed because one will wait more to take the next sample and/or the next sample will be smaller than usual. When the X̄ or R values fall in the warning region the control is tightened because one will wait less to take the next sample and the next sample will be larger than usual. The action limits are also made variable. This paper proposes to draw the action limits (for both charts) wider than usual, when the control is relaxed and narrower than usual when the control is tightened. The Vp feature improves the joint X̄ and R control chart performance in terms of the speed with which the process mean and/or variance shifts are detected. © 1998 IIE.

AATS for the (X)over-bar chart with variable parameters

A Fortran computer program is given for the computation of the adjusted average time to signal, or AATS, for adaptive (X) over bar charts with one, two, or all three design parameters variable: the sample size, n, the sampling interval, h, and the factor k used in determining the width of the action limits. The program calculates the threshold limit to switch the adaptive design parameters and also provides the in-control average time to signal, or ATS.

A hierarchy of adaptive (X)over-bar control charts

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Control charts: an application in shrimp canning

Control chart is a statistical tool which can be employed with advantage to learn the situation in the process (whether it is under control or not). There are different kinds of control charts but one which is most commonly used is the control chart for variables, known as X-R chart. This chart can be used for measurable characteristics in food industry like appearance, colour, sizes and dimensions for chemical properties such as moisture, fat and many other analytical counts and measurements. Since construction and maintenance of such charts involve a recognizable amount of time and effort, they should not be used indiscriminately but only where it can be definitely shown that their use improves the overall operation. Since one control chart can be used for only one quality attribute, those for which the charts are used should be selected with care (Kramer and Twigg, 1962). In this article, the procedure of setting up a variable control chart is described with observations taken on filling operation of cans in a shrimp canning factory.

Control charts for monitoring the mean vector and the covariance matrix of bivariate processes

In this article, we propose new control charts for monitoring the mean vector and the covariance matrix of bivariate processes. The traditional tools used for this purpose are the T (2) and the |S| charts. However, these charts have two drawbacks: (1) the T (2) and the |S| statistics are not easy to compute, and (2) after a signal, they do not distinguish the variable affected by the assignable cause. As an alternative to (1), we propose the MVMAX chart, which only requires the computation of sample means and sample variances. As an alternative to (2), we propose the joint use of two charts based on the non-central chi-square statistic (NCS statistic), named as the NCS charts. Once the NCS charts signal, the user can immediately identify the out-of-control variable. In general, the synthetic MVMAX chart is faster than the NCS charts and the joint T (2) and |S| charts in signaling processes disturbances.

Bivariate control charts with double sampling

In this article, we consider the T(2) chart with double sampling to control bivariate processes (BDS chart). During the first stage of the sampling, n(1) items of the sample are inspected and two quality characteristics (x; y) are measured. If the Hotelling statistic T(1)(2) for the mean vector of (x; y) is less than w, the sampling is interrupted. If the Hotelling statistic T(1)(2) is greater than CL(1), where CL(1) > w, the control chart signals an out-of-control condition. If w < T(1)(2) <= CL(1), the sampling goes on to the second stage, where the remaining n(2) items of the sample are inspected and T(2)(2) for the mean vector of the whole sample is computed. During the second stage of the sampling, the control chart signals an out-of-control condition when the statistic T(2)(2) is larger than CL(2). A comparative study shows that the BDS chart detects process disturbances faster than the standard bivariate T(2) chart and the adaptive bivariate T(2) charts with variable sample size and/or variable sampling interval.

Adaptive control charts: A Markovian approach for processes subject to independent disturbances

Recent studies have shown that adaptive X control charts are quicker than traditional X charts in detecting small to moderate shifts in a process. In this article, we propose a joint statistical design of adaptive X and R charts having all design parameters varying adaptively. The process is subjected to two independent assignable causes. One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. It is assumed that the quality characteristic is normally distributed and the time that the process remains in control has exponential distribution. Performance measures of these adaptive control charts are obtained through a Markov chain approach. (c) 2005 Elsevier B.V. All rights reserved.

Adaptive control charts for attributes

We develop a general model for adaptive c, np, u and p control charts in which one, two or three design parameters (sample size, sampling interval and control limit width) switch between two values, according to the most recent process information. For a given in-control average sampling rate and a given false alarm rate, the adaptive chart detects changes in the process much faster than a chart with fixed parameters. Moreover, this study also offers general guidance on how to choose an effective design.

Synthetic control charts with two-stage sampling for monitoring bivariate processes

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control bivariate processes. During the first stage, one item of the sample is inspected and two correlated quality characteristics (x;y) are measured. If the Hotelling statistic T1 2 for these individual observations of (x;y) is lower than a specified value UCL 1 the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the Hotelling statistic T2 2 for the sample means of (x;y) is computed. When the statistic T2 2 is larger than a specified value UCL2, the sample is classified as nonconforming. According to the synthetic control chart procedure, the signal is based on the number of conforming samples between two neighbor nonconforming samples. The proposed chart detects process disturbances faster than the bivariate charts with variable sample size and it is from the practical viewpoint more convenient to administer.

Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Variable structure control with chattering elimination and guaranteed stability for a generalized T-S model

In this paper, a fuzzy based Variable Structure Control (VSC) with guaranteed stability is presented. The main objective is to obtain an improved performance of highly non-linear unstable systems. The main contribution of this work is that, firstly, new functions for chattering reduction and error convergence without sacrificing invariant properties are proposed, which is considered the main drawback of the VSC control. Secondly, the global stability of the controlled system is guaranteed.The well known weighting parameters approach, is used in this paper to optimize local and global approximation and modeling capability of T-S fuzzy model.A one link robot is chosen as a nonlinear unstable system to evaluate the robustness, effectiveness and remarkable performance of optimization approach and the high accuracy obtained in approximating nonlinear systems in comparison with the original T-S model. Simulation results indicate the potential and generality of the algorithm. The application of the proposed FLC-VSC shows that both alleviation of chattering and robust performance are achieved with the proposed FLC-VSC controller. The effectiveness of the proposed controller is proven in front of disturbances and noise effects.