Monitoring the coefficient of variation (CV) allows process monitoring to be performed when both the process mean and the standard deviation are not constant but, nevertheless, proportional. Until ...now, few research papers have investigated the monitoring of the CV in a short production run context. This paper investigates the design and implementation of a Variable Sampling Interval Shewhart control chart to monitor the coefficient of variation in a short production run context. Formulas for the truncated average time to signal are derived and a performance comparison is carried out with a Fixed Sampling Rate Shewhart chart monitoring the CV. An example illustrates the use of this chart on real industrial data.
In the context of public health surveillance, the aim is to monitor the occurrence of health-related events. Among them, statistical process monitoring focuses very often on the monitoring of rates ...and proportions (i.e. values in
(
0
,
1
)
) such as the proportion of patients with a specific disease. A popular control chart that is able to detect quickly small to moderate shifts in process parameters is the exponentially weighed moving average control chart. There are various models that are used to describe values in
(
0
,
1
)
. However, especially in the case of rare health events, zero values occur very frequently which, for example, denote the absence of the disease. In this paper, we study the performance and the statistical design of exponentially weighed moving average control charts for monitoring proportions that arise in a health-related framework. The proposed chart is based on the zero-inflated Beta distribution, a mixed (discrete-continuous) distribution, suitable for modelling data in
0
,
1
)
. We use a Markov chain method to study the run length distribution of the exponentially weighed moving average chart. Also, we investigate the statistical design as well as the performance of the proposed charts. Comparisons with a Shewhart-type chart are also given. Finally, we provide an example for the practical implementation of the proposed charts.
In the industrial practice, control charts are frequently implemented assuming that the quality characteristic of interest can be accurately measured without errors. In general, this assumption is ...not realistic: measurement error always exists in quality control applications and may considerably affect the performance of control charts in detecting the occurrence of an out-of-control condition. In this paper, the effect of measurement error on the statistical performance of Shewhart
t
and EWMA
t
control charts is investigated. Several tables are provided to show how the statistical performance of these control charts changes with different sources of the measurement error. The obtained results show that the measurement errors have a significant influence on the performance of both the Shewhart
t
and EWMA
t
control charts. Two examples in the analytical chemistry and food industry are presented to illustrate the use of the proposed charts.
In production, it is common to deal with short production runs, where flexibility is required in the built-up of parts to produce numerous variants of manufactured goods. Monitoring the multivariate ...coefficient of variation (MCV) is an effective method to monitor the relative multivariate variability compared with the mean. Monitoring the relative multivariate variability is important when practitioners are not interested in the changes in the mean vector or the covariance matrix. Monitoring the univariate coefficient of variation in short production runs has already been successfully executed. In this paper, the statistical performance of one-sided charts for monitoring the MCV of a multivariate process with finite horizon is investigated. Prior to this work, no attempt has been made to study process monitoring of MCV in short production runs. Investigations are made when the exact shift size can be specified and when there is a random shift size. It is found that the proposed upward chart detects an increasing shift in the MCV quicker than its downward counterpart detects a decreasing shift, for the same shift size (from the nominal value). An example is presented to illustrate the implementation of the new method.
Monitoring the coefficient of variation is an effective approach to Statistical Process Control when the process mean and standard deviation are not constant but their ratio is constant. Until now, ...research has not investigated the monitoring of the coefficient of variation for short production runs. Viewed under this perspective, this paper proposes a new method to monitor the coefficient of variation for a finite horizon production by means of one-sided Shewhart-type charts. Tables are provided for the statistical properties of the proposed charts when the shift size is deterministic. Two illustrative examples are given in order to illustrate the use of these charts on real data.
In this work, we study upper-sided cumulative sum control charts that are suitable for monitoring geometrically inflated Poisson processes. We assume that a process is properly described by a ...two-parameter extension of the zero-inflated Poisson distribution, which can be used for modeling count data with an excessive number of zero and non-zero values. Two different upper-sided cumulative sum-type schemes are considered, both suitable for the detection of increasing shifts in the average of the process. Aspects of their statistical design are discussed and their performance is compared under various out-of-control situations. Changes in both parameters of the process are considered. Finally, the monitoring of the monthly cases of poliomyelitis in the USA is given as an illustrative example.
Monitoring schemes are typically designed under the assumption of perfect measurements. However, in real-life applications, data tend to be subjected to measurement errors, that is, a difference ...between the real quantities and the measured ones mostly exist even with highly sophisticated advanced measuring instruments. Thus, in this paper, the negative effect of measurement errors on the performance of the homogenously weighted moving average (HWMA) scheme is studied using the linear covariate error model for constant and linearly increasing variance. Monte Carlo simulations are used to evaluate the performance of the proposed HWMA scheme in terms of the run-length characteristics. It is observed that as the smoothing parameter increases, measurement errors have a higher negative effect on the performance of the HWMA
X
¯
scheme. More importantly, it is shown that the negative effect of measurement errors is reduced by using multiple measurements and/or by increasing the slope coefficient of the covariate error model. Moreover, the performance of the HWMA
X
¯
scheme is compared with the corresponding exponentially weighted moving average (EWMA) and cumulative sum (CUSUM)
X
¯
schemes. An illustrative example is provided to help in implementing this monitoring scheme in a real-life situation.
•This article presents theoretical bases of three methods for determining the probability distribution of the sum of i.i.d. hypergeometric random variables: (1) direct convolution, (2) recursive ...algorithm by De Pril, (3) approximation.•We provide associated MATLAB codes (including context-specific customizations) for direct implementation of these methods and discuss technical aspects and essential details of the tweaks we have made.•A representative application example in SPM shows that the proposed approximation is considerably simpler in application than both other methods and it ensures a remarkable high accuracy of the results while reducing computational time considerably.
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In probability theory and statistics, the probability distribution of the sum of two or more independent and identically distributed (i.i.d.) random variables is the convolution of their individual distributions. While convoluting random variables following a binomial, geometric or Poisson distribution is a straightforward procedure, convoluting hypergeometric-distributed random variables is not. The problem is that there is no closed form solution for the probability mass function (p.m.f.) and cumulative distribution function (c.d.f.) of the sum of i.i.d. hypergeometric random variables. To overcome this problem, we propose an approximation for the distribution of the sum of i.i.d. hypergeometric random variables. In addition, we compare this approximation with two classical numerical methods, i.e., convolution and the recursive algorithm by De Pril, by means of an application in Statistical Process Monitoring (SPM). We provide MATLAB codes to implement these three methods for computing the probability distribution of the sum of i.i.d. hypergeometric random variables in an efficient way. The obtained results show that the proposed approximation has remarkable properties and may be helpful in all fields, where the problem of convoluting hypergeometric-distributed random variables occurs. Therefore, the approximation considered in this paper is well suited to make a change over established practices.•This article presents theoretical bases of three methods for determining the probability distribution of the sum of i.i.d. hypergeometric random variables: (1) direct convolution, (2) recursive algorithm by De Pril, (3) approximation.•We provide associated MATLAB codes (including context-specific customizations) for direct implementation of these methods and discuss technical aspects and essential details of the tweaks we have made.•A representative application example in SPM shows that the proposed approximation is considerably simpler in application than both other methods and it ensures a remarkable high accuracy of the results while reducing computational time considerably.
In this article, we describe a taxonomy of generic graph related tasks along with a computer-based evaluation designed to assess the readability of two representations of graphs: matrix-based ...representations and node-link diagrams. This evaluation encompasses seven generic tasks and leads to insightful recommendations for the representation of graphs according to their size and density. Typically, we show that when graphs are bigger than twenty vertices, the matrix-based visualization outperforms node-link diagrams on most tasks. Only path finding is consistently in favor of node-link diagrams throughout the evaluation.
•An overview on profile monitoring papers published during the period 2008–2018.•Providing a comprehensive classification of articles in this area.•Presenting an analytical overview on the researches ...in this area.•Introducing research gaps in this area to motivate future studies.
Sometimes the quality of a process is best expressed by a relationship between response variables and explanatory variables. Checking over the time the stability of such functional relationships using statistical methods is called “profile monitoring”. Since 2007, when a detailed review paper in the field of profile monitoring was presented, an increasing number of papers have been published in this area. In this paper, we present a conceptual classification scheme and classify the papers in this area since 2008 up to 2018. The relevant papers are categorized and analyzed under different metrics and directions for future studies are recommended.
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