Athanasios C. Rakitzis

University of Piraeus · Department of Statistics and Insurance Science

Control charts for zero-inflated processes have attracted the interest of the researchers in the recent years. In this work we investigate the performance of Shewhart-type charts for zero-inflated Poisson and zero-inflated Binomial processes, in the case of estimated parameters. This is a case that usually occurs in practice, especially prior to st...

In this work, a control chart with multiple runs rules is proposed and studied in the case of monitoring inflated processes. Usually, Shewhart-type control charts for attributes do not have a lower control limit, especially when the in-control process mean level is very low, such as in the case of processes with a low number of defects per inspecte...

The main aim of this book is to present both traditional Nonparametric Methodologies (such as tests based on ranks, runs, goodness-of-fit tests) as well as subsequent developments (estimation of the probability density function, bootstrap, nonparametric regression). Specifically, in Chapter 1 a review of basic definitions and concepts from Probabil...

This article proposes a run sum Max chart for monitoring a process and detecting changes in mean and variability simultaneously. A Markov chain method is applied to evaluate the statistical performance of the chart by using both average run length (ARL) and expected average run length (EARL) criteria. The numerical analysis demonstrates an improved...

Time between events (TBE) control charts play an important role in many applications, particularly in the monitoring of high-yield processes. In this article, we discuss the most common types of control charts for time between events , along with some illustrations of their practical implementation. The usual distributional assumption for the time...

The EWMA Sign control chart is a distribution-free scheme used for monitoring shifts in the location parameter during process monitoring. In this work, we propose a modified Phase II EWMA chart based on a general Sign statistic, capable of monitoring shifts in the process variability. Regarding the determination of the proposed chart's in- and out-...

In this paper, we propose and study nonparametric exponentially weighted moving average (EWMA) control charts based on the sign statistic, which are suitable for detecting changes in process dispersion. The sign statistic is defined by using appropriate deciles of the in‐control process distribution. The statistical performances of the proposed cha...

The statistical monitoring of count data has received much attention in the recent years, with applications in several areas of applied research. The basic tool for monitoring an integer-valued process is the Shewhart control chart. In this work we investigate the performance of two Synthetic-type charts in the monitoring of a general inflated Pois...

In this work, we study the performance of two-sided EWMA charts for monitoring double bounded processes using individual observations. Specifically, the term double bounded refers to observations in the interval (0, 1) and thus, these charts are suitable for monitoring rates, proportions and percentages. There are several models that can be used to...

Control charts are useful to monitor if a process is in a state of statistical control (in-control) or if changes have occurred due to the presence of any assignable causes. To this end, the pattern of points displayed on a control chart plays an important role. A process is declared as in-control when the plotted points display a random pattern. O...

In monitoring high-yield processes the time between events (TBE) control charts play an important role. In this paper, Phase II Shewhart-type t_r-charts, with various runs rules, are considered for monitoring TBE exponential data and charts’ performance is examined in terms of the average time to signal (ATS). The ATS metric is more suitable due to...

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 [Formula: see text]) such as the proportion of patients with a specific disease. A popular control chart that is able to...

In this work we study one-sided and two-sided EWMA and Double EWMA control charts for monitoring an integer-valued autocorrelated process with a bounded support. The performance of the proposed charts is studied via simulation. We compare the performance of the proposed charts and provide aspects for the statistical design and practical implementat...

Maxwell distribution has several applications in modeling physical and chemical processes, as well as in reliability and lifetime data analysis. In this paper, we propose the one- and two-sided SPRT control charts for monitoring the scale parameter of a Maxwell distributed process. Using a Markov chain approach, we obtain the measures of statistica...

In this article we propose and study one‐ and two‐sided control charts for monitoring a first order binomial integer‐valued ARCH process. This model can be used for modeling integer‐valued time series of counts with a finite support, which also exhibit overdispersion. We consider Shewhart as well as exponentially weighted moving average control cha...

It is well known that the Shewhart control charts are not very sensitive for detecting small and moderate shifts in the process parameters. A synthetic chart, which is a combination of a Shewhart control chart and a conforming run-length (CRL) chart, has been proposed and studied as a viable alternative for that purpose. The advantage of a syntheti...

The EWMA Sign control chart is an efficient tool for monitoring shifts in a process regardless the observations’ underlying distribution. Recent studies have shown that, for nonparametric control charts, due to the discrete nature of the statistics being used (such as the Sign statistic), it is impossible to accurately compute their Run Length prop...

Attribute control charts assuming a Poisson (c chart) or a binomial distribution (np chart) are usually used when the quality characteristic cannot be measured on a continuous scale. For equivalent sample sizes, Shewhart type attribute control charts are known to be less efficient than their measurement counterparts (like the X¯ chart) and, for thi...

Among the anomaly detection methods, control charts have been considered important techniques. In practice, however, even under the normal behaviour of the data, the standard deviation of the sequence is not stable. In such cases, the coefficient of variation (CV) is a more appropriate measure for assessing system stability. In this paper, we consi...

In this work, we develop and study upper and lower one-sided EWMA control charts for monitoring correlated counts with finite range. Often in practice, data of that kind can be adequately described by a first-order binomial or beta-binomial autoregressive model. Especially, when there is evidence that data demonstrate extra-binomial variation, the...

In practice, there are processes where the in-control mean and standard deviation of a quality characteristic is not stable. In such cases, the coefficient of variation (CV) is a more appropriate measure for assessing process stability. In this paper, we consider the statistical design of Run Rules based control charts for monitoring the CV of mult...

In this paper, we provide an overview of the use of run and scan rules in statistical process monitoring. Although we focus on control charts, supplemented with various stopping rules based on run and scan statistics, several other monitoring procedures that incorporate run and scan statistics are reviewed as well. Rules based on the notion of scan...

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 me...

In this work, a new Phase II EWMA-type chart for count data, based on the sign statistic, is proposed and applied to the monitoring of the location of an unknown continuous distribution. The most valuable characteristics of this new chart are that: a) it only uses positive integer- valued weights to account for the past process history, b) the plot...

Recent studies show that the Shewhart median chart is widely used for detecting shifts in a process, but it is often rather inefficient in detecting small or moderate process shifts. In order to overcome this problem, a Synthetic chart can be used. This chart outperforms the Shewhart type chart because it uses the information about the time interva...

This study aimed at estimating the homogeneity of the ingredients of cereal-based baby food by comparing the results obtained by a pneumatic mixing system (PMS) in relation to the limits set by the current legislation and labeling requirements for the specific products. The results were then compared to the results from a ribbon-type mixer. The hom...

In the classical setup used in process monitoring, the times between the collection of successive plotted samples are considered as nonrandom. However, in several real‐life applications, it seems plausible to assume that the time needed to collect the necessary information for plotting a point in the control chart has a stochastic nature. Under thi...

The zero-inflated Poisson (ZIP) distribution has been extensively studied in the literature during recent years. It is one of the most appropriate models for overdispersed data with an excessive number of zeros. Data of this type frequently arise in manufacturing processes with a low fraction of defective items. A ZIP model has two parameters; one...

Correlated count data processes with a finite range can be adequately described by a first-order binomial autoregressive model. However, in several practical applications, these data demonstrate extra-binomial variation, and a more appropriate choice is the first-order beta-binomial autoregressive model. In this paper, we propose and study control...

High-yield processes with a low defect rate, the recommendation is to monitor the times between events (TBE) with variables control charts in order to overcome the weaknesses of conventional attribute control charts. In this paper, we incorporate supplementary runs rules into one of the existing Shewharttype TBE charts, namely the tr-chart, in orde...

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 val...

In this paper, we consider the renewal risk model and we are interested in the distribution of the number ν of claims until the first time that insurer's surplus process falls below zero (ruin) or exceeds a predefined upper barrier b>u (safety level), immediately after the payment of a claim. By using exponentially tilted measures we derive an expr...

A two-sided run sum S control chart is proposed and its average run length performance is evaluated via a Markov chain technique. The performance of the chart is compared to several well-known control-charting procedures for the monitoring of process variability. One-sided counterparts of the proposed run sum charts are also discussed. The numerica...

The zero-inflated Poisson distribution serves as an appropriate model when there is an excessive number of zeros in the data. This phenomenon frequently occurs in count data from high-quality processes. Usually, it is assumed that these counts exhibit serial independence, while a more realistic assumption is the existence of an autocorrelation stru...

Zero-inflated probability models are used to model count data that have an excessive number of zeros. Shewhart-type control charts have been proposed for the monitoring of zero-inflated processes. Usually their performance is evaluated under the assumption of known process parameters. However, in practice, their values are rarely known and they hav...

In this work, we propose and study a two-parameter modification of the ordinary Poisson distribution that is suitable for the modeling of non-typical count data. This model can be viewed as an extension of the zero-inflated Poisson distribution. We derive the proposed model as a special case of a general one and focus our study on it. The theoretic...

The monitoring of count data arise in several industrial applications in which quality characteristics cannot be measured on a continuous numerical scale. Usually, in such cases the interest is on the number of defects or nonconformities that are produced from a manufacturing process. In this work, a new control scheme with memory, suitable for mon...

It is known that Shewhart chart is not sensitive in the detection of small process average shifts. A solution to this problem is the use of stopping rules based on the theory of runs. However, their practical implementation is based on the assumption that the parameters of the process are known, which rarely happens in practice. In this work, the p...

In this paper, we introduce and study three new start-up demonstration tests with two types of unsuccessful start-ups. The proposed tests use run and frequency quotas acceptance/rejection criteria, providing extensions of binary start-up demonstration tests that have previously appeared in the literature. Using a Markov chain approach we establish...

In this article, new two-sided control charts with runs rules, suitable for the monitoring of exponential data, are proposed and studied. The proposed schemes are suitable to identify changes (upward or downward) in the mean of an exponential distribution. Also, they have the desired in-control performance as well as unbiased performance. Guideline...

Zero-inflated probability models are used to model count data that have an excessive number of zeros. These models are mostly useful in modeling high-yield or health-related processes. The zero-inflated binomial distribution is an extension of the ordinary binomial distribution that takes into account the excess of zeros. In this paper, one-sided c...

In this work, we propose and study general inflated probability distributions that can be used for modelling and monitoring unusual count data. The considered models extend the well-known zero-inflated Poisson distribution because they allow the excess of values, other than zero. Four simple upper-sided control schemes are considered for the monito...

Zero-inflated probability models are recommended when there is an excessive number of zeros in count data. In the context of statistical process control, such cases arise in high-yield processes where the fraction of non-conforming units produced is very low. Other applications can be also found in the monitoring of health-related process, where it...

Let T be a stopping time associated with a sequence of independent and identically distributed or exchangeable random variables taking values in {0, 1, 2, …, m}, and let S T,i be the stopped sum denoting the number of appearances of outcome 'i' in X1, …, X T , 0 ≤ i ≤ m. In this paper we present results revealing that, if the distribution of T is k...

We investigate several aspects of the recently introduced consecutive successes distance failures start-up demonstration test under an exchangeable model. By assuming that the probability of a successful start-up attempt p is a random variable, instead of a fixed value, the outcomes of the successive start-ups become s-dependent exchangeable binary...

In this work, we introduce and study one-sided variable sampling interval S control charts supplemented with signalling and switching rules based on runs. The proposed control schemes demonstrate an improved performance in the detection of small and moderate shifts (increasing or decreasing) in process standard deviation, retaining at the same time...

The Hotelling’s χ2 control chart is one of the most widely used multivariate charting procedures for monitoring the vector of means of several quality characteristics. As a Shewhart-type control chart, it incorporates information pertaining to most recently inspected sample and subsequently it is relatively insensitive in quickly detecting small ma...

The most common charting procedure used for monitoring the variance of the distribution of a quality characteristic is the S control chart. As a Shewhart-type control chart, it is relatively insensitive in the quick detection of small and moderate shifts in process variance. The performance of the S chart can be improved by supplementing it with ru...

Let $T\$ be a stopping time associated with a sequence of independent random variables $Z_{1},Z_{2},...$ . By applying a suitable change in the probability measure we present relations between the moment or probability generating functions of the stopping time $T$ and the stopped sum $%S_{T}=Z_{1}+Z_{2}+...+Z_{T}$. These relations imply that, when...

The most popular tool used in the industry for monitoring a process is the Shewhart control chart. The major disadvantage of the Shewhart control chart is that it is not very efficient in detecting small process average shifts. To increase the sensitivity of Shewhart control charts to small shifts additional supplementary runs rules has been sugges...

To increase the sensitivity of Shewhart control charts in detecting small process shifts sensitizing rules based on runs and scans are often used in practice. Shewhart control charts supplemented with runs rules for detecting shifts in process variance have not received as much attention as their counterparts for detecting shifts in process mean. I...

An acceptance/rejection rule suitable for use in start-up demonstration tests is discussed. The rule allows acceptance of equipment if k consecutive successes occur, while the equipment is rejected if two failures separated by at most r – 2 successes are observed. General formulas and analytic expressions are provided for the probability mass funct...

It is well known that the Shewhart control chart is relatively insensitive to detect small process average shifts. In this article, we introduce and investigate the basic features of the modified r out of m control chart. The new control chart outperforms the Shewhart control chart for small to moderate process average shifts and the corresponding...

Sensitizing rules based on runs and scans are widely used to increase the sensitivity of the classical Shewhart control chart in detecting small process shifts. The use of these rules frequently results in a substantial reduction of the in-control average run length ARL and/or in a poor performance of the out-of-control average run length for moder...

The main purpose of this article is the development and the study of runs rules applied to a Shewhart type control chart for the mean in order to detect non-random patterns in Phase I. We are interested to conclude if the process is in a stable condition for a specific number of preliminary samples in order to estimate the process' parameters. A ch...

The main purpose of this article is the development and the study of runs rules applied to a Shewhart type control chart for the mean in order to detect non-random patterns in Phase I. We are interested to conclude if the process is in a stable condition for a specific number of preliminary samples in order to estimate the process' parameters. A ch...

The main purpose of this article is the development and the study of runs rules applied to a Shewhart type control chart for the mean in order to detect non-random patterns in Phase I, when we are interested to conclude if the process is in a stable condition for the first twenty five or thirty samples in order to estimate the process' parameters....