Athanasios C. Rakitzis

Monitoring exponential data using two-sided control charts with runs rules

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. Guidelines for the most effective scheme in practice are provided, along with comparisons with other competitive schemes. Finally, the practical application of the proposed schemes is also discussed.

A new memory-type monitoring technique for count data

A new control scheme with memory is proposed and studied.It can be used for monitoring count data of any type.Its theoretical properties can be exactly derived.It has an increased sensitivity in the detection of small and moderate shifts.It can be used for monitoring industrial and non-industrial processes. 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 monitoring discrete data, is proposed and studied. It only uses integer-valued weights in the recent as well as in the past observations, while the plotted statistic is also a positive integer. An appropriate Markov chain technique is used for the determination of the entire run-length distribution of the proposed chart. Also, practical guidelines and comparisons with other competitive schemes are provided, demonstrating an increased sensitivity in the detection of small magnitude shifts, especially the decreasing ones. Finally, the practical application of the proposed scheme is illustrated with two numerical examples.

CUSUM Control Charts for the Monitoring of Zero-inflated Binomial Processes

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 cumulative sum (CUSUM)-type control charts are proposed for monitoring increases or decreases in the parameter p of a zero-inflated binomial process. The results of an extensive numerical study concerning the statistical design of the proposed schemes as well as their practical implementation are provided. Copyright

The effect of parameter estimation on the performance of one-sided Shewhart control charts for zero-inflated processes

ABSTRACT 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 have to be estimated from an in-control historical Phase I sample. In the present paper, we investigate the performance of Shewhart-type control charts for zero-inflated processes with estimated parameters and propose practical guidelines for the statistical design of the examined charts, when the size of the preliminary sample is predetermined.

Cumulative sum control charts for monitoring geometrically inflated Poisson processes: An application to infectious disease counts 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.

Control Charts for Monitoring Correlated Poisson Counts with an Excessive Number of Zeros

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 structure between them. In this work, we study control charts for monitoring correlated Poisson counts with an excessive number of zeros. Zero-inflation in the process is captured via appropriate integer-valued time series models. Extensive numerical results are provided regarding the performance of the considered charts in the detection of changes in the mean of the process as well as the effects of zero-inflation on them. Finally, a real-data practical application is given. Copyright

On the Modelling and Monitoring of General Inflated Poisson Processes

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 monitoring of count data based on the proposed general inflated Poisson distributions, and their performance is evaluated under various out-of-control situations. The usefulness of the considered models and techniques is illustrated via two real-data examples, while practical guidelines are provided as well. Copyright

A Comparative Study of Control Charts for Zero-Inflated Binomial Processes

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 is of interest the monitoring of rare health-events like the number of congenital malformations or the rate of wound infections. In this work, we present one-sided and two-sided control charts that are suitable for the monitoring of changes in the parameters of a zero-inflated binomial process. We consider Shewhart-, EWMA- and CUSUM-type control charts, and we present aspects of their statistical design. Numerical comparisons between the different schemes are given as well.