Lupércio F. Bessegato

Variable Interval Sampling in Economical Designs for Online Process Control of Attributes with Misclassification Errors

Online process control consists of inspecting a single item at every mth items produced, where m is an integer greater than two. Based on the results of the inspection, one decides if the process is in-control (the fraction of conforming item is p1—state I) or out-of-control (the fraction of conforming item is p2—state II). If the inspected item is non-conforming, the process is designated as out-of-control and production is stopped for possible adjustment; otherwise, production goes on. In this paper, a contribution to online process control is presented, where the inspection system is considered to be subject to classification errors. After every adjustment, the sampling interval is L units (L⩾m), and in the case of non-adjustment, the sampling interval is m units. The expression for the average cost per produced item is calculated, and optimum parameters (the sampling intervals L and m) are obtained by a direct search. The procedure is illustrated by a numerical example.

On-Line Process Control using Attributes with Misclassification Errors: An Economical Design for Short-Run Production

On-line process control consists of inspecting a single item for every m (integer and m ≥ 2) produced items. Based on the results of the inspection, it is decided whether the process is in-control (the fraction of conforming items is p 1; State I) or out-of-control (the fraction of conforming items is p 2 < p 1; State II). If the inspected item is non conforming, it is determined that the process is out-of-control, and the production process is stopped for an adjustment; otherwise, production continues. As most designs of on-line process control assume a long-run production, this study can be viewed as an extension because it is concerned with short-run production and the decision regarding the process is subject to misclassification errors. The probabilistic model of the control system employs properties of an ergodic Markov chain to obtain the expression of the average cost of the system per unit produced, which can be minimised as a function of the sampling interval, m. The procedure is illustrated by a numerical example.

Online control by attributes in the presence of classification errors with variable inspection interval

ABSTRACT The procedure for online control by attribute consists of inspecting a single item at every m items produced (m ≥ 2). On each inspection, it is determined whether the fraction of the produced conforming items decreased. If the inspected item is classified as non conforming, the productive process is adjusted so that the conforming fraction returns to its original status. A generalization observed in the literature is to consider inspection errors and vary the inspection interval. This study presents an extension of this model by considering that the inspected item can be rated independently r (r ≥ 1) times. The process is adjusted every time the number of conforming classifications is less than a, 1 ≤ a ≤ r. This method uses the properties of an ergodic Markov chain to obtain the expression for the average cost of this control system. The genetic algorithm methodology is used to search for the optimal parameters that minimize the expected cost. The procedure is illustrated by a numerical example.

A Comparison of Simulated Annealing, Elliptic and Genetic Algorithms for Finding Irregularly Shaped Spatial Clusters

Methods for the detection and evaluation of the statistical significance of spatial clusters are important geographic tools in epidemiology, disease surveillance and crime analysis. Their fundamental role in the elucidation of the etiology of diseases (Lawson, 1999; Heffernan et al., 2004; Andrade et al., 2004), the availability of reliable alarms for the detection of intentional and non-intentional infectious diseases outbreaks (Duczmal and Buckeridge, 2005, 2006a; Kulldorff et al., 2005, 2006) and the analysis of spatial patterns of criminal activities (Ceccato, 2005) are current topics of intense research. The spatial scan statistic (Kulldorff, 1997) and the program SatScan (Kulldorff, 1999) are now widely used by health services to detect disease clusters with circular geometric shape. Contrasting to the naive statistic of the relative count of cases, the scan statistic is less prone to the random variations of cases in small populations. Although the circular scan approach sweeps completely the configuration space of circularly shaped clusters, in many situations we would like to recognize spatial clusters in a much more general geometric setting. Kulldorff et al. (2006) extended the SatScan approach to detect elliptic shaped clusters. It is important to note that for both circular and elliptic scans there is a need to impose size limits for the clusters; this requisite is even more demanding for the other irregularly shaped cluster detectors. Other methods, also using the scan statistic, were proposed recently to detect connected clusters of irregular shape (Duczmal et al., 2004, 2006b, 2007, Iyengar, 2004, Tango & Takahashi, 2005, Assuncao et al., 2006, Neill et al., 2005). Patil & Tallie (2004) used the relative incidence cases count for the objective function. Conley et al. (2005) proposed a genetic algorithm to explore a configuration space of multiple agglomerations of ellipses; Sahajpal et al. (2004) also used a genetic algorithm to find clusters shaped as intersections of circles of different sizes and centers. Two kinds of maps could be employed. The point data set approach assigns one point in the map for each case and for each non-case individual. This approach is interested in finding, among all the allowed geometric shape candidates defined within a specific strategy, the one that encloses the highest ratio of cases vs. non-cases, thus defining the most likely cluster. The second approach assumes that a map is divided into M regions, with total population N and C total cases. Defining the zone z as any set of connected regions, the