Browsing by Author "Wessman, Peter"

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Evaluation of univariate surveillance procedures for some multivariate problems
(University of Gothenburg, 1996-04-01) Wessman, Peter
The continual surveillance to detect changes has so far received large attention in the area of industrial quality control, where the monitoring of manufacturing processes to detect decreases in quality play an important role. However, also in other areas important examples can be found such as the surveillance of intensity care patients or the monitoring of economic trends. Often more than one measurement is made, resulting in a multivariate observation process. Many surveillance procedures for multivariate observation processes are based on summarizing statistics that reduces the multivariate process to a univariate process. This thesis studies such surveillance procedures when a change to a specific alternative is of interest. We give special attention to procedures based on likelihood ratio statistics of the observation vectors since these are known to have several optimality properties. Also, many procedures in use today can be formulated in terms of likelihood ratios. In report I we consider the surveillance of a multivariate process with a common change point for all component processes. We show that the univariate reduction using the likelihood ratio statistic for the observation vector from each observation time is sufficient for detecting the change. Furthermore, the use of a likelihood ratio-based method, the LR method, for constructing surveillance procedures is suggested for multivariate surveillance situations. The LR procedure, as several other multivariate surveillance procedures, can be formulated as univariate procedures based on the univariate process of likelihood ratios. Thus, evaluating these multivariate surveillance procedures which are based on this reduction can be done by using results for univariate procedures, for example those given in report II. The effects of not using a sufficient univariate statistic is also illustrated. In the second report a simulation study of some methods based on likelihood ratios of univariate processes is made. The LR method and the Roberts procedure are compared with two methods that today are in common use, the Shewhart and the CUSUM methods. Several different measurements of performance are used, such as the probability of successful detection, the predictive value and the expected delay of an alarm. The evaluation is made for geometrically distributed change points. For this situation the LR procedure meets several optimality criteria and is therefore suitable as a benchmark. The LR procedure is shown to be robust against misspecifications of the intensities. The CUSUM method appears in the simulations to be closer to the Shewhart method than to the Roberts method in several of the properties investigated, for example the run length distribution and the predictive value. Furthermore, the Roberts procedure is shown to have properties close to the LR procedure for moderately large intensities. It has therefore near optimal properties in these cases.
Evaluations of likelihood ratio methods for surveillance
(University of Gothenburg, 1996-03-01) Frisén, Marianne; Wessman, Peter
Methods based on likelihood ratios are known to have several optimality properties. When control charts are used in practice, knowledge about several characteristics of the method is important for the judgement of which action is appropriate at an alarm. The probability of a false alarm, the delay of an alarm and the predictive value of an alarm are qualities (besides the usual ARL) which are described by a simulation study for the evaluations. Since the methods also have interesting optimality properties, the results also enlighten different criteria of optimality. Evaluations are made of the "The Likelihood Ratio Method" which utilizes an assumption on the intensity and has the Shiryaevoptimality. Also, the Roberts and the CUSUM method are evaluated. These two methods combine the likelihood ratios in other ways. A comparison is also made with the Shewhart method, which is a commonly used method.
Evaluations of likelihood ratio methods for surveillance. Differences and robustness.
(University of Gothenburg, 1998-02-01) Frisén, Marianne; Wessman, Peter
In many areas there is a need for continual observation of a time series, with the goal of detecting an important change in the underlying process as soon as possible after it has occurred. In recent years there have been a growing number of papers in economics, medicine, environmental control and other areas dealing with the need of methods for surveillance. Examples are given in Frisen (1992) and Frisen (1994a). The timeliness of decisions is taken into account in the vast literature on quality control charts where simplicity is often a major concern. Also, the literature on stopping rules is relevant. For an overview, see the textbook by Wetherill and Brown (1990) the surveys by Zacks (1983) or Lai (1995) and the bibliography by Frisen (1994b). Methods based on likelihood ratios are known to have several optimality properties. Evaluations are made of the full likelihood ratio (LR) method, which will be expressed as a certain combination of conditional likelihood ratios. In the cases studied here, the LR method has the Shiryaev optimality. Also, the Shiryaev-Roberts and the CUSUM methods are evaluated. These two methods combine conditional likelihood ratios in other ways. A comparison is also made with the Shewhart method that is a commonly used method. When control charts are used in practice, it is necessary to know several characteristics of the method. Asymptotic properties have been studied by Srivastava and Wu (1993) and Siegmund and Venkatraman (1995) and others. Here, properties for fInite time of change are studied. The usual ARLo and ARLl (which are the average nm lengths until an alarm under the hypothesis of no change and the hypothesis of immediate change, respectively) are used. Besides that, the probability of a false alarm, the expected delay, the probability of successful detection and the predictive value are used for evaluations. Since the methods have interesting optimality properties, the results also enlighten different criteria of optimality .
Some power aspects of methods for detecting different shifts in the mean
(University of Gothenburg, 1999-07-01) Järpe, Erik; Wessman, Peter
We study, by means of simulations, the performance of the Shewhart method, the Cusum method, the Shiryaev-Roberts method and the likelihood ratio method in the case when the true shift differs from the shift for which the methods are optimal. The methods are compared for a fixed expected time until false alarm. The comparisons are made with respect to some measures associated with power such as probability of alarm when the change occurs immediately, expected delay of true alarm and predictive value of an alarm.
Some principles for surveillance adopted for multivariate processes with a common change point
(University of Gothenburg, 1996-02-01) Wessman, Peter
The surveillance of multivariate processes has received growing attention during the last decade. Several generalizations of well-known methods such as Shew hart , CUSUM and EWMA charts have been proposed. Many of these multivariate procedures are based on a univariate summarized statistic of the multivariate observations, usually the likelihood ratio statistic. In this paper we consider the surveillance of multivariate observation processes for a shift between two fully specified alternatives. The effect of the dimension reduction using likelihood ratio statistics are discussed in the context of sufficiency properties. Also, an example of the loss of efficiency when not using the univariate sufficient statistic is given. Furthermore, a likelihood ratio method, the LR method, for constructing surveillance procedures is suggested for multivariate surveillance situations. It is shown to produce univariate surveillance procedures based on the sufficient likelihood ratios. As the LR procedure has several optimality properties in the univariate, it is also used here as a benchmark for comparisons between multivariate surveillance procedures.
Studies on the surveilllance of univariate and multivariate processes
(1999) Wessman, Peter
The surveillance of several processes with different change points
(University of Gothenburg, 1999-02-01) Wessman, Peter
A statistical surveillance situation which involves the simultaneous surveillance of several processes is treated. Some recently suggested multivariate methods are discussed together with a new method based on the likelihood ratio. The emphasis in the discussion is put on different ways to combine information from each time point. The methods treated represent different approaches in this aspect to the construction of multivariate surveillance methods. Shewhart type methods are used to handle the information over time. Comparisons of these methods are made when two processes, which are observed through bivariate normal variables, are surveilled for sudden shifts in the means with known and constant covariance structure. Also, the effects of different change points for the variables are considered. Generalisations to the multivariate case of the ARL and the probability of a successful detection are suggested. The main difference in performance between the compared methods is shown to be between methods based on the marginal and joint distributions of the variables. It is also shown how the choice of method depends on both on the correlation between the variables and when the time when a second change point can be expected.