Abstract: Predictive maintenance methods and systems, including a method of applying transfer entropy techniques to find a causal link between parameters; a method of applying quality weighting to context data based on a priori knowledge of the accuracy of the context data; a method of detecting a maintenance action from parameter data by detecting a step and a process capability improvement; a method of managing unattended alerts by considering cost/benefit of attending to one or more alerts over time and assigning alert expiry time and/or ranking the alerts accordingly; a method of displaying components of a complex system in a functional way enabling improvements in system diagnostics; a method of determining the time of an event indicator in time series parameter data; a method of classifying an event associated with a fault condition occurring within a system; and a method of determining whether an event recorded in parameter data is attributable to an external factor.

Abstract: Methods and apparatus for determining a subset of a plurality of relationships between a plurality of parameters describing operation of a lithographic apparatus, the method comprising: determining a first set of data describing first relationships between a plurality of parameters of a reference apparatus; based on one or more measurements, determining a second set of data describing second relationships between the plurality of parameters of the reference or a further apparatus; comparing the first set of data and the second set of data; and selecting from the second set of data a subset of the second relationships based on differences between the first set of data and the second set of data.

Abstract: A method for determining a causal relationship between events in a plurality of parameter time series, the method including: identifying a first event associated with a parameter excursion event; identifying a second event associated with a failure event, wherein there are a plurality of events including the first events and second events; determining values of transfer entropy for pairs of the events to establish a causal relationship for each of the pairs of events; using the determined values of transfer entropy and identified causal relationships to determine a process network, wherein each of the events is a node in the process network, the edges between nodes being dependent upon the values of transfer entropy; identifying a directed cycle within the plurality of events and the causal relationships; classifying a directed cycle; and classifying one or more events having a causal relation to the classified directed cycle.

Abstract: Methods and apparatus for determining a subset of a plurality of relationships between a plurality of parameters describing operation of a lithographic apparatus, the method comprising: determining a first set of data describing first relationships between a plurality of parameters of a reference apparatus; based on one or more measurements, determining a second set of data describing second relationships between the plurality of parameters of the reference or a further apparatus; comparing the first set of data and the second set of data; and selecting from the second set of data a subset of the second relationships based on differences between the first set of data and the second set of data.

Abstract: A method for determining a causal relationship between events in a plurality of parameter time series, the method including: identifying a first event associated with a parameter excursion event; identifying a second event associated with a failure event, wherein there are a plurality of events including the first events and second events; determining values of transfer entropy for pairs of the events to establish a causal relationship for each of the pairs of events; using the determined values of transfer entropy and identified causal relationships to determine a process network, wherein each of the events is a node in the process network, the edges between nodes being dependent upon the values of transfer entropy; identifying a directed cycle within the plurality of events and the causal relationships; classifying a directed cycle; and classifying one or more events having a causal relation to the classified directed cycle.

Abstract: Predictive maintenance methods and systems, including a method of applying transfer entropy techniques to find a causal link between parameters; a method of applying quality weighting to context data based on a priori knowledge of the accuracy of the context data; a method of detecting a maintenance action from parameter data by detecting a step and a process capability improvement; a method of managing unattended alerts by considering cost/benefit of attending to one or more alerts over time and assigning alert expiry time and/or ranking the alerts accordingly; a method of displaying components of a complex system in a functional way enabling improvements in system diagnostics; a method of determining the time of an event indicator in time series parameter data; a method of classifying an event associated with a fault condition occurring within a system; and a method of determining whether an event recorded in parameter data is attributable to an external factor.