The article overviews current trends in research studies related to reliability prediction and prognostics. The trends are organized into three major types of prognostic models: failure data models, stressor models, and degradation models. Methods in each of these categories are presented and examples are given. Additionally, three particular computational prognostic approaches are considered; these are Markov chainbased models, general path models, and shock models. A Bayesian technique is then presented which integrates the prognostic types by incorporate prior reliability knowledge into the prognostic models. Finally, the article also discusses the usage of diagnostic/prognostic predictions for optimal control.

This paper investigates the issues related to variability in degradation-based reliability models and how the variability affects the remaining useful life prognosis being made by those models. Particularly, uncertain failure thresholds in cumulative damage models are of primary interest in this study. Many degradation-based reliability approaches make use of a predefined deterministic value of the failure threshold. However, in real-world cases, the designer may not be aware of the precise critical degradation level. In such situations it is suitable to define the critical degradation level as a range of values having certain probabilities of being critical. If no prior information is available regarding the failure threshold; the critical value has to be estimated from experimental reliability data that are subject to uncertainty due to imperfect measurements and random deviations in reliability properties of the tested components. In these circumstances, it is desirable to model the critical threshold as a random variable. Otherwise, the model can be oversimplified since it neglects the failure threshold uncertainty, whose influence onto the reliability prediction can be significant. This paper presents uncertainty analysis regarding how variability in the failure threshold affects the reliability prediction in conjunction with cumulative damage models. Three types of cumulative damage models are investigated; these are a Markov chainbased model, a linear path degradation model, and a Wiener process with drift. Closed-form equations quantifying the threshold uncertainty propagation into the model prediction are given. A numerical example is presented to illustrate how the critical threshold uncertainty reshapes the predicted timeto-failure distribution, supporting the need for considering the critical threshold uncertainty in accurate reliability computations.

Purpose: The purpose of this study was to determine the effects of Multi Leaf Collimator (MLC) leaf velocity on leaf positional accuracy during modulated arc delivery. Method and Materials: MLC performance was measured for intensity modulated arcs delivered on a Varian21EX equipped with a 120‐leaf dynamic MLC. The performance of the MLC was tested using arc‐based delivery sequences developed by the investigators for routine MLC leaf velocity testing. MLC performance was also tested using actual VMAT delivery sequences created with a commercially available inverse planning system. Errors in the MLC leaf positions were measured using the MLC controller, which recorded positions of each leaf every 50 milliseconds. To characterize the performance of MLC leaves we introduce the notion of MLC leaf performance curve, which is defined to be a dependency between the MLC leaf velocity and the expected leaf position error. Results: At leaf velocities below 2 cm/sec, the MLC leaves were within 2‐mm of the planned position during 98% of the test sequences. The performance of the MLC leaves did not significantly vary with the MLC moving into or out of the carriage. However, there was a significant difference in the performance between the 5‐mm and 1‐cm MLC leaves. Large leaf velocities translate into large magnitudes of MLC leaf positional errors. The typical shape of the leaf performance curve is linear. Summary: The maximum allowable leaf speed for VMAT treatment delivery will depend on the leaf sequencing. If the intensity is modulated with small MLC leaf separations, then the leaf velocity will need to be limited to 1 cm/sec. Leaf position errors of greater than 1‐mm can have a detrimental impact on the delivered dose distributions for small leaf pair separations. Analyzing the leaf performance curves estimated for each leaf one can easily reveal poorly performing MLC leaves.

Purpose: A technique has been developed to retrospectively sort helical tomotherapy sinogram detector data based on the respiration phase. It is not possible to obtain complete sinograms for multiple respiration phases without delivering excessive imaging doses. As such, the sinogram detector data for each respiration phase will be missing projection data necessary to reconstruct an image. The purpose of this study was to develop and test a technique for replacing these missing projections. Method and Materials: An algorithm has been developed that re‐bins raw detector data into specific respiration phases. Redundant rays are used to further complete missing sinogram data. In CT imaging, the attenuation along a ray through a medium can be assumed to be independent of the direction it originates. In rigid slip‐ring geometry, the detector data from the opposite direction may be used in place of the missing projections. To fill in the remaining missing data, In‐Painting is used. In‐Painting is a technique that has been used for many years in the restoration of photographs and museum artwork. Digital In‐Painting, however, is a newer technique that has been used in this study to complete missing sinogram data. Results: The incorporation of redundant ray data and In‐Painting showed a considerable improvement in image quality, especially during periods of fast movement (mid‐inspiration, mid‐cycle, mid‐expiration). The resulting increase in image quality represents a significant improvement over previous 4D‐MVCT techniques. Conclusion: A custom 4D‐MVCT application was developed that retrospectively sorts the sinogram detector based on the measured respiration cycle, calculates and adds redundant rays into the reconstruction, and uses iterative In‐Painting to fill any additional gaps. Tests performed with a moving CT resolution plug indicate that the image quality could be increased without additional dose delivered to the patient. Conflict of Interest : Research sponsored by TomoTherapy, Inc.

This paper discusses the problem of optimal control for systems performing in uncertain environments, where little information is available regarding the system dynamics. A reinforcement learning approach is proposed to tackle the problem. A particular method to incorporate Prognostics and Health Management information derived on the system of interest is proposed to improve the reinforcement learning routine. The ideas behind reinforcement learning-based search for optimal control strategies are outlined. A numerical example illustrating the benefits of using PHM information is given. 1 2