Linear Distances between Markov Chains

We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results

A Reliability Case Study on Estimating Extremely Small Percentiles of Strength Data for the Continuous Improvement of Medium Density Fiberboard Product Quality

The objective of this thesis is to better estimate extremely small percentiles of strength distributions for measuring failure process in continuous improvement initiatives. These percentiles are of great interest for companies, oversight organizations, and consumers concerned with product safety and reliability. The thesis investigates the lower percentiles for the quality of medium density fiberboard (MDF). The international industrial standard for measuring quality for MDF is internal bond (IB, a tensile strength test). The results of the thesis indicated that the smaller percentiles are crucial, especially the first percentile and lower ones. The thesis starts by introducing the background, study objectives, and previous work done in the area of MDF reliability. The thesis also reviews key components of total quality management (TQM) principles, strategies for reliability data analysis and modeling, information and data quality philosophy, and data preparation steps that were used in the research study. Like many real world cases, the internal bond data in material failure analysis do not follow perfectly the normal distribution. There was evidence from the study to suggest that MDF has potentially different failure modes for early failures. Forcing of the normality assumption may lead to inaccurate predictions and poor product quality. We introduce a novel, forced censoring technique that closer fits the lower tails of strength distributions, where these smaller percentiles are impacted most. In this thesis, such a forced censoring technique is implemented as a software module, using JMP® Scripting Language (JSL) to expedite data processing which is key for real-time manufacturing settings. Results show that the Weibull distribution models the data best and provides percentile estimates that are neither too conservative nor risky. Further analyses are performed to build an accelerated common-shaped Weibull model for these two product types using the JMP® Survival and Reliability platform. The use of the JMP® Scripting Language helps to automate the task of fitting an accelerated Weibull model and test model homogeneity in the shape parameter. At the end of modeling stage, a package script is written to readily provide the field engineers customized reporting for model visualization, parameter estimation, and percentile forecasting. Furthermore, using the powerful tools of Splida and S Plus, bootstrap estimates of the small percentiles demonstrate improved intervals by our forced censoring approach and the fitted model, including the common shape assumption. Additionally, relatively more advanced Bayesian methods are employed to predict the low percentiles of this particular product type, which has a rather limited number of observations. Model interpretability, cross-validation strategy, result comparisons, and habitual assessment of practical significance are particularly stressed and exercised throughout the thesis. Overall, the approach in the thesis is parsimonious and suitable for real time manufacturing settings. The approach follows a consistent strategy in statistical analysis which leads to more accuracy for product conformance evaluation. Such an approach may also potentially reduce the cost of destructive testing and data management due to reduced frequency of testing. If adopted, the approach may prevent field failures and improve product safety. The philosophy and analytical methods presented in the thesis also apply to other strength distributions and lifetime data

Tailoring Machine Learning for Process Mining

Machine learning models are routinely integrated into process mining pipelines to carry out tasks like data transformation, noise reduction, anomaly detection, classification, and prediction. Often, the design of such models is based on some ad-hoc assumptions about the corresponding data distributions, which are not necessarily in accordance with the non-parametric distributions typically observed with process data. Moreover, the learning procedure they follow ignores the constraints concurrency imposes to process data. Data encoding is a key element to smooth the mismatch between these assumptions but its potential is poorly exploited. In this paper, we argue that a deeper insight into the issues raised by training machine learning models with process data is crucial to ground a sound integration of process mining and machine learning. Our analysis of such issues is aimed at laying the foundation for a methodology aimed at correctly aligning machine learning with process mining requirements and stimulating the research to elaborate in this direction.Comment: 16 page

Learning a Static Analyzer from Data

To be practically useful, modern static analyzers must precisely model the effect of both, statements in the programming language as well as frameworks used by the program under analysis. While important, manually addressing these challenges is difficult for at least two reasons: (i) the effects on the overall analysis can be non-trivial, and (ii) as the size and complexity of modern libraries increase, so is the number of cases the analysis must handle. In this paper we present a new, automated approach for creating static analyzers: instead of manually providing the various inference rules of the analyzer, the key idea is to learn these rules from a dataset of programs. Our method consists of two ingredients: (i) a synthesis algorithm capable of learning a candidate analyzer from a given dataset, and (ii) a counter-example guided learning procedure which generates new programs beyond those in the initial dataset, critical for discovering corner cases and ensuring the learned analysis generalizes to unseen programs. We implemented and instantiated our approach to the task of learning JavaScript static analysis rules for a subset of points-to analysis and for allocation sites analysis. These are challenging yet important problems that have received significant research attention. We show that our approach is effective: our system automatically discovered practical and useful inference rules for many cases that are tricky to manually identify and are missed by state-of-the-art, manually tuned analyzers

Uncertainty estimation of shape and roughness measurement

One of the most common techniques to measure a surface or form is mechanical probing. Although used since the early 30s of the 20th century, a method to calculate a task specific uncertainty budget was not yet devised. Guidelines and statistical estimates are common in certain cases but an unambiguous method for all kinds of measurements and measurement tasks is absent.Anew method, the virtual measurement machine, already successfully implemented in CMMs, is now applied on a specific group of stylus measurement instruments namely for: • roughness; • roundness; • contracers (form measurement). Each of these types of machines use the same measurement principle; a stylus is pressed against the object with a well specified force, moved across the object and the trajectory of the stylus tip is registered. The measurement process and its disturbances can be described theoretically and mathematically. Each disturbance or influencing factor which contributes to the uncertainty of the measurement is modeled and with this model simulated (virtual) measurements are generated. The virtual measurement depends upon the magnitude and range of the influencing factor. Some examples of influencing factors are; tip geometry, measurement force, probe gain factors, squareness of measurement axes, etc... The sensitivity of each factor upon the measurement is calculated with so-called virtual measurements. Recalculation of the describing parameters of the measured object with the virtual measurements gives the amount of uncertainty attributed to the influencing factor or machine parameter. The total uncertainty budget is composed out of each contribution in uncertainty of each machine parameter. The method is successfully implemented on two machines: the SV 624-3D (roughness and shape) and theRA2000 (roundness, form and cylindricity). It is shown that an on-line uncertainty budget can be calculated specifying each contributor. As not only gain factors need to be calibrated, but more input variables, e.g. calibration data of machine parameters, are required by the uncertainty calculation, calibration artefacts are developed to perform such a task. The artefacts can be used to perform a total and fast calibration on the shopfloor directly traceable to the appropriate primary standard. Combining the virtual measurement machine, implemented for roughness, roundness and form in high quality software, with the calibration artefacts, a powerful measurement tool is realised which allows to calculate a task specific uncertainty budget for these types of machines and creates a traceable measurement result which can be accredited by accreditation organizations