1. Introduction 1.1 An Overview 1.2 Some Examples 1.3 A Brief History 1.4 A Chapter Summary 2. Probability 2.1 Introduction 2.2 Sample Spaces and the Algebra of Sets 2.3 The Probability Function 2.4 Conditional Probability 2.5 Independence 2.6 Combinatorics 2.7 Combinatorial Probability 2.8 Taking a Second Look at Statistics (Monte Carlo Techniques) 3. Random Variables 3.1 Introduction 3.2 Binomial and Hypergeometric Probabilities 3.3 Discrete Random Variables 3.4 Continuous Random Variables 3.5 Expected Values 3.6 The Variance 3.7 Joint Densities 3.8 Transforming and Combining Random Variables 3.9 Further Properties of the Mean and Variance 3.10 Order Statistics 3.11 Conditional Densities 3.12 Moment-Generating Functions 3.13 Taking a Second Look at Statistics (Interpreting Means) Appendix 3.A.1 MINITAB Applications 4. Special Distributions 4.1 Introduction 4.2 The Poisson Distribution 4.3 The Normal Distribution 4.4 The Geometric Distribution 4.5 The Negative Binomial Distribution 4.6 The Gamma Distribution 4.7 Taking a Second Look at Statistics (Monte Carlo Simulations) Appendix 4.A.1 MINITAB Applications Appendix 4.A.2 A Proof of the Central Limit Theorem 5. Estimation 5.1 Introduction 5.2 Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments 5.3 Interval Estimation 5.4 Properties of Estimators 5.5 Minimum-Variance Estimators: The Crami?½r-Rao Lower Bound 5.6 Sufficient Estimators 5.7 Consistency 5.8 Bayesian Estimation 5.9 Taking A Second Look at Statistics (Beyond Classical Estimation) Appendix 5.A.1 MINITAB Applications 6. Hypothesis Testing 6.1 Introduction 6.2 The Decision Rule 6.3 Testing Binomial Dataâ H0: p = po 6.4 Type I and Type II Errors 6.5 A Notion of Optimality: The Generalized Likelihood Ratio 6.6 Taking a Second Look at Statistics (Statistical Significance versus â Practicalâ Significance) 7. Inferences Based on the Normal Distribution 7.1 Introduction 7.2 Comparing Y-i?½ s/ vn and Y-i?½ S/ vn 7.3 Deriving the Distribution of Y-i?½ S/ vn 7.4 Drawing Inferences About i?½ 7.5 Drawing Inferences About s2 7.6 Taking a Second Look at Statistics (Type II Error) Appendix 7.A.1 MINITAB Applications Appendix 7.A.2 Some Distribution Results for Y and S2 Appendix 7.A.3 A Proof that the One-Sample t Test is a GLRT Appendix 7.A.4 A Proof of Theorem 7.5.2 8. Types of Data: A Brief Overview 8.1 Introduction 8.2 Classifying Data 8.3 Taking a Second Look at Statistics (Samples Are Not â Validâ !) 9. Two-Sample Inferences 9.1 Introduction 9.2 Testing H0: i?½X =i?½Y 9.3 Testing H0: s2X=s2Yâ The F Test 9.4 Binomial Data: Testing H0: pX = pY 9.5 Confidence Intervals for the Two-Sample Problem 9.6 Taking a Second Look at Statistics (Choosing Samples) Appendix 9.A.1 A Derivation of the Two-Sample t Test (A Proof of Theorem 9.2.2) Appendix 9.A.2 MINITAB Applications 10. Goodness-of-Fit Tests 10.1 Introduction 10.2 The Multinomial Distribution 10.3 Goodness-of-Fit Tests: All Parameters Known 10.4 Goodness-of-Fit Tests: Parameters Unknown 10.5 Contingency Tables 10.6 Taking a Second Look at Statistics (Outliers) Appendix 10.A.1 MINITAB Applications 11. Regression 11.1 Introduction 11.2 The Method of Least Squares 11.3 The Linear Model 11.4 Covariance and Correlation 11.5 The Bivariate Normal Distribution 11.6 Taking a Second Look at Statistics (How Not to Interpret the Sample Correlation Coefficient) Appendix 11.A.1 MINITAB Applications Appendix 11.A.2 A Proof of Theorem 11.3.3 12. The Analysis of Variance 12.1 Introduction 12.2 The F Test 12.3 Multiple Comparisons: Tukeyâ s Method 12.4 Testing Subhypotheses with Contrasts 12.5 Data Transformations 12.6 Taking a Second Look at Statistics (Putting the Subject of Statistics togetherâ the Contributions of Ronald A. Fisher) Appendix 12.A.1 MINITAB Applications Appendix 12.A.2 A Proof of Theorem 12.2.2 Appendix 12.A.3 The Distribution of SSTR/(kâ 1) SSE/(nâ k)When H1 is True 13. Randomized Block Designs 13.1 Introduction 13.2 The F Test for a Randomized Block Design 13.3 The Paired t Test 13.4 Taking a Second Look at Statistics (Choosing between a Two-Sample t Test and a Paired t Test) Appendix 13.A.1 MINITAB Applications 14. Nonparametric Statistics 14.1 Introduction 14.2 The Sign Test 14.3 Wilcoxon Tests 14.4 The Kruskal-Wallis Test 14.5 The Friedman Test 14.6 Testing for Randomness 14.7 Taking a Second Look at Statistics (Comparing Parametric and Nonparametric Procedures) Appendix 14.A.1 MINITAB Applications Appendix: Statistical Tables Answers to Selected Odd-Numbered Questions Bibliography Index

http://library.um.ac.id/free-contents/downloadpdf.php/buku/an-introduction-to-mathematical-statistics-and-its-applications-richard-j-larsen-morris-l-marx-12385.pdf

An introduction to mathematical statistical and its applications / Richard J. Larsen, Morris L. Marx

Rapid Prototyping technologies, especially 3D printing are becoming increasingly popular due to their usability and the constant decrease in price of printing equipment and materials. The article focuses on the study of selected mechanical strength properties of 3D-printed elements, which are not very important if the element is only a model for further manufacturing techniques, but which are important when 3D-printed elements will be a part of a functioning device, e.g. a part of unique scientific equipment. The research was carried out on a set of standardised samples, printed with low-cost standard materials (ABS), using a cheap 3D printer. The influence of parameters (such as the type of infill pattern, infill density, shell thickness, printing temperature, the type of material) on selected mechanical properties of the samples, were tested. The obtained results allows making conscious decisions on the printing of elements to be durable enough, either on a non-professional printer, or when to ordered by a professional manufacturer.

https://iopscience.iop.org/article/10.1088/1757-899X/227/1/012033/pdf

The influence of printing parameters on selected mechanical properties of FDM/FFF 3D-printed parts

Essential steps in bioprinting: From pre- to post-bioprinting

Challenges and Opportunities of Condition-based Predictive Maintenance: A Review

The application of the fused filament fabrication (FFF) or fused deposition modeling (FDM) may be limited due to relatively poor mechanical properties of the 3D-printed components. The present experimental investigation quantifies the effect of the three process parameters viz. raster angle, layer height, and raster width on the tensile properties of the FFF-printed PLA, using an open-source 3D printer. The mean effect of each process parameters on the tensile properties and the effect of the interaction are discussed. From the result analysis, it is found that raster angle, raster width, and interaction of layer height and raster width have a significant influence on the tensile properties. Tensile test results show that parts printed at 0° raster angle exhibit higher tensile strength as compared to those with 90° raster angle. Furthermore, fractography was performed on the tensile specimen using a high-precision measuring microscope to determine the effect of process variables on modes of failure. A close relationship between the raster angle and failure mode has been observed and critically discussed.

Analysis of tensile strength of a fused filament fabricated PLA part using an open-source 3D printer

The problem of production flow in manufacturing systems is analyzed. The machines can be operated by workers or by robots, since breakdowns and human factors destabilize the production processes that robots are preferred to perform. The problem is how to determine the real difference in work efficiency between humans and robots. We present an analysis of the production efficiency and reliability of the press shop lines operated by human operators or industrial robots. This is a problem from the field of Operations Research for which the Discrete Event Simulation (DES) method has been used. Three models have been developed, including the manufacturing line before and after robotization, taking into account stochastic parameters of availability and reliability of the machines, operators, and robots. We apply the OEE (Overall Equipment Effectiveness) indicator to present how the availability, reliability, and quality parameters influence the performance of the workstations, especially in the short run and in the long run. In addition, the stability of the simulation model was analyzed. This approach enables a better representation of real manufacturing processes.

https://www.mdpi.com/2073-431X/6/1/10/pdf

Discrete Event Simulation Method as a Tool for Improvement of Manufacturing Systems

The accuracy of prediction and detection capability have a strong influence over the efficiency of the bottleneck, all equipment and the production system The function of predictive scheduling is 

The model of maintenance planning and production scheduling for maximising robustness

The high productivity of a production process has a major impact on the reduction of the production cost and on a quick response to changing demands. Information about a failure-free machine operation time obtained in advance allows the users to plan preventive maintenance in order to keep the machine in a good operational condition. The introduction of maintenance work into a schedule reduces the frequency of unpredicted breaks caused by machine failures. It also results in higher productivity and in-time production. The foregoing of this constitutes the main idea of the predictive scheduling method proposed in the paper. Rescheduling of disrupted operations, with a minimal impact on the stability and robustness of a schedule, is the main idea of the reactive scheduling method proposed. The first objective of the paper is to present a hybrid multi-objective immune algorithm (H-MOIA) aided by heuristics: a minimal impact of disrupted operation on the schedule (MIDOS) for predictive scheduling and a minimal impact of rescheduled operation on the schedule (MIROS) for reactive scheduling. The second objective is to compare the H-MOIA with various methods for predictive and reactive scheduling. The H-MOIA + MIDOS is compared to two algorithms, identified in reference publications: (1) an algorithm based on priority rules: the least flexible job first (LFJ) and the longest processing time (LPT) (2) an Average Slack Method. The H-MOIA + MIROS is compared to: (1) an algorithm based on priority rules: the LFJ and LPT and (2) Shifted Gap-Reduction. This paper presents the research results and computer simulations.

/pdf/a-hybrid-multi-objective-immune-algorithm-for-predictive-and-1nwg51np3r.pdf

A hybrid multi-objective immune algorithm for predictive and reactive scheduling

In the paper a classical model of failures is considered in that successive failure-free times are supposed to have Gamma distributions and are followed by exponentially distributed times of repairs. It is assumed that parameters of these distributions, in general, change with time. Basing on information about the number of failures and failure-free times in a number of periods of the same duration in the past, three different methods of estimation unknown parameters of the model are proposed. Next, predictions of the most important reliability characteristics are found.

Estimation of Reliability Characteristics in a Production Scheduling Model with Failures and Time-Changing Parameters Described by Gamma and Exponential Distributions

Iwona Paprocka

Papers

The influence of printing parameters on selected mechanical properties of FDM/FFF 3D-printed parts

Discrete Event Simulation Method as a Tool for Improvement of Manufacturing Systems

The model of maintenance planning and production scheduling for maximising robustness

A hybrid multi-objective immune algorithm for predictive and reactive scheduling

Estimation of Reliability Characteristics in a Production Scheduling Model with Failures and Time-Changing Parameters Described by Gamma and Exponential Distributions