The Operational Safety (OS) of Industrial Systems is today a true engineering discipline, applied in all the different phases of the life of an industrial system, from its conception to its decommissioning, going through the stages of development and operation. In a broad sense, the Operational Safety of Systems can be defined as "Science of Failures". It thus includes knowledge, assessment, prediction, measurement, and control of system failures. In a strict sense, the Operational Safety of Systems is the ability of a system to successfully accomplish the mission for which it was designed, without the occurrence of events with undesirable consequences not only for the components of the system but also the operators, the general public and environment with which the system is in interaction. The objective of the present work is to present the basic concepts and probabilistic methods applied in the different phases of the life of an industrial system to provide an adequate Operational Safety. For this, it begins by presenting some fundamental concepts, deepening in the main component concepts of OS: Reliability, Availability, Maintainability and Security. Next, the use of probabilities is discussed, as well as their most significant laws within the application fields of OS and formalizing the concept of risk. The allocation methods and the assessment methods of the safety of an industrial system are then presented and discussed. Finally, it is proposed a rational procedure for the safety analysis of systems, and ways of using this procedure to the design of systems. Contents: SUMMARY INDEX OF IMAGES, CHARTS AND TABLES……………… PREFACE……………… 1. DEFINITIONS……………… 1.1 SYSTEMS GENERAL THEORY……………… 1.1.1 CHARACTERISTICS OF A SYSTEM……………… 1.1.2 SYSTEM ANALYSIS……………… 1.1.3 FAILURE……………… 1.1.4 BREAKDOWN……………… 1.1.5 RELATIONS AMONG DEFECT, FAILURE AND BREAKDOWN……………… 1.2 FAILURE MODES……………… 1.2.1 CONCEPTION……………… 1.2.2 DEPENDENCY AMONG FAILURES……………… 1.2.3 COMMON CAUSE AND CASCADING FAILURES……………… 1.2.4 CLASSIFICATION OF COMMON CAUSE FAILURES……………… 1.3 OPERATIONAL SAFETY OF SYSTEMS……………… 1.3.1 CONCEPT……………… 1.3.2 RELIABILITY……………… 1.3.3 AVAILABILITY……………… 1.3.4 MAINTAINABILITY……………… 1.3.5 SECURITY (OR SAFETY) ……………… 1.3.6 CINDINISTIC……………… 1.3.7 SAFETY LEVELS……………… 1.3.8 COMMITMENT BETWEEN RELIABILITY AND SAFETY……………… 1.3.9 CLASSIC SAFETY STANDARDS……………… 1.3.10 SAFETY AS QUALITY……………… 1.3.11 SAFETY AND DECISION-MAKING PROCESS……………… 1.3.12 MURPHY’S “LAWS”……………… 1.4 RISK……………… 1.4.1 CONCEPT OF DANGER……………… 1.4.2 CONCEPT OF RISK……………… 1.4.3 RISK QUANTIFICATION……………… 1.4.4 RISK CLASSIFICATION……………… 1.5 ABSOLUTE SAFETY AND ACCEPTABLE RISK……………… 1.5.1 ABSOLUTE SAFETY……………… 1.5.2 RISK ACCEPTABILITY……………… 1.5.3 RISK TOLERABILITY……………… 1.5.4 COMMITMENT BETWEEN LOCAL RISKS AND GLOBAL RISKS……………… 1.5.5 ECONOMIC AND FINANCIAL ASPECTS……………… 2. PROBABILITY SYSTEMS SAFETY……………… 2.1 USE OF PROBABILITY……………… 2.1.1 PROBABILITY THEORY……………… 2.1.2 GENERAL ASPECTS……………… 2.1.3 KNOWLEDGE DOMAIN AND ZONE OF CERTAINTY……………… 2.1.4 PRINCIPLE OF PRACTICAL CERTAINTY……………… 2.1.5 NOTION OF CHANCE……………… 2.2 DIFFERENT DEFINITIONS OF PROBABILITY……………… 2.2.1 CLASSIC DEFINITION……………… 2.2.2 AXIOMATIC DEFINITION (OR COUNTABLE MEASURE) ……………… 2.2.3 RELATIVE FREQUENCY……………… 2.2.4 LIKELIHOOD……………… 2.3 RETURN PERIOD OF AN EVENT……………… 2.3.1 NOTION OF QUANTILE……………… 2.3.2 RETURN PERIOD OF A QUANTILE……………… 2.4 APPROXIMATIONS AND ERRORS……………… 2.4.1 POINCARÉ’S GENERAL FORMULA……………… 2.4.2 PARTICULAR CASES OF POINCARÉ’S FORMULA……………… 2.4.3 SIMPLIFICATIONS TO POINCARÉ’S FORMULA……………… 2.4.4 ACCUMULATED FREQUENCY……………… 2.5 REFLECTIONS ABOUT FIXATION OF PROBABILITY MINIMUM LIMITS……………… 2.5.1 PRELIMINARY CONSIDERATIONS……………… 2.5.2 CREDIBILITY OF SAFETY OBJECTIVES……………… 2.5.3 SELECTING SCENARIOS FOR ANALYSIS……………… 2.5.4 ABSOLUTE LIMIT OF NEGLIGIBLE PROBABILITY……………… 3. FORMALIZING THE CONCEPT OF RISK……………… 3.1 DEFINITION AND CONCEPT……………… 3.1.1 ORIGINS OF RISK……………… 3.1.2 NATURE OF RISK……………… 3.2 GRAVITY OF CONSEQUENCES……………… 3.2.1 INCIDENCE OF CONSEQUENCES……………… 3.2.2 CLASSIFICATION OF CONSEQUENCES BY TYPES OF MANIFESTATION OF THEIR EFFECTS……………… 3.2.3 CLASSIFICATION OF CONSEQUENCES BY GRAVITY CLASS OF THEIR EFFECTS……………… 3.3 DETERMINATION OF SAFETY OBJECTIVES……………… 3.3.1 ACCEPTABLE RISK……………… 3.3.2 DEFINITION OF GENERAL SAFETY OBJECTIVES OF THE SYSTEM……………… 3.3.3 QUALITATIVE SAFETY OBJECTIVES……………… 3.3.4 QUANTITATIVE SAFETY OBJECTIVES……………… 3.4 REPRESENTATION OF RISK AND SAFETY OBJECTIVES……………… 3.4.1 DESCRIPTION……………… 3.4.2 NATURE OF REPRESENTATIVE RISK CURVE……………… 3.4.3 AVERAGE GRAVITY AND OBJECTIVE AVERAGE RISK……………… 3.5 TRANSITION FROM UNACCEPTABLE RISK TO ACCEPTABLE RISK……………… 3.5.1 SAFETY ACTIONS……………… 3.5.2 PREVENTIVE ACTIONS……………… 3.5.3 PROTECTIVE ACTIONS……………… 3.5.4 REINSURANCE ACTIONS……………… 3.6 FORMALIZING THE NOTION OF RISK……………… 3.6.1 RETURN PERIOD ASSOCIATED WITH A RISK……………… 3.6.2 EMPIRIC AVERAGE RISK……………… 3.7 INTEREST AND INCONVENIENCES OF RISK QUANTIFICATION……………… 3.7.1 INTEREST OF PROBABILISTIC LANGUAGE……………… 3.7.2 LIMITATION OF THE USE OF PROBABILISTIC LANGUAGE……………… 3.7.3 PRINCIPLES OF THE USE OF PROBABILISTIC LANGUAGE……………… 3.7.4 OBSERVATIONS ON THE USE OF PROBABILISTIC LANGUAGE USE……………… 4. SAFETY ALLOCATIONS……………… 4.1 DEFINITION……………… 4.2 BASIC PRINCIPLES……………… 4.3 MAIN METHODS……………… 4.3.1 EQUIDISTRIBUTION OF RISKS……………… 4.3.2 WEIGHTING RISKS ‘A PRIORI’……………… 4.3.3 WEIGHTING RISKS BY NUMBER OF STRUCTURAL RELATIONS……………… 4.3.4 WEIGHTING RISKS BY OBJECTIVES OR RELIABILITY ASSESSMENTS……………… 5. LAWS OF PROBABILITY……………… 5.1 LAWS OF DISCRETE AND CONTINUOUS VARIABLES……………… 5.2 SELECTING LAW OF PROBABILITY……………… 5.3 EXTREME VALUES LAWS……………… 5.3.1 CONCEPT……………… 5.3.2 STATISTICS OF ORDER ……………… 5.3.3 ASYMPTOTIC DISTRIBUTION OF MAXIMA……………… 5.3.4 TYPES OF ASYMPTOTIC LAWS……………… 5.3.5 GUMBEL’S LAW APPLICATIONS……………… 5.3.6 FRECHET’S LAW APPLICATIONS……………… 5.3.7 SELECTING A LAW OF EXTREME VALUES……………… 6. METHODS OF ANALYSIS AND ASSESSMENT OF SYSTEMS SAFETY……………… 6.1 GENERAL TYPES OF ANALYSIS……………… 6.1.1 EVENT ANALYSIS……………… 6.1.2 ZONE ANALYSIS ……………… 6.1.3 TIME ANALYSIS……………… 6.2 STATIC METHODS……………… 6.2.1 PRELIMINARY RISK ANALYSIS (PRA)……………… 6.2.2 ANALYSIS OF FAILURE MODES AND THEIR EFFECTS (AFME) ……………… 6.2.3 SUCCESS DIAGRAM METHOD (SDM) ……………… 6.2.4 TRUTH TABLE METHOD (TTM) ……………… 6.2.5 BRIEF BREAKDOWNS COMBINATION METHOD (BBCM) ……………… 6.2.6 CAUSE TREE METHOD (CTM) ……………… 6.2.7 CONSEQUENCE TREE METHOD (CQTM) ……………… 6.2.8 CAUSE-CONSEQUENCE DIAGRAM METHOD (CCDM)……………… 6.2.9 STRUCTURED ANALYSIS AND DESIGN TECHNIQUE (SADT)……………… 6.3 ANALYTICAL AND SIMULATION METHODS……………… 6.3.1 STATE SPACE METHOD (SSM)……………… 6.3.2 STOCHASTIC PETRI NET (SPN)……………… 6.4 ADVANTAGES AND INCONVENIENCES OF DIVERSE METHODS……………… 6.4.1 ANALYSIS OF FAILURE MODES AND THEIR EFFECTS (AFME)……………… 6.4.2 SUCCESS DIAGRAM METHOD (SDM)……………… 6.4.3 TRUTH TABLE METHOD (TTM)……………… 6.4.4 BRIEF BREAKDOWNS COMBINATION METHOD (CBBM)……………… 6.4.5 CONSEQUENCE TREE METHOD (CQTM)……………… 6.4.6 CAUSE TREE METHOD (CTM)……………… 6.4.7 CAUSE-CONSEQUENCE DIAGRAM METHOD (CCDM)……………… 6.4.8 STATE SPACE METHOD (SSM)……………… 6.5 COMPARISON OF SEVERAL METHODS……………… 6.5.1 INTRINSIC CHARACTERISTICS……………… 6.5.2 SYSTEM-DEPENDENT FEATURES……………… 6.6 CRITERIA FOR SELECTION OF METHODS……………… 6.7 SPECIFIC METHODS……………… 6.7.1 DEPENDENT FAILURES ANALYSIS METHODS……………… 6.7.2 HUMAN FACTORS……………… 6.7.3 MECHANICS OF STRUCTURE……………… 6.7.4 “SOFTWARE” DEVELOPMENT……………… 7. GENERAL PROCEDURE OF SYSTEM SAFETY ANALYSIS……………… 7.1 CONCEPT……………… 7.1.1 DESCRIPTION OF THE PROCEDURE……………… 7.1.2 STEP 1: INTRINSIC OR INTEGRATED SAFETY (E1)……………… 7.1.3 STEP 2: IMPLEMENTED SAFETY (E2)……………… 7.1.4 STEP 3: SAFEGUARD (E3)……………… 7.1.5 STEP 4: EMERGENCY (E4)……………… 7.1.6 SIMPLIFIED APPLICATION EXAMPLE……………… 7.2 FAILURE MODES ANALYSIS……………… 7.2.1 FAILURE IN DELAY AND FAILURE IN ADVANCE OF ELEMENTS IN TOTAL REDUNDANCY……………… 7.2.2 FAILURE IN DELAY OF ELEMENTS IN PARTIAL REDUNDANCY……………… 7.2.3 COMMON CAUSE FAILURE MODES……………… 7.3 PROBABILITY ASSESSMENTS FROM A LAW OF MORTALITY……………… 7.4 LIMITATIONS OF ANALYSIS……………… 7.4.1 LIMITS OF QUALITATIVE ASSESSMENT……………… 7.4.2 LIMITS OF QUANTITATIVE ASSESSMENT ……………… 7.5 ANALYSES VALIDATION……………… 7.6 ORGANIZATION AND MANAGEMENT OF SAFETY ANALYSIS……………… 7.7 USE OF SAFETY ANALYSIS……………… 7.7.1 USE IN DESIGN OF SYSTEMS……………… 7.7.2 “DETERMINISTIC” DESIGN AND “PROBABILISTIC” DESIGN……………… 7.7.3 USE IN OPERATION OF SYSTEMS……………… 8. BIBLIOGRAPHY………………