Marvin Rausand - System Reliability Theory

This chapter defines, delimits, and classifies the study object. The system boundary and its operating context are defined. The concepts of system functions and their performance criteria are defined and discussed, and some simple approaches to functional modeling and analysis are presented. This is followed by a brief introduction to the Newtonian–Cartesian paradigm and its implications for system analysis. Systems are classified as simple, complicated, or complex, and it is argued why complex systems are outside the scope of this book. The chapters end with an introduction to system structure modeling by reliability block diagrams .

A (technical) system may be defined as follows:

A set of interrelated elements that are organized to achieve one or more stated purposes.

The term “system” is derived from the Greek word systema , which means an organized relationship among functioning items. Aslaksen (2013) considers a system as the combination of three related sets: (i) a set of elements , (ii) a set of internal interactions between elements, and (iii) a set of external interactions between one or more elements and the external world (i.e. interactions that can be observed from outside the system).

For the purpose of a reliability study, the system elements are usually classified as subsystems, subsubsystems, and so on, down to the component level. The system elements may be organized by a system breakdown structure as shown (simplified) in Figure 2.1. The levels of the hierarchy are called indenture levels , where the first level is called indenture level 1, the next indenture level 2, and so on. 1The number of levels required depends on the size of the system and the objectives of the reliability study. The various subsystems may have different numbers of levels.

Figure 2.1System breakdown structure (simplified).

The lowest level in the system breakdown structure – and in the reliability study – is called component . A component may itself be a system with many parts, but is considered a black box in the study. A black box is an element that is viewed in terms of its inputs and outputs, without concern about its internal structure and functions. When investigating the causes of a component failure, we sometimes need to study the states and conditions of the various parts of the component.

Subsystems are also referred to as modules . In system maintenance, terms such as maintanable item and least replaceable unit (LRU) are often used. A maintainable item is the lowest level in the system hierarchy that is specified for maintenance. A plethora of notions is used in the literature. Among these are the following: apparatus, component, element, equipment, instrument, item, module, part, product, system, and subsystem.

To simplify the notation, the element we are currently studying is referred to as the item , whether it is a system, a subsystem, or a component. An item is defined as

An entity that is able to perform at least one function of its own, under specified operational and environmental conditions and when the required energy and controls are available.

We use the term item , unless when it is important to stress that we study a system consisting of subsystems, sub‐subsystems, and so on.

Embedded software is computer software that is written to control the technical item. An embedded item is a combination of hardware and software that together form a part of a larger item. An example of an embedded item is a microprocessor that controls a car engine. An embedded item is designed to run on its own without human intervention, and may be required to respond to events in real time. Today, we find embedded items in almost all our electric household units, such as refrigerators, washing machines, and ovens.

A reliability study is always based on a range of assumptions and boundary conditions. The most notable is the system boundary that specifies which items are included in the study object and which are not. All systems are used in some sort of environment that may influence and be influenced by the system. To delimit the study object, a system boundary is drawn between the study object and its environment. The inputs to and outputs from the study object are drawn up, as shown in Figure 2.2. A slightly more detailed definition of the term system boundary is

Figure 2.2A study object (system) and its boundary.

A system boundary is a boundary that separates the internal components and processes of a system from external entities. Internal to its boundary, the system has some degree of integrity, meaning the parts are working together, and this integrity gives the system a degree of autonomy.

All assumptions and boundary conditions should be clearly stated in the documentation of the reliability study. Examples include answers to questions, such as

What are the objectives of the study?

What level of detail is required?

What are the environmental conditions for the system?

How is the system operated?

Which operational phases are to be included in the study (e.g. start‐up, steady state, maintenance, and disposal)?

Which external stresses should be considered (e.g. earthquakes, lightning strikes, and sabotage)?

The study object may be a closed or an open system. A closed system may be defined as follows:

A system where the interface to the environment is static and always according to the assumptions specified.

In a closed system, the required inputs are always available, and random disturbances in the environment that may influence the study object are nonexisting. Most of the study objects considered in this book are closed systems. An open system is defined as follows:

A system where disturbances in the environment may influence the study object and where required system inputs and outputs may fluctuate or even be blocked.

Open system are generally much more difficult to analyze than closed systems. Some open systems allow users to manipulate the system structure.

Items are generally designed and built for an intended operating context that should be clearly stated in the item specification and in the user documentation. The operating context specifies how the item is to be operated and maintained, limits to inputs, usage, and loads, and also which environmental conditions the item is supposed to work in and to tolerate. The user manual of a washing machine may, for example, specify intervals for the voltage and frequency of the power supply, the pressure and temperature of the water supply, the type and weight of laundry (e.g. clothes, carpets) put into the machine, the temperature in the room where the machine is located, and the surface on which the machine is placed. The operating context of the item is defined as follows: