This research book is well organized and provides an excellent introduction to the topics: The evolution of reliability in the age of automation: A historical perspective and Finding a solution and analyzing a model. The research book is written in simple language. The materials have been divided into two chapters and are presented in lucid manner in order to make this research book appealing to students.

When something functions as expected when needed, it is considered trustworthy in everyday use. However, a more exact definition that can make use of our scientific understanding to classify, quantify, and evaluate dependability is necessary in order to create a valid theory from this intuitive meaning. Reliability is typically defined as the likelihood that a piece of equipment or technology will work as intended for the duration of its intended usage, under the operating circumstances stated. When a gadget fails to perform as planned, we might consider it to have failed. Of fact, there are more detailed ways to define failure. Failure is defined as any event or circumstance that results in the degradation or unsuitability of an industrial facility, manufactured good, process, material, or service for operating in a way that is satisfactory, safe, dependable, and economical (Witherell, 1994). Understanding the pattern in which failures occur for various mechanisms under various operating situations is one of the main goals of dependability theory. Because the timing of breakdowns is unpredictable, a probabilistic framework must be used to address a system's or device's dependability.

The previous several decades have seen rapid advancements in technology, leading to the creation of new goods, tools, and services designed to improve human comfort. These include a broad spectrum of things, from everyday consumer goods to high-tech equipment for interplanetary travel. Everyone, from the manufacturer to the consumer, wants to make sure the product operates without any problems, at least for a predetermined amount of time. A collection of ideas, procedures, and methods known as reliability theory aims to achieve this goal.

Reliability modeling, reliability analysis, reliability engineering, reliability science, and reliability management are the five primary domains that Blischke and Murthy (2000) have defined as means of achieving the objectives in reliability. Reliability modeling is concerned with identifying the process that yields findings on the failure times in a certain research.

The identification of the rule governing the device lifespan may be made possible by a number of notions that explain the failure mechanism and their characteristics and provide some insight into the patterns in the data. Numerous findings in statistics, stochastic processes, and probability theory serve as the primary inputs in this regard. Inferences regarding the dependability may then be made using the actual data and an appropriate mathematical model. The primary focus of dependability analysis is this. The goal of reliability engineering is to create more dependable goods via product testing, design, and construction. Reliability science studies certain important material qualities that might lead to failure as well as the influence of the production process.

Reliability management places a strong emphasis on preventing unreliability in goods by managing their design, operation, and production, as well as on the financial costs, loss of goodwill, and maintenance requirements. This book solely addresses the modeling and analysis of dependability among these several topics.

In Chapters 2 through 8, the essential mathematical theory is thoroughly explained with many examples. The focus of the conversations so far has been on product dependability and the function of reliability theory in evaluating it. A device's lifespan is frequently defined as the period of uninterrupted functioning. Lifespan, however, may be seen in a broader context. The idea of dependability may easily find applications in life tables, nuptiality studies, term of service before quitting a particular job in manpower planning, and so on if the duration spent by an element or object in a given condition is regarded to be the lifespan. In addition, there are several practical uses for reliability principles in bibliometry, underreported earnings, human settlement analysis, and income distribution construction. In Chapter 9, some significant applications are surveyed. As a result, a study of dependability theory's foundational ideas and methods is crucial in many fields of scientific inquiry.

Reliability theory talks often regard the lifetime as continuous. The processes and distributions used in the modeling and analysis often reflect a continuous, non-negative random variable. In contrast, there is comparatively less information accessible when the lifetime is discrete. Nonetheless, there exist strong arguments in favor of regarding failure times as distinct random variables that assume non-negative integer values. A piece of equipment has a clearly distinct lifetime when it functions in cycles and the observation is the number of cycles completed before breakdown. This also holds true if the device is merely tracked in terms of completed time intervals, such as the number of failures that have happened after an hour, two hours, and so on.

Discrete lives might potentially result from measuring instruments' inaccuracies. Even when clock time is available, there are times when counts are preferable. When it comes to weapon dependability, the quantity of rounds fired matters more than the age at failure. The number of kilometers driven before a car tire becomes unusable is preferable over the number of days before failure in terms of tire lives. The study of dependability in discrete time is strongly motivated by these kinds of issues. Though definitions and meanings may vary, the ideas in discrete and continuous timeframes are the same. Occasionally, continuous distributions are discretized in order to get dependability qualities similar to the continuous case.

However, neither the discretization procedure nor the distributional features must always provide meaningful discrete models in such situations.

Consequently, creating discrete reliability theory involves conceptual and mathematical issues. These topics will be discussed in the following chapters at the relevant locations. Reliability theory for discrete lifetimes requires techniques from probability theory, statistics, and mathematics among other fields for its development. The subsequent portions of this chapter provide a brief description of them.