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Inherent reliability and serviceability. The inherent reliability refers to the reliability which is realized in the products during the whole designing and manufacturing process of the system. It is the inherent function that is to say that when a system is worded out, its inherent serviceability is defined. If the reliability is ignored in the designing process, such as inappropriate choices for components and materials, low safety coefficient, inconvenient inspection and maintenance etc, it is difficult to meet the reliability requirements in future work, no matter what kind of means of manufacturing, how carefully when it is used.
DOI: 10.1016/j.psep.2018.04.011
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Reliability is a product's reliability in use. because the products will also be subjected to the process of wrapping, transportation, storage, installation, use and maintenance after production, and the physical environment are often inconsistent with the required environment.
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Characteristic quantity of reliability. Characteristic quantity of reliability refers to every quantity quantifying the reliability of the system ability. The characteristic quantity of reliability consists of reliability, failure rate, average working time (no fault), mean time between failures, mean repair time, maintain and effectiveness.
DOI: 10.1016/0026-2714(87)90784-0
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1 Reliability refers to the probability of the product to fulfill the assigned function under the provided conditions within the required time. It is a quantitative indicator, a probability value as well, typically represented by r; so R agrees with 0≤R≤1. Reliability refers tp the probability of the normal working time under the stipulated conditions, (0, t), and it is a function of time t and a non-increasing function.
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2 The unreliability refers to the abnormal probit in which the system is in (0, t), usually represented by F, which is also a function of time. When the time t increases, F is increasing all the time. So the function R(t) +F (t) = 1 is defined by the reliability and unreliability.
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3 The function of failure or error probility In practice the fault probility is replaced with frequency of failure probability. Suppose there are N0 products keeping working under the required condition from the time 0, in which r(t) represents the time 0~t cumulative number of failures, and moments 0~t cumulative failure probability F (t) =. So the reliability is R(t)=1-F(t)= . From this it is seen that when t=0, r(t)=0，R（r）=1; when t=∞，r(t)= N0，R(t)=0. Suppose r (t) is differentiable F(t)= == =. So is called the failure density function, indicating the ratio of number of product failures compared with that of total number of the products in a certain time. Accordingly, F(t) has the nature of the distributing function, so it is called the cumulative failure distributing function. Under normal circumstances, the analysis on reliability of product R(t) begins from analyzing f(t) and F(t). Different products tend to have different types of failure distribution, and reflect different types of f (t), so different types of F(t) occur.
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4 Failure rate refers to the failure probability per unit-time after the time when the system produces valid products, usually written as λ(t), which is a function of time t, also known as the failure rate function. Simply put, the failure rate refers the ratio between the effective products number after time t and the product number at time t. It can be expressed as λ(t)= , in which Ns(t)is the number of vaid products at the moment t, while dr(t )the number of the failed after t and during dt. Failure rate can visually reflect the failure of each moment.
DOI: 10.1007/978-1-4419-6348-2_7
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5 Mean-time-to failure is the residue mean life for the unrepairable product, usually written as MTTF（Meantime To Failure）, the average trouble-free time for the repairable product, MTBF (Meantime Between Failure). Components are not usually repaired, failure of one component means it does not work properly. Sometimes if one component does not work properly, system failure may come.
DOI: 10.2478/jok-2021-0017
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6 Meantime To Reliability(MTTR) refers to the average maintenance time required after a failure of the system . It is usually MTTR=, N is repair times, ti is the repair time of ith. System reliability model System reliability model refers to the reliable logical chart and mathematical model of the system. The Reliability Index of the system can be calculated quantitativly by the reliability model. When designing, analyzing and studying the system reliability, the block plan showing the relationship among every parts of the system needs to be set up, to displaying the inter physical relation, and then the block plan showing the reliablity among each function. The prediction and distribution of the system reliability can be made according to the mathematical model. Because system reliability associates not only with the composition and structure of the system but also the reliability of the system changes over time t, when discussing the calculation of system reliability, that is the system is in a steady state, and assumed that within the established periods reliability of components, are constant. That is, only two situations: normal or fail, and each unit are independent from each other, and failure will not affect the other units of a cell. Tandem system, refers to the system is made up of several parts. If parts fail, failure or malfunction of the system as a whole comes out. Fig1 Logic diagram of tandem system According to the definition of series system, reliability of the entire system is the product of the reliability of the constituent elements and its mathematical model is: R(t)== Ri(t) R2(t)…Rn(t). So, the more units cascade system consists of, the more less reliable the system becomes. Therefore, in order to improve the reliability of series system, we can improve the reliability of the unit, to minimize the number of units and shorten the time Parallel model means that when all modules of the system fail, the system fails. Logic diagrams: Fig2 Logic diagram of Parallel system Mathematical model for parallel system: R(t)=1- If the reliability of each unit are equal, R1(t)=R2(t)=…=Rn(t), the system's reliability is: R(t)=1-[1-Rn(t)]n. The reliability of parallel system is higher than each component's reliability. Parallel redundant system is simple, complete system. Functionally, only one unit can complete it; multi-unit parallel is applied to improve the reliability of the system. Series-parallel hybrid model is the most common model, consisting of series and parallel components of a composite system. The systems in many designs are mostly complex ones. To get the reliability of complex systems, the first step is to draw the logical block diagram according to the structure of the system, and then to get their reliability by series and parallel models. Conclusion Reliability engineering is an integrated discipline. With the continuous progress of science and technology, human studies on it increasingly deer, involving systems engineering, mathematics, management, and other related disciplines. This article is just a simple research on the reliability, discussing some theoretical basis of reliability, mathematical description and reliability model.
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