PUESTAS A TIERRA

Generally failure rate data is available for components or sub-systems of complex systems. System reliability modelling methods provide a process of aggregating the failure rates of all system components to arrive at a system faire rate or reliably prediction.

2.3.5.1 Reliability Block Diagram (RBD)

Reliability block diagrams (RBD) are a popular method for modelling a system while carrying out a reliability assessment and have been used in [7],[47] [49] [77] [78]. RBDs are used for reliability prediction and life cycle management because they can diagrammatically represent a system’s reliability performance. RBDs require defining what is considered as a successful operation of the system and is hence often contracted based on the functional block diagram of a system[78]. It comprises equipment (represented by blocks) which represent the logical behaviour of the system. The blocks are statistically independent and are preferably large. A stochastic representation of the systems probability of failure is obtained by linking these blocks and forming a success path. The final failure rate of the system is calculated by converting the failure rates from all branches (series and parallel) of the block diagram into a series and then summing them up.

RBDs are suitable for modelling systems with non-repairable sub components and can model systems which have either failed or in operation. They may be used to model repairable systems to some extent, in that they may be used to obtain probability of failure between two failures. The interconnection between components may be in Series, Parallel or cross linked.

2.3.5.2 Fault Trees

By using this Fault trees, it is possible to identify events which interact with other events through logic gates to form new events. The analysis starts with an undesirable event. To carry out the analysis, the failure modes of the components have to be identified. The interconnection between components also needs to be identified. This is easily done by a functional layout diagram. Boundary conditions

are also required to identify the situations in which the fault tree is to be drawn. Fault tree analysis may be either qualitative or quantitative. Qualitative methods use Monte-Carlo simulations or deterministic methods to define minimum cut sets or path sets. The Monte Carlo simulation assigns a failure rate to each of the components usually based upon exponential distribution. A comprehensive review of the early works of fault tree analysis is given by [79].

2.3.5.3 Reliability Allocation

Some components of a system are more critical to reliability than others. This has been confirmed by Thies et [80] highlighted that some components in marine energy converters are more critical than others. A reliability apportionment method may be implemented to influence how the reliability of a system is affected by its various components. The reliability goals may be spread across the system using one of the allocation methods presented below [81]

 Equal apportionment-The dependence of the system’s reliability on its components is equally shared among all the components.

 Base apportionment- this involves applying normalised weight factor to subsystems to compensate for the difference in complexity, environment and manufacturing and other variables.

 ARINC-This method is similar to Base apportionment however weight factors are determined by the predicted failure rates of the components of the system

 AGREE- in this system reliability is allocated by a formula which is based on the systems importance, number of sub systems and mission time.  Feasibility of objective- this is uses a weight factor to allocate reliability

goal based on four ranking values of complexity, state of the art, performance and environment.

 Repairable system- the reliability allocation is carried out based on the required availability, mean time to repair (MTTR) and number of sub systems.

2.3.5.4 Failure

rate

modelling

(Failure

rate

function)

Reliability analysis is often carried out to find the constant failure rate at the bottom of the bathtub curve, however it is understood that failure rate evolved over time.

Several failure rate distributions have been presented in the literature based on statistical probability distributions due to their ability to mimics the evolution of failure rates of components over time.

 Exponential model

The exponential model is used for simple systems where a constant failure rate is observed. Given that that reliability analysis is often carried out over the useful life period, this is not often applicable for modelling many components. The exponential model is given by

( ) =1 ( ( )/ ) (EQN 2.28)

 Weibull model

This is a very common statistical distribution which has been used to model various behaviours, for example wind speeds. The Weibull distribution can be used to model a non-constant failure rate and may come in the form of a single parameter, a two parameter and the three parameter failure rate model. The three parameter Weibull distribution which forms the basis for the Weibull model is given by

( ) =

( )

( )/ (EQN 2.29)

Here, is called the shape parameter, is called the scale parameter and is the location parameter. The equation reduces to a two parameter version when = 0 , and further reduces to a single parameter when = 1 and = 0.

The single parameter Weibull model takes the same form as the exponential model thus is appropriately used in the same context as when the exponential model applies. The two parameter model was used in [82] to model the “infant mortality stage” of the bathtub curve. The Weibull distribution is suitable for representing failure rate distribution in many components including electronic components, gears, ball bearings and relays [83] [84] advocated the three parameter Weibull distribution for the failure rates of mechanical components, but insisted the addition of more parameters to account for environmental factors and processing anomalies which may lead to variation in failure rate will help model failure rates more

accurately. Although the Weibull distribution is eminent, other like Wolfram [78] suggested a lognormal distribution for modelling changing failure rates.

2.3.5.5 Bayesian statistics

Fitting data of failure rates to form a model requires the estimation of parameters of the statistical distribution being used. The most common method for estimating the parameters of the Weibull probability density function (PDF) include maximum likelihood estimation, probability plot and regression analysis such as least squares [85] [86]. Andrawus et al [85] proposed a quantitative technique for maintenance optimisation using a two parameter Weibull probability density function to predict failure rate. The parameter estimation for the Weibull PDF was carried out using maximum likelihood. An alternative to the afore-mentioned techniques (classical techniques) is the Bayesian Statistics approach. Theis et al [82]demonstrated how the Bayesian technique can be used to reduce the uncertainties surrounding failure rate predictions of a marine energy converter.

2.3.5.6 Repairable systems

Most complex systems such as Tidal and wind turbines, aircrafts and communication systems are repairable; hence the treating failure rate by a homogeneous Poisson process may be erroneous. Efforts have been made by various researchers to accommodate this error. Crow [87]presented a non- homogenous Poisson process model for evaluating the reliability of repairable systems. The model applies a generalised form of the Poisson process which allows failure intensity to be dependent on age. Cateneanu and Milhalache [88] proposed a reliability model for mechanical components which exhibit age-dependant failures and may recover to their original state (good as new) or operate at a deteriorated state. They also propose that the minimum cut sets can be evaluated using fault trees and followed by a Monte Carlo simulation to obtain failure distribution. A three parameter Weibull distribution was used by Guo et al [57]to model the reliability growth of German and Danish wind turbines. The three parameters included the common shape and scale parameters and a bespoke time factor parameter which describes the past running time. The parameters of the Weibull

distribution were estimated using the maximum likelihood technique and the regressive least squares method. Modelling a system using Markovian method has also been suggested my [89]. Moss and Andrew [45] described how reliability of age dependent mechanical systems can be addressed by using fault trees, Failure mode and effect (FMEA) , and Monte Carlo simulations.

2.3.5.7 Physics of failure

Reliability prediction can be carried out using the Physics of Failure approach. Components incur some damage as they are subjected to loads in their environment. These are irreversible changes to the microstructure of the components which evolve with time and number of load cycles. The expected life of the component can be estimated if the physics that defines the damage evolution is well understood. The Physics of failure approach has been used extensively in the electronics industry and entails the combination of damage calculation with the root cause analysis and probabilistic methods. The analysis in initiated by obtaining the accurate definition of the system under consideration. This includes material specifications, details of component design and after processes. The potential failure modes for the individual components are identified. Each component can have several modes of failure hence its essential that the significant ones are identified. A damage model is developed which is used to calculate the rate of damage accumulation due to the operating environment of the component. This model is supposed to capture the accurate description of the damage kinetics, such that the relative impact of the different load conditions on damage can be quantified, as well as critical operating conditions.

Gray and Watson [68] used this technique to predict the reliability of a 3 stage gearbox of a wind turbine. McLeish [90] suggested incorporating this technique into the Mil HDBK to improve reliability prediction. White and Bernstien [67] described how the PoF technique can be applied to determine the reliability of electronic components. They also presented the difference between the PoF approach and traditional approaches as one advocated by Mil HDBK [91].