Multiple failure state components

Continuous analytical solutions can be obtained for Markov models with multiple failure states. Figure D-4 shows a single component with two failure modes. 

ABSTRACT We consider coherent systems subject to common-cause failures described by multiple failure rates. After giving the generalized expression of the failure frequency v as a function of the failure rates and the derivatives of the system reliability TZ, we expand ft, and v in terms of the covariances of the components probabilities of correct operation. Assuming multiple repair rates also, we show that the evolution of the coupled populations of system states may be solved quite generally in successive steps. When all the failure and repair rate are constant, we give the analytical expressions of the steady-state populations for an arbitrary number of dependent components. 

Even if we know the exact (formal) expression ofthe reliabihty of the system, the fact that components are dependent — even if there is no multiple failure rate, the mere existence of coupled repair rales would ensure it anyway—implies that the probability (PiP2>, where ( ) represents a statistical average over replicas as in (Dorre 1989) (it may depend on lime in the case of reliabihty, but not for the steady-state availabUity), is such that... 

For instance, if = 4, Xn = X12 +X123 -FX124 -FX1234. Equation (3) originates with the inclusion-exclusion principle for the probability of joint events ), because Ai2...m affects all systems states for which at least one component /( < / < ) is still operating before the multiple failure ... 

Up to now, we have only rewritten what we want to calculate/evaluate, namely (72) and (v). We stiU have to compute the (p,) s and the associated covariances. As mentioned in the Introduction, we consider here multiple-failure rates ky, etc. and also multiple-repair rates p., etc. The usual way to deal with such a configuration is to consider all the transitions between individual states of the system, solve the equations describing its evolution. If the system is made of n components, it has 2" possible states, which... 

The identification of CCFs among reported failures would overlook many possible causes of CCFs if focusing on complete CCFs alone. Systematic failures, i.e., failures that are due to errors made in specification, design, installation, or operation and maintenance, and which are not due to natural degradation of the component state, may be replicated for several components. When a systematic failure is found, it is important to also ask if other components may have been affected. Therefore, in the failure reviews, it has, for each systematic failure, been questioned whether the failure could have resulted in multiple failures within a relatively short time window. If yes, the failure has been defined as a potential CCF. 

Fail-safe is a common industry term for a specific design safety method, whereby a system reverts to a safe mode or state when a failure occurs. Often a system design requirement will state that the system must be designed to be fail-safe. Although fail-safe design seems like an intuitively obvious method, and is used quite universally, it involves nuances that can allow it to easily be misused and misapplied. Many questions arise, such as does fail-safe cover all possible failures and does it cover only SPFs or multiple failures Does failsafe apply to components, black boxes, subsystems, functions, or combinations of these ... 

Sometimes, a structural system may consist of multiple structural components, each of which has its own limit state. In a series system, the failure of any one component implies the failure of the entire structural system. In a parallel system, it is imperative that all the components fail individually to imply that the system has failed. The probability of system failure can be expressed as a union of component-level failures in the former case, while it is expressed as an intersection of component-level failures in the latter case. Methods for predicting system reliability have been studied by several researchers and documented in several research articles (Hohenbichler and Rackwitz 1983 Cruse et al. 1994) and textbooks (Ditlevsen and Madsen 1996 Haidar and Mahadevan 2000). Sometimes, even a single structural component may have multiple limit states methods for system reliability methods are applicable even to such situations since it is necessary to evaluate probability of union or intersection of different events that correspond to failure across multiple limit states. 

Total probability of failure analysis takes into account the influence of multiple random input variables on the device s Pf. As was stated earlier, in many applications the variability of parameters other than strength can be significant and must be taken into account. The CARES/Life code has been coupled to the ANSYS Probabilistic Design System (PDS) to consider the total probability of failure using the entire space of random input variables [3-5]. When coupled with the CARES/Life program, PDS computes the total probability of failure by accounting for uncertainty in the component s... 

The main purpose of the literature review was to investigate the state of the art for methods for determining model parameters of CCF models. Very comprehensive approaches like what is used in the nuclear power industry to support multiple-Greek letter CCF models, see e.g., NUREG/CR-5485 (1998) and NUREG/CR-6268 (2007), have not been studied in detail in this paper. Instead, the focus has been on identifying methods available for determining the P in the beta factor model, and on the definitions of CCF that may be useful as assistance in the analysis and classification of failures reported for safety-critical components. Literature referenced in a study by Rausand and Hokstad (2008) has been key for the review. 

Multiple fault injections between error models and nominal models are possible. An automatic procedure, the so-called model extension, is employed to integrate both models and the given fault injections. It yields a combined specification that represents both the nominal and the faulty behavior of the system. Its semantics is formally defined by a transition system (cf. Definition 1) whose states are determined by the current modes and error states of all components, together with the current values of their data elements. Its transitions are derived from both the (nominal) mode and the (faulty) error state transitions, attaching a unique transition label to each. The latter can be used by the subsequent analyses, such as the failure effect analysis which is described in the present paper, to distinguish different types of transitions. More details on the specification language and its formal semantics can be found in [2]. 

Markov methods are useful for evaluating components with multiple states, for example, normal, degraded and critical states (Norris (1998)). Consider the system in Hguie 3.9 with three possible states, 0, 1 and 2 with failure rate X and repair rate p. In the Markovian model, each transition between states is characterised by a transition rate, which could be expressed as failure rate, repair rate, etc. If it is defined that ... 

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