Reliability & Dependency In the name of Allah Reliability & Dependency Teacher: Mahdi Karbasian Student: Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran Email: seyedmohammadmortazavi@ymail.com

Reliability & Dependency Dependent failure one way Negative Dependency Failure Cascading Failure Common Cause Failure Interactive Failure Immediate Intractive Failure Gradual Degradation Interactive Failures Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Definition 1 2 Negative Dependency Failure : Negative dependency failure is defined as failure that can prevent other components in a system from further failing. 1 2 Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Definition 1 2 3 Cascading Failure : Cascading failure is defined as multiple sequential failures. These failures are initiated by the failure of one component,which leads to sequential failures of other components. 1 2 3 Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Definition 1 2 3 Common Casuse Failure : A Common Cause Failure event is defined as the failure (or unavailable state) of more than one component due to a shared cause during the system mission 1 2 3 Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Attention A definition of CCF must encompass the following six attributes : 1. The components affected are unable to perform as required. 2. Multiple failures exist within (but not limited to) redundant configurations. 3. The failures are “first in line” type of failures and not the result of cascading failures. 4. The failures occur within a defined critical time period (e.g., the time a plane is in the air during a flight). 5. The failures are due to a single underlying defect or a physical phenomenon (the common cause of failures). 6. The effect of failures must lead to some major disabling of the system’s ability to perform as required.

Definition 1 2 3 Interactive failure : Interactive failure is defined as mutually dependent failures, that is, the failures of some components will affect the failures of other components and vice versa. 1 2 3 Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Definition 1 2 1- Immediate Interactive Failures : The failure of the influencing component will cause its affected components to fail immediately. The conditions of the two components before failure are independent. Immediate 1 2 Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Definition Gradual Degradation Interactive Failures : The conditions of two components before failure are dependent. A component deteriorates with time, that is, the failure rate of a component increases with time Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Common Cause Failure Explicit Modeling : When the specific causes of CCFs can be identified and the causes are dependent failures, it is better to model CCFs explicitly System Fail Componen 1 & Component 2 Fail Independently Componen 1 & Component 2 Fail due to a CCF Design Error Human Error Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Common Cause Failure Implicit Modeling : When the causes of CCFs are difficult to be identified or cannot be identified, then the CCFs will be modeled implicitly System Fail All the following models belong to implicit models : • The basic parameter (BP)model • Beta factor model • C-factor model • The Multiple Greek Letter (MGL) Model • The Multiple Beta-factor (MBF) Model • The Binomial Failure Rate (BFR) Model • The Alpha Factor (AF) model Componen 1 & Component 2 Fail Independently Componen 1 & Component 2 Fail due to a CCF CCF Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Common Cause Failure Beta-Factor Model : The b-factor model was proposed by Fleming in 1975. is the independent failure rate, which will not cause other component’s failure. is the common cause failure rate, which denotes all the component’s failure caused by a shared cause. Therefore, the total failure rate for component is Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Common Cause Failure Beta-Factor Model : denotes the fraction of common cause failure among all failures of a component. The relationship between CCF and independent failure is expressed by Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Common Cause Failure Beta-Factor Model Advantages : • It is simple. • Only one parameter beta need to be estimated when the data are available. • It is easy and widely used. Some standards recommend this b-factor model to assess the reliability of SIS. • Many models are developed based on beta-factor model, such as C-factor model, multiple Beta-Factor model, Multiple Greek Letter model and so on. • Many checklist methods are proposed to determine plant specific b-factor, such as IEC 61508-6 checklist and IEC 62061checklist.

Common Cause Failure Beta-Factor Model Disadvantages : • It is simple for simple parallel systems, but it is not used for high redundancy systems. • It is not reward for different levels of redundancy. • The traditional probability of the possible multiplicities of failure rates. Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

References Misra, K. B. (2008). Handbook of performability engineering: Springer Science & Business Media. Sun, Y., Ma, L., Mathew, J., & Zhang, S. (2006). An analytical model for interactive failures. Reliability Engineering & System Safety, 91(5), 495-504. Mosleh, A. (1991). Common Cause Failures:An Analysis Methodology and Examples. Reliability Engineering and System Safety, 34(3), 249-292. Mosleh, A., & Siu, N. (1987). A multi-parameter common cause failure model. Paper presented at the Transactions of the 9th international conference on structural mechanics in reactor technology. Vol. M. Seyed Mohammad Mortazavi Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran