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Abstract: In recent years, the advent of technology has necessitated the use of ‘smart’ transmitters. A transmitter is described as ‘smart’ if it incorporates signal conditioning and processing functions that are carried out by embedded microprocessors. Smart transmitters generally have the features like self-diagnosis, fault detection, digital communication etc. However, with the advancement in the features and capabilities, the complexity of the smart transmitter has increased and also the estimation of its reliability. In this paper, we have carried out reliability analysis of a smart pressure transmitter. Incorporation of the smart features requires use of many electronic items/components. These components of the system may or may not fail independently, and their failure may lead to unavailability or degraded performance of the system. This has been modelled using the Goal tree (GT) and Success tree (ST) methodology. GT defines system objective which is a set of functions that shall be fulfilled to achieve the goal. Success tree ST defines the structure of the system and comprises system components used to achieve the GT functions. The system performance is considered as a function of its components. The interdependency between the system performance and its components is modelled using the Master Logic Diagram (MLD) wherein the potential faults/failures are introduced into the system. Nine potential faults/failure modes were identified and their impact on the system capability to perform was studied. The cause and effect relationship captured using the MLD is then translated into the mathematical model. The evaluation of this model is carried out using fault tree, which provides an estimate of the unavailability of the system. The unavailability of the system for a mission time of 1 year has been found to be 4.75E-2.
Keywords: Reliability Analysis, Smart Transmitter, Goal Tree, Success Tree and Fault Tree
Smart transmitters are the advanced versions of the conventional analog transmitters. A typical analog transmitter senses some process parameter, which could be temperature, pressure, flow etc., and produce an output signal proportional to the input (measured signal). Smart transmitter comprises microprocessor that helps it perform calculations and is more accurate than its analog counterpart. Also, it has a digital communication protocol which is useful in reading the transmitter’s measured output, in configuring various setting in transmitters, to know the device status, to have its diagnostic information etc. Because of these advantages, smart transmitters are now finding their application even in the sophisticated industries like Nuclear Power Plants (NPPs). However, in order to make the transmitter ‘smart’ requires incorporation of electronic devices which increases system complexity. Hence, it becomes necessary to estimate their reliability in order to ensure that their performance meet the industrial criteria, especially in the safety critical systems.
A complex system that can perform multiple functions and is composed of a large number of components can fail in many ways. For such a complex system there may exist dependency between the modes of failure and the system components. Traditional techniques to perform the system reliability analysis like the Fault Trees (FTs), Event Trees (ETs) have very limited ability to model the dependencies. Petri Nets and Markov models are equipped to model the system dependencies, but they are generally not suitable to model large and complex systems because of their inherent problem of state space explosion. In this paper Goal Tree – Success Tree (GT-ST) methodology has been adopted to perform the reliability analysis of smart transmitters. GT-ST model can completely and rigorously describe a system and its operations. It incorporates a structured approach that shows how a specific objective in a plant is achieved (1). Firstly, the objective of the system is described. This is referred to as ‘goal’ in GT-ST methodology. In the GT, the objective or goal is divided/ broken-down into sub goals or main functions that should be fulfilled in order to achieve the objective. Similarly, the sub goals are further broken down into their supporting functions and the process continues until no more breaking down of the sub functions is possible. However, in order to achieve the system goal by performing various functions as covered in the GT, some system hardware is required. This forms the basis for Success Tree (ST). Similar to the GT, at the first level the main hardware systems are described that are necessary to achieve the system goal. Then, the main hardware systems are further broken down into the supporting hardware systems that must be in healthy state for the main hardware system to be active. This breaking down process continues until further breaking down is not possible.Because of the large number of equipment, people, and software in very complex systems such as nuclear power plants, development of a complete success tree becomes a major and often limiting task. In addition, because of the huge number of interacting parts, the GT-ST representation becomes very complex. In order to present the success logic of a very complex interacting system in a compact and transparent fashion, the MLD can be used (2).The MLD explicitly shows the interrelationships among the independent parts of the systems, including all of the support items (2).
System Architecture of the Smart Transmitter
ELPRT-100SPT is a compact and light weight 24 V DC powered 2 wire Pressure Transmitter with HART communication protocol. It contains a piezo resistive type sensing element for pressure measurement. Output of piezo resistive sensor is converted electronically to 2 wire 4-20 mA DC signal. The system architecture is depicted as shown in Figure .
Figure : System architecture of the smart transmitter
Earlier, reliability prediction of smart pressure transmitter for use in NPP (3) was performed, wherein the total failure rate of the transmitter was calculated as the cumulative of the failure rates of different components in the transmitters. Relex Architect software tool (4) was used to predict the failure rate of different electronic components. To perform the reliability analysis, following assumptions and boundary conditions were considered:
a) All components in a circuit are connected in series i.e. worst configuration
b) Failure rate calculated took into account only the failure modes found from FMEA analysis (MIL-STD-1629A 1980) of the components and the safe failure modes were eliminated
c) All components under study were assumed to be of commercial grade
d) Following operating profile was considered:
I. GSI: ground, stationary, indoors
II. Temperature: 40 degree Celsius
III. Relative humidity: 70%
IV. Duty cycle : 80%
e) Wherever the component failure rate model was not available in the Relex Prediction Software, the failure rates for those components were calculated manually from the MIL-STD-217F handbook.
MLD model for smart pressure transmitter
The GT-ST methodology along with the MLD has been utilized to perform the reliability analysis of the smart pressure transmitter (5).
Goal Tree model
The GT describes the objective/goal of the system. The objective/goal function is decomposed into sub-functions at increasing levels of detail (6). The main purpose of the decomposition is to define physically meaningful functions, realization of which assures that the designated objective can be attained. Such functional decomposition provides a rich explanation of the underlying design, the thinking process of a designer and role of various parts and entities of the system (2). The goal function of the smart pressure transmitter for this case study has been considered as “to obtain the measurements”. This goal function can be decomposed into 2 main functions:
1. Obtain the process data (henceforth called ‘measured data’)
2. Process measured data
These main functions are linked with the ‘AND’ logic i.e. both these functions shall be attained in order to achieve the system goal.
Success Tree model
The ST focuses on the physical aspects of the system and is developed from top to bottom, looking at all levels at which the system can be analysed. In essence, the physical elements collect all the components of the system necessary to achieve any of thefunctions present in the GT (6).
The success tree part of the GTST model is a logicalmodel of a hardware or plant system from which success paths can be determined. A success path shows various components whose proper operation guarantees the successful operation of the system (1).
The necessary hardware components required for the successful operation of the main functions thereby ensuring attainment of the goal function are:
1. Input board
2. Signal conditioning board
3. Display board
4. CPU board
Relationship between the GT-ST MLD has been considered to be of logical type. Logical relations are used to show the redundancy and connectivity between various nodes (objects, functions, behaviours, goals, and classes). In a logical relationship the states of the input and output nodes are binary (2).
Faults and Failures
For performing the reliability analysis, faults and failures are introduced which provide the dysfunctional aspects (5). It is very difficult to identify or define all the possible faults and failure. So, only the significant fault and failures that may affect the system have been considered for the analysis.A fault is an abnormalcondition that may cause a reduction in, or loss of, the capacity of an entity to perform a required function; a failure is the termination of the ability of an entity to perform a required function or in anyway other than as required (7). 9 significant/potential faults/failures were identified for the smart pressure transmitter as shown in Figure 2. The data for some of these failures is taken from Table .
Master Logic Diagram
Due to the huge number of interacting parts, the GT-ST representation becomes very complex. In order to present the success logic of a very complex interacting system in a compact and transparent fashion, the MLD is a good choice (2).The MLD explicitly shows the interrelationships among the independent parts of the systems, including all of the support items (2). The hierarchy of the MLD is displayed by using the interdependency matrix in the form of a lattice. Bottom left side of the MLD constitutes the success tree. The top right side of the MLD constitutes the goal tree.
Relationship modelling in the MLD
The relationship/dependency between the entities is displayed by using the interdependency matrix in the form of a lattice. This relationship is represented in the MLD by filled dots. The degree of relationship is further specified by using a suitable colour of the dot. Strong relationship is represented by a black dot. Medium relationship is represented by grey dot. No dot is placed if there is no relationship between the elements.
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