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ShipRelated Failures and their CausesTable of Contents:
The shipping industrial sector is made up of many types of ships such as bulk cargo ships, container ships, tankers, and carriers. These ships contain various types of systems, equipment, and components/parts that can occasionally fail. Some examples of these systems, equipment, component/part failures are as follows:
The consequences of these failures can vary quite considerably. Nonetheless, there are many distinct causes of ship failures’ occurrence. Some of the common causes are shown in Figure 7.2. Failures in Marine Environments and Microanalysis Techniques for Failure InvestigationMalfunctioning of systems, equipment, or parts/components operating in marine environments can have catastrophic effects. Nonetheless, before ships sink or lie FIGURE 7.2 Ship failures’ common causes. dead in the water, a process generally occurs that causes the systems, equipment, or parts/components to breakdown. The failure mechanism may be electrical, mechanical, thermal, or chemical [20]. An electrical failure, for example, could occur as the result of internal partial discharges that degraded the insulation of a ship’s propulsion motor. A mechanical failure could occur as the result of an impact between a ship and another moving vessel or a stationary object. A thermal failure could be the result of heat produced by current flowing in an electrical conductor, causing insulation degradation. Finally, a chemical failure could occur as the result of poorly protected partsVcomponents’ corrosion on an offshore wind turbine. Nowadays, modern vessel contains many polymeric components/parts, such as pressure seals and electrical insulation, and some of these are very critical to the vessel operation. There are many microanalysis techniques that are considered quite useful in failure investigations involving polymers. Four commonly used microanalysis techniques are described in the following sections [20]. Thermomechanical AnalysisThis technique involves measuring variations in a sample’s volume or length as a function of time or/and temperature. The technique is quite commonly used for determining thermal expansion coefficients as well as the glasstransition temperature of polymer or composite materials. A weighted probe is placed on the specimen surface, and the vertical movement of the probe is monitored on continuous basis while the sample is heated at a controlled rate. Thermogravimetric AnalysisThis technique measures variations in the weight of a sample under consideration as a function of temperature or time. The technique is used for determining polymer degradation temperatures, levels of residual solvent, the degree of inorganic (i.e., noncombustible) filler in polymer or composite material compositions, and absorbed moisture content. Finally, it is to be noted that the technique can also be quite useful in deformulation of complex polymerbased products. Differential Scanning CalorimetryThis technique measures heat flow to a polymer. This is very important because, by monitoring the heat flow as a function of temperature, phase transitions such as glass transition temperatures and crystalline melt temperatures can be characterized quite effectively. This, in turn, is very useful for determining how a polymer will behave at operational temperatures. The technique can also be utilized in forensic investigations for determining the maximum temperature that a polymer has been subjected to. This can be quite useful in establishing whether an equipment/system/component has been subjected to thermal overloads during service. Finally, this technique can also be employed for determining the thermal stability of polymers by measuring the oxidation induction temperature/time. Fourier Transform Infrared SpectroscopyThis technique is used for identifying and characterizing polymer materials and their additives. This is an extremely useful method, particularly in highlighting defects or inclusions in plastic films or molded parts. Additional information on this method is available in Dean [20]. Mathematical Models for Performing Reliability Analysis of Transportation SystemsMathematical modeling is a commonly used approach for performing various types of analysis in the area of engineering. In this case, the components of an item are denoted by idealized elements assumed to have all the representative characteristics of reallife components, and whose behavior can be described by mathematical equations. However, a mathematical model’s degree of realism very much depends on the type of assumptions imposed upon it. Over the years, a large number of mathematical models have been developed for performing various types of reliabilityrelated analysis of engineering systems. Most of these models were developed using the Markov method. This section presents four such models considered useful for performing various types of transportation system reliabilityrelated analysis. 7.8.1 Model I This mathematical model represents a transportation system that can fail either due to human errors or hardware failures. A typical example of such a transportation system is a truck. The failed transportation system is towed to the repair workshop for repair. The statespace diagram of the transportation system is shown in Figure 7.3. The numerals in circles and boxes denote system states. The model is subjected to the following assumptions: ^{[1]} FIGURE 7.3 Statespace diagram for Model I. X_{hr} is the transportation system constant failure rate due to human errors. Aj is the transportation system constant towing rate from state 1 to state 3. Aj is the transportation system constant towing rate from 2 to state 3. Pj (/) is the probability that the transportation system is in state j at time t, for j = 0, 1,2,3. Using the Markov method presented in Chapter 4 and Figure 7.3, we write down the following equations [2123]:
By solving Equations (7.1)—(7.4), we get the following state probability equations [2123]: where
where
where
where
The transportation system reliability is given by where R_{ls} (r) is the transportation system reliability at time t. The transportation system mean time to failure is expressed by [2124]. where MTTF,_{S} is the transportation system mean time to failure. Example 7.1 Assume that a transportation system hardware failure and failure due to human error rates are 0.0004 failures/hour and 0.0003 failures/hour, respectively. Calculate the transportation system reliability during a 10hour mission and mean time to failure. By substituting the given data values into Equation (7.13), we obtain Also, by substituting the specified data values into Equation (7.14), we obtain
Thus, the transportation system reliability and mean time to failure are 0.9930 and 1428.57 hours, respectively. 7.8.2 Model II This mathematical model represents a threestate transportation system in which a vehicle can be in any one of the three states: vehicle functioning normally in the field, vehicle failed in the field, and failed vehicle in the repair workshop. The failed vehicle is taken to the repair workshop from the field. The repaired vehicle is put back to its normal operating/functioning state. The transportation system statespace diagram is shown in Figure 7.4. The numerals in the circles and box denote transportation system states. The model is subjected to the following assumptions:
The following symbols are associated with the model: у is the y'th state of the vehicle/transportation system, where у = 0 (vehicle functioning normally in the field), у = 1 (vehicle failed in the field), у = 2 (failed vehicle in the repair workshop). FIGURE 7.4 Statespace diagram for Model II. Ay is the vehicle constant failure rate. A, is the vehicle constant towing rate. fi_{v} is the vehicle constant repair rate. P: (r) is the probability that the vehicle/transportation system is in state j at time t, for j = 0, 1,2. Using the Markov method presented in Chapter 4 and Figure 7.4, we write down the following equations [25]:
By solving Equations (7.15)—(7.17), we obtain the following steadystate probability equations [25]:
where P_{0}, P,and P_{2} are the steadystate probabilities of the vehicle/transportation system being in states 0, 1, and 2, respectively. The vehicle/transportation system steadystate availability is given by where A V_{v} is the vehicle/transportation system steadystate availability. By setting = 0 in Equations (7.15)—(7.17) and then solving the resulting equations, we get
where R_{v} (/) is the vehicle/transportation system reliability at time t. P_{0}(t) is the probability of the vehicle/transportation system being in state 0 at time t. The vehicle/transportation system mean time to failure is expressed by [24] where MTTF_{V} is the vehicle/transportation system mean time to failure. Example 7.2 Assume that a threestate transportation system constant failure rate is 0.0002 failures/hour. Calculate the transportation system reliability during a 5hour mission and mean time to failure. By substituting the specified data values into Equation (7.22), we obtain
Also, by substituting the given data value into Equation (7.23), we get
Thus, the transportation system reliability and mean time to failure are 0.9990 and 5,000 hours, respectively. 7.8.3 Model III This mathematical model represents a threestate transportation system in which a vehicle is functioning in alternating weather (e.g., normal and stormy). The vehicle can malfunction either in normal or stormy weather. The failed (i.e., malfunctioned) vehicle is repaired back to both its operating states. The system statespace diagram is shown in Figure 7.5. The numerals in circles and a box denote system states. The model is subjected to the following assumptions:
The following symbols are associated with the model: j is the yth state of the vehicle/transportation system, where j = 0 (vehicle functioning in normal weather), у = 1 (vehicle functioning in stormy weather), j = 2 (vehicle failed). X_{n} is the vehicle constant failure rate for normal weather state. A_{s} is the vehicle constant failure rate for stormy weather state. /r, is the vehicle constant repair rate (normal weather) from state 2 to state 0. ц_{2} is the vehicle constant repair rate (stormy weather) from state 2 to state 1. в is the weather constant changeover rate from state 0 to state 1. FIGURE 7.5 Statespace diagram for Model III. у is the weather constant changeover rate from state 1 to state 0. Pj (/) is the probability that the vehicle/transportation system is in state j at time t, for j = 0, 1,2. Using Markov method presented in Chapter 4 and Figure 7.5, we write down the following equations [26]:
By solving Equations (7.24)(7.26), we get the following steadystate probability equations [26]:
where
where P_{0}, P_{x},and P_{2} are steadystate probabilities of the vehicle/transportation system being in states 0, 1, and 2, respectively. The vehicle steadystate availability in both types of weather is expressed by where VA_{SS} is the vehicle steadystate availability in both types of weather. By setting q, = q_{2} = 0 in Equations (7.24)(7.26) and then solving the resulting equations [24, 26], we obtain
where MTTF_{ve} is the vehicle mean time to failure, x is the Laplace transform variable. R_{ve} (.?) is the Laplace transform of the vehicle reliability. P_{0} (.9) is the Laplace transform of the probability that the vehicle is in state 0. P_{x} (.9) is the Laplace transform of the probability that the vehicle is in state 1. Example 7.3 Assume that in Equation (7.36), we have the following given data values: 0 = 0.0004transitions/hour у = 0.0005 transitions/hour А_{и} = 0.0006 failures/hour k_{s} = 0.0008 failures/hour Calculate mean time to failure of the vehicle. By substituting the specified data values into Equation (7.36), we obtain
Thus, mean time to failure of the vehicle is 1545.45 hours. 7.8.4 Model IV This mathematical model represents a fourstate transportation system in which a transportation system can be in any one of the four states: transportation system operating normally in the field, transportation system failed safely in the field, transportation system failed with accident in the field, and failed transportation system in the repair workshop. The failed transportation system is taken to the repair workshop from the field. The repaired transportation system is put back into its normal operation. The transportation system statespace diagram is shown in Figure 7.6. The numerals in circles and boxes denote transportation system states. The model is subjected to the following assumptions:
FIGURE 7.6 Statespace diagram for Model IV.
The following symbols are associated with the model: ) is the )th state of the transportation system, where / = 0 (transportation system operating normally in the field),) = 1 (transportation system failed safely in the field),) = 2 (transportation system failed with accident in the field),) = 3 (failed transportation system in the repair workshop). A. is the transportation system failsafe constant failure rate. A_{0} is the transportation system failaccident constant failure rate. А,_{д} is the transportation system constant towing rate from state 1. A,„ is the transportation system constant towing rate from state 2. fi is the transportation system constant repair rate. P: (?) is the probability that the transportation system is in state) at time t, for) = 0, 1,2,3. Using the Markov method presented in Chapter 4 and Figure 7.6, we write down the following equations [25]: I I I I
By solving Equations (7.37)(7.40), we get the following steadystate probability equations [25]:
where P_{0}, P_{x}, P_{2}, and P_{3} are the steadystate probabilities of the transportation system being in states 0, 1,2, and 3, respectively. The transportation system steadystate availability is expressed by where A V_{ls} is the transportation system steadystate availability. By setting jU = 0 in Equations (7.37)(7.40) and then solving the resulting equations, we obtain
where R_{lf} (/) is the transportation system reliability at time t. The transportation system mean time to failure is expressed by [24]
where MTTF,_{S} is the transportation system mean time to failure. Example 7.4 Assume that in Equation (7.41), we have the following given data values: X_{s} = 0.0008 failures/hour А_{я} = 0.0004 failures/hour A,_{s}. = 0.0007 towings/hour X_{la} = 0.0004 towings/hour /л = 0.0005 repairs/hour Calculate the transportation system steadystate availability. By substituting the given data values into Equation (7.41), we get
Thus, the transportation system steadystate availability is 0.1804.

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