- Ship-Related Failures and their Causes
- Failures in Marine Environments and Microanalysis Techniques for Failure Investigation
- Thermomechanical Analysis
- Thermogravimetric Analysis
- Differential Scanning Calorimetry
- Fourier Transform Infrared Spectroscopy
- Mathematical Models for Performing Reliability Analysis of Transportation Systems

# Ship-Related Failures and their Causes

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:

- • Propulsion system failures
- • Heat-exchanger failures
- • Weldment failures
- • Pump failures
- • Sensor failures
- • Boiler failures
- • Piping failures
- • Fuel tank failures.

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 Investigation

Malfunctioning 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 Analysis

This 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 glass-transition 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 Analysis

This 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., non-combustible) 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 polymer-based products.

## Differential Scanning Calorimetry

This 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 Spectroscopy

This 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 Systems

Mathematical 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 real-life 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 reliability-related 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 reliability-related 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 state-space 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 State-space 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 [21-23]:

By solving Equations (7.1)—(7.4), we get the following state probability equations [21-23]:

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 [21-24].

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 10-hour 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 three-state 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 state-space 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:

- • Vehicle failure and towing rates are constant
- • Vehicle repair rate is constant
- • A repaired vehicle is as good as new
- • Vehicle failures occur independently.

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 State-space 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 steady-state probability equations [25]:

where

*P _{0}, P,and P_{2}* are the steady-state probabilities of the vehicle/transportation system being in states 0, 1, and 2, respectively.

The vehicle/transportation system steady-state availability is given by where

*A V _{v}* is the vehicle/transportation system steady-state 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 three-state transportation system constant failure rate is 0.0002 failures/hour. Calculate the transportation system reliability during a 5-hour 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 three-state 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 state-space 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:

- • Vehicle failure and repair rates are constant
- • Alternating weather transition rates (i.e., from normal weather state to stormy weather state and vice versa) are constant
- • Vehicle failures occur independently
- • A repaired vehicle is as good as new.

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 State-space 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 steady-state probability equations [26]:

where

where

*P _{0}, P_{x},and P_{2}* are steady-state probabilities of the vehicle/transportation system being in states 0, 1, and 2, respectively.

The vehicle steady-state availability in both types of weather is expressed by where

*VA _{SS}* is the vehicle steady-state 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 four-state 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 state-space 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:

- • Transportation system safe failure and accident repair rates are constant.
- • Transportation system towing and repair rates are constant.

FIGURE 7.6 State-space diagram for Model IV.

- • Transportation system failures occur independently.
- • A repaired transportation system is as good as new.

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 fail-safe constant failure rate.

A_{0} is the transportation system fail-accident 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 steady-state probability equations [25]:

where

*P _{0}, P*

_{x},

*P*

_{2}, and P

_{3}are the steady-state probabilities of the transportation system being in states 0, 1,2, and 3, respectively.

The transportation system steady-state availability is expressed by where

*A V _{ls}* is the transportation system steady-state 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*= 0.0004 towings/hour

_{la}*/л =*0.0005 repairs/hour

Calculate the transportation system steady-state availability.

By substituting the given data values into Equation (7.41), we get

Thus, the transportation system steady-state availability is 0.1804.

- [1] Failure and towing rates of the transportation system are constant. • Transportation system can fail completely either due to hardware failures orhuman errors. • Failures and human errors occur independently. The following symbols are associated with the model: j is the yth state of the transportation system, where j = 0 (transportation systemoperating normally), j = l (transportation system failed in the field due to ahardware failure), у = 2 (transportation system failed in the field due to a humanerror), у = 3 (transportation system in the repair workshop). XM is the transportation system constant hardware failure rate.