12.2.1 Liftboat Fractional Factorial Design of Experiments

To explore the possibility of constructing liftboats with deeper water capability, a DOE was defined using a two-level five-factor fractional factorial design. This notional example DOE was used to study the design possibilities for reaching deeper operational water depths using various factors of leg diameters, lengths, and thicknesses and responses of displacement and lift weight. The leg internals are not used in this first trade-off, as they would be designed after the overall liftboat study of displacement and lift weight based on leg diameter, length, and thickness. The results were analyzed using regression analysis using JMP statistical analysis software. The fractional factorial was chosen as the ability to synthesize liftboat designs to cover the design space was limited by the ability of the existing ship design synthesis tools to formulate liftboat designs, from both a technical aspect and the amount of time needed to design ship alternatives. The resulting set of liftboats for the analysis is shown in Table 12.1, which is a condensed version of the full data table limited to three factors and two responses (the full data table is available on the textbook website).

For displacement, the leg length is found using JMP to be statistically significant, with a p-value of 0.0013. For lift weight, both leg diameter, p-value of 0.0142, and leg thickness, p-value of 0.0209, were found to be statistically significant in the JMP analysis. Figure 12.4 presents an example leg configuration in terms of leg length, leg diameter, and leg thickness. Recall that operating depths of over 300 ft are desirable; accordingly, the leg length is fixed as 335 ft, the leg diameter is set at 9 ft, and the leg thickness is set at 1.875 ft. More detailed examination of this complete trade-off space is required to investigate the appropriateness of the values for leg diameter and leg thickness.

12.2.2 Liftboat Design Trade-Off Space

A potential desired design for a liftboat to achieve 335 ft leg length, indicated in Figure 12.4 by the lines on the x and y axes, shows a predicted displacement of 654 Ltons and a lift weight of 2,231,000 lb. Figure 12.5 shows a different view of the variable relationships in the form of a “cut” through the trade-off space. The graph shows displacement and lift weight as a function of leg diameter and leg length. Constraint for the designer's desired limit for minimum lift weight is set to 2,200,000 lb and the limit for maximum displacement is set to 675 Ltons. The gray shaded areas are regions that do not meet the constraints where the shaded on the left hand side of the graph corresponds to the leg length and leg diameter combinations that do not satisfy the lift weight constraint and the region shaded in the upper portion of the graph corresponds to the combinations that do not satisfy the displacement constraint. The white, unshaded region is the feasible trade-off space. The crosshairs on the right-hand side of the plot are set to a leg diameter of 9 ft and a leg length of 335 ft based on the values chosen in Figure 12.4. Further investigation of the trade-off space, with the leg thickness set to 1.875 inches, shows that the projected design appears feasible, as it is within the white space on the graph shown in Figure 12.5.

A quick investigation of existing liftboat designs reveals an existing liftboat, the Robert, that has a leg length of 335 ft, a leg diameter of 9.5 ft, a leg thickness of 1.875 in., with a displacement of 500 Ltons, a maximum water depth of operation at 280 ft, and a lift weight of 1,500,000 lb. Although the Robert's actual lift weight exceeds the constraint associated with this example trade-off, it is a reasonable choice to use for a quick check to verify the output of the liftboat design model as there are a very limited number of existing liftboat designs. The Robert is within the feasible region limit with respect to displacement. A brief study of the predicted design, based on the liftboat model, and an actual design, the Robert, can be accomplished by performing an uncertainty analysis.

12.2.3 Liftboat Uncertainty Analysis

To investigate the difference between the predicted result and the existing liftboat, a simulation with 5000 data points was performed using JMP to study the distribution of possible displacements in the model. The distribution, Figure 12.6, shows that the model has a mean of 655 Ltons and a standard deviation of 160 Ltons. The model shows a wide variability in the output. This is not surprising as there were few data points for this rough model. If a smaller variation about the mean were desired before using the model for decision-making, more time and effort would have to be put into developing more ship variants or collecting more actual ship data points design to attempt to reduce the variation and improve the prediction capability.

12.2.4 Liftboat Example Summary

This example shows that DOE can be used to define the test points for a model of a liftboat before deciding on the detailed design for construction. The results of model analysis of the test points specified by the DOE can be used as a surrogate for available design tools when data, information, and design tools are limited or not available. The tradespace is then used to investigate the design possibilities, including using uncertainty analysis to further study the resulting liftboat design trade-off space.

12.3.1 Cruise Ship Taguchi Design of Experiments

In order to study the ramifications of early design decisions, a Taguchi screening experiment was performed on a notional cruise ship design. A set of eight factors was chosen to vary the technical aspects of the ship design, and three responses were selected to study their impact on the possible outcomes. The three responses are related to economic aspects are the ones used for decision-making. The fourth, the beam of the ship, is included since the beam can be limiting for transport through various canals, such as the Panama Canal. A Taguchi L18 design was selected for the experiment, Table 12.2.

12.3.2 Cruise Ship Design Trade-Off Space

The cruise ship L18 point designs shown in Table 12.2 were synthesized using a Microsoft Excel spreadsheet model provided on the textbook website. The Microsoft Excel spreadsheet was used to synthesize the ships, while JMP provided the DOE and resulting statistical analysis. The results were analyzed using JMP. The JMP results are shown in Figure 12.7 for the design point with the highest revenue.

The design space can be used to vary the factors to study the possibilities for different ship characteristics, such as number of passengers, propulsion type, power plant, and number of propulsors, and the range of possibilities for costs and revenue, within desired beam restrictions. The technical variable factors on the x-axes of Figure 12.7 can be set interactively in JMP, and the resulting business variable responses on the y-axes. The results show that five factors (operational range, days of stores, propulsion type, number of propulsors, and number of engines) have little or no impact on any of the MOEs that are the primary concern of the stakeholders. These do, however, maintain a link to the variables that the shipbuilders are primarily concerned with, so they are valuable to maintain an ability to discuss the ship characteristics among all stakeholders. The ship characteristics technical variables are set in Figure 12.7 to indicate the maximum revenue, while showing the ship beam in case this becomes an important consideration for passage through canals and other restricted waterways.

The design space can also be explored using the trade-off approach employed for the liftboat example. Figure 12.8 shows revenue, acquisition cost, operating cost, and beam as a function of passenger capacity and brand quality. A $10,000 minimum constraint is set for the Revenue at $10,000, a $1500 maximum constraint is set for the acquisition cost, a $5600 maximum constraint is set for the operating cost, and a 120 ft maximum constraint is set for the beam.

The gray shaded areas correspond to the regions of the design space that do not meet the constraints (where referring to the right hand side of the graph where labels for the respective shaded regions are located the region corresponds to combinations that do not satisfy the revenue constraint, the shaded region just above the white region corresponds to operating cost, the next region up corresponds to the acquisition cost, and top-most shaded region corresponds to the beam). Note that the white, feasible region suggests that as the brand quality Increases, fewer passengers can be included in the ship. Currently, Figure 12.8 identifies a ship configuration with a budget brand quality and 2500 passengers as a feasible ship configuration. Note that the size of the feasible region will be reduced if the constraints are altered (Figure 12.9 presents an example).

Figure 12.9 shows the impact of a reduction in the allowable ship beam (note that it has been reduced from 120 ft in Figure 12.8 to 110 ft in Figure 12.9). This has rendered the previous ship configuration of 2500 passengers with a budget brand quality infeasible. Now it is only possible to accommodate 2400 passengers, even with a budget brand quality, due to the reduction in acceptable ship beam.

12.3.3 Cruise Ship Example Summary

This example shows a more basic trade-off structure where technical variables can be set to indicate the levels of business variable outcomes. The technical variables summarize the various ship variant alternatives that can be designed in order to meet desired business goals, while simultaneously checking a technical variable that might constrain operations in some desired concepts of operation.

12.4.1 NATO Surface Combatant Ship Stakeholder Need

The first step in this project is to determine the high-level stakeholder needs and requirements. Based on the NATO report, the stakeholder needs for this example are listed in Table 12.3.

Understanding the priorities for these stakeholder needs is useful to accomplish a decision analysis. Using value functions, the stakeholders were found to have priorities as shown in Table 12.4.

Next, the stakeholder value function curves for each of the needs were determined, with the results shown in Figure 12.11.

The individual value functions were rolled up into an alternative value, labeled in this case as Overall Measure of Effectiveness (OMOE), by multiplying the value for each need as indicated in the design outcome by the priority weight for each respective need (see Chapter 2 for further discussion of the additive value model).

12.4.2 NATO Surface Combatant Ship Box–Behnken Design of Experiments

In order to study the possibility for surface combatant ships that might meet the mission requirements, a DOE is conducted. The DOE used is a Box–Behnken design, with four factors at three levels, summarized in Table 12.5.

For this envisioned combatant ship, as is typical for many combatant ship designs, both speed and range have a key interest to both stakeholder and naval architects. The amount of payload that can be carried in this case is used as a surrogate for the weight of the weapons and combat systems equipment that the ship can carry. This is related to the OMOE, as the weapons and combat systems determine the warfighting capability of the ship, but is not modeled explicitly in this example. The margin variable reflects both a design margin, used during ship design to account for design uncertainties, and through-life margin, used to allow for growth in added ship systems that can be accommodated without negatively impacting the level of the design waterline, in the ship during the operation phase of the ship life cycle. The larger the margin, the more flexible the ship is in its ability to allow for engineering changes or upgrades to weapons and other ship systems, while still being able to meet ship operational requirements such as stability and maximum speed through the maintenance of the ship at the design waterline through the life cycle. Margin then has an upside value to stakeholders as it provides for a hedge against uncertainty during design and for a more robust ship over the operational life cycle in that it can adapt to technology advancements in ship systems. The downside to margin is that it adds to displacement at the expense of payload in the end result.

The ship variants for this design study are synthesized using a Microsoft Excel spreadsheet computer program with the factors as inputs. Each ship variant is created individually and balanced from a naval architecture perspective to achieve a feasible ship for each variant.

12.4.3 NATO Surface Combatant Ship Cost-Effectiveness Trade-Off

Displacement and length are model responses of interest to the naval architects and marine engineers, and for comparison to other existing ships during a decision-making process, so they are kept in the model results. The key responses of interest for the decision-makers are the cost and the OMOE, so these are the focus of this example. These results are summarized in Table 12.6, with each variant given a unique alternative design number, labeled as A1 through A25.

A plot of the cost versus OMOE is shown in Figure 12.12.

The variants that fall on the Pareto frontier are the ones with the highest OMOE at the lowest cost. These are clustered along a line that traces a path along the upper left edge of the plot. This region is magnified in Figure 12.13 to show the four variants that are nondominated. The four variants range in cost from $314.7 to $394.9 M, and OMOE from 0.629 to 0.966. The selection of the best variant is up to the decision-makers in trading off cost versus effectiveness, as all four solutions are equally optimal in a multiple criteria sense. Affordability considerations (Chapter 4) will be important in this decision. All other variants are dominated by these four, and unless there is significant uncertainty in the variants, these do not need to be considered further in the decision-making process.

12.4.4 NATO Surface Combatant Ship Design Tradespace

In order to more thoroughly explore the design space, the factors and response outputs from the DOE are studied using interaction profilers as well as contour profilers. The variables for the design variants are explored by studying their relationship to the outputs used for overall decision-making; in this case, cost and effectiveness, as indicated by OMOE, are used as the basis for decision-making. The resulting Effects plot is shown in Figure 12.14.

By visually inspecting the curves, lines with steep slopes correspond to variables that have substantial impacts on each MOE. The factor that impacts cost the most is speed, while the factor that impacts the OMOE the most is payload. This is confirmed by examining the JMP Effects Pareto Plots, Figures 12.15 and 12.16, with the x-axis as percent effect.

Since payload and speed have the most impact on the design decisions, as indicated by the longest bars in Figures 12.15 and 12.16, respectively, these factors are the primary ones varied to explore the design space. This exploration provides a more detailed look at design possibilities beyond the four Pareto solutions by including variations in the design variables that fall between the data points used for creation of the bounds of the design space.

12.4.5 NATO Surface Combatant Ship Design Trade-Off

To begin with, a series of design space portions have to be viewed on trade-off space plots generated by JMP. The plots can be studied interactively in JMP, but static images are used here to demonstrate a process for investigating the tradespace. The two factors of payload versus speed are plotted with several responses overlaid. For now, the high cost limit is set to $400 M and the low OMOE value is set to 0.83. The resulting feasible design decision space is now shown with a white background in Figure 12.17. The trade-off example is not exhaustive and is used only to show how the process of studying a trade-off space can be accomplished.

The design variant defined by Figure 12.17 is detailed in Table 12.7. Note that Ship A11 is one of the original variants from the DOE table.

Ship variant A11 is the best performing alternative with respect to the OMOE that also satisfies the cost constraint of $400 M. However, it may be useful to examine alternative scenarios. As designs mature from concept to preliminary stages, information generated about the design details may make a design impossible to achieve. Unforeseen design changes may also make it impossible to actually create Ship A11. Examination of Figure 12.17 suggests that it may be interesting to examine an alternative ship (termed Ship A11a) that is unable to achieve a total payload of 350 Ltons and can only achieve a payload of 320 Ltons. A visualization of this ship is shown in Figure 12.18; note that it is incapable of satisfying the OMOE constraint of 0.83 and is therefore currently an infeasible system alternative.

The utility of the interactive design space exploration approach is easily demonstrated through presentation of additional design trade-off spaces. For instance, while Figure 12.18 suggests that Ship A11a, which can only achieve a payload of 320 Ltons, is incapable of satisfying the OMOE constraint, examination of an alternative visualization of the trade-off space suggests a potential solution. Figure 12.19 presents a visualization of the same trade-off space but presents the speed and the range (rather than speed and payload, as shown in the previous visualizations).

Note that Ship A11a is still shown as infeasible, but the alternative visualization suggests that by increasing the range to 6600 nm, the ship (now termed Ship A11b in Figure 12.20) becomes feasible.

The impact of this change can be visualized more clearly by a reexamination of the original trade-off space of speed and payload. Figure 12.21 presents an example of Ship A11b from this perspective. Note that Ship A11b is feasible with respect to both the OMOE and cost despite only having a payload of 320 Ltons (compared to 350 Ltons for the original Ship A11). This is a result of the increase in range from 6000 nm for Ship A11 to 6600 nm for Ship A11b.

Further study of the feasibility of Ship B with respect to payload versus speed at 5% margin is shown in Figure 12.22. This ship alternative is within the feasible region, indicated with a white background. This example highlighted the utility of the design trade-off space exploration approach for scenarios where constraints are imposed that cause the system to become infeasible. The design trade-off space exploration approach is also useful when requirements are imposed by a stakeholder that may conflict with analysis results. For example, a stakeholder may desire a modification to Ship A11 that increases the speed from 30 to 32 knot while also reducing the payload to 325 Ltons. A visualization of such a scenario is shown in Figure 12.22 (the ship is now termed Ship A11c).

The stakeholder requirement for increased speed, coupled with the decrease in the acceptable payload, has caused the ship to become infeasible with respect to cost. Note that the system can actually become feasible by decreasing the speed to the original value of 30 knot. However, if the stakeholder is unwilling to accept a restricted speed, the design trade-off approach can explore alternative views to define an acceptable system. Figure 12.23 presents a visualization of the trade-off space between the margin and the payload. Note that there is a small feasible region associated with ship configurations with a payload of 325 Ltons and a margin of 5% (reduced from the original value of 7.5%). This ship configuration is plotted as Ship A11d.

Ship A11d is feasible within the cost and OMOE constraints, even though the ship speed is increased to 32 knot and the payload is restricted to 325 Ltons. This highlights the alternative usage of the design trade-off space exploration approach, which allows a stakeholder to examine the impact that system requirements may have on the size of the total number of feasible system configurations as well as the interactions between input factors that must be investigated as a result of each new system requirement.

12.4.6 NATO Surface Combatant Ship Trade-Off Summary

This example shows a design trade-off beginning with consideration of stakeholder needs and requirements and continuing to the development of a DOE trade-off space. Several cost versus Effectiveness optimal solutions are identified from the DOE results. Next, a possible design trade-off is then studied by varying design variable factors and responses to investigate the space for solutions that are interpolated between the DOE points. The resulting designs are summarized in a form that decision-makers can review as a series of variant alternatives that are both feasible and reach the limits of the trade-off since the variables cannot be set to achieve all of the available values simultaneously.