Cost Model Classification

The cost of a new aircraft at the earliest stages of conception can often be best predicted based on an intuitive estimate based on expert judgement using previous knowledge. However, as the project progresses further, more detailed calculation based methods become useful [155].

Calculation-based cost models can generally be split into two categories: Parametric Cost Models (PCM) and Manufacturing Process Cost Models (MPCM) [156]. These two categories of model attempt the overcome the difficulties of estimating the cost of an engineering project from different perspectives and at different levels of fidelity.

Parametric Cost Models

Parametric cost models make use of historical data to establish a statistical relationship be-tween variables. In the case of cost estimation, this will be bebe-tween the cost of the aircraft and the design parameter or parameters found to correlate well with cost. The relationship between the dependent variable cost and its independent variables can be determined using a regres-sion analysis to create a cost estimating relationship (CER). Such relationships are strongly reliant on the size and suitability of the historical database used to create the relationship, in addition to the independent variables selected. The availability of data is also a key factor in the creation of a suitable CER, as program or component manufacturing cost data will typically be proprietary information. Previous research has found a number of parameters that are suit-able for use as CER varisuit-able, such as aircraft empty weight or aircraft flight speed [157, 158].

Aircraft empty weight in particular shows a clear correlation to list price (Figure 6.6), as aircraft cost is a function of the cost of materials and manufacture and hence is closely linked to the aircraft size.

A321-200

Figure 6.6: Aircraft list price versus operating empty weight [159]

The fastest method to predict cost is to create a relationship to list price based on aircraft design parameters or that may be obtained from publicly available data. However, a list price estimation limits the inclusion of novel factors such as new engine designs or other concepts as estimates the aircraft price as a whole product without the nuances of a more detailed breakdown. Simple single-variable relationships can be limited in applicability, for example, a weight-based cost estimation model will predict the same cost for two components of the same weight, regardless of material expense or component complexity. Similarly, speed is not suit-able as a single-varisuit-able predictor of cost, as commercial aircraft typically fly within the same range of cruise Mach numbers but will nonetheless have significantly different costs. Relation-ships therefore employ multiple variables to account for the various factors that correlate with cost. Additionally, it is important to select a variable that has a strong relationship with cost, rather than a variable that correlates only loosely or by chance alone.

As CERs are based on correlations and data fits, a certain measure of uncertainty will always be present. Selection of a suitable model relies on identifying the model with the best fit, or the highest value of R², known as the coefficient of determination. In a best case scenario R²= 1, implying a perfect fit. A basic form of regression analysis relationship is a simple linear relationship between cost and the independent variable [160]:

Y = β₀+ β₁X + E (6.6)

Where β0 and β1 represent the y-intercept and gradient, respectively. The parameter E rep-resents the model error and provides a random factor to the equation which accounts for un-certainty. Such a factor emphasises that a cost model will never perfectly predict cost. As an alternative to a linear relationship, a non-linear power law CER may be used. As it is common to use more than one variable to describe cost, a regression model using multiple linear and non-linear components, or a combination, will often be used.

Rais-Rohani and Dean [156] describe a simplified general expression for cost using a power law relationship:

Cost = e^qY

x^a (6.7)

Each product term represents a parameter contributing to the cost of the product through the power relationship x^a. Complexity is identified as a key cost contributor by the use of the term q, representing the manufacturing complexity. The complexity term represents factors such as part count, tolerance, machining difficulty, and surface finish. It follows that relaxing these requirements will reduce cost. As this is a generalised form, suitable data to define the

6. Acquisition Cost Estimation

relationship for both the complexity and the overall CER is required.

A selection of historic parametric equations for aircraft are available. Roskam separates the cost estimation of an aircraft into a number of subcomponents, split between manufacturing, production, and labour costs [158]. Cost is estimated using power law CERs based on data from a number of sources. These relationships are based on multiple regression formulae originally using data for 29 post-1945 aircraft obtained from the Aeronautical Manufacturers Planning Report, with a database modified over time. The relationships developed by the RAND corporation were used to create the Development and Procurement Costs of Aircraft model (DAPCA) [161]. As the model was based on conventional aircraft for the time, it underestimates the cost of advanced and non-aluminium designs [116]. With a sample set primarily constituted by military aircraft and particularly fighters, the equations are better suited to prediction of military fighter aircraft costs [162]. Additional components not included in the DAPCA equations are accounted for in Roskam’s cost estimation procedure, including the cost of interiors and avionics. Costs reported by such models must be adjusted for inflation in order to represent current value of money, however, it has been noted that the same inflation rate might not apply to all sections of production [163]. As commercial aircraft are produced in reasonably large numbers, models often produce the costs estimate as a cumulative cost for a ‘lot’ of aircraft, from which an average unit cost can be obtained [157, 164].

Sample size and homogeneity have been identified as key factors that influence models [160]. Aircraft with common characteristics ensure homogeneity of the database, however this also limits the data points for a regression analysis, and certain classes of aircraft may be more challenging to define than others [162]. The applicability of a PCM becomes more limited for new technology that is not represented in the historical database. A key issue in the application of old PCM models to current and future aircraft is the increasing use of composite materials, unlike the primarily metallic structure of the historical databases. Added complexity and higher material cost can increase the overall aircraft cost, despite a lower weight [165], a factor partially accounted for by a complexity factor such as the one mentioned by Rais-Rohani and Dean [156].

The most accurate PCM estimation will rely on proprietary data from similar aircraft using a manufacturers experience from previous projects. In the absence of both historical data and detailed manufacturer cost information, the accuracy of a PCM cost estimation is limited. How-ever, the collection of data can be a challenging task due to either the unavailability of internal cost records for commercial projects, or the over-abundance of information in the case of pub-lications for public defence projects [166]. It is also important to ensure the accuracy of the data used in the model, as any inaccuracy will introduce further errors into a model entirely reliant on historical data. Cost model inaccuracy will also be compounded by uncertainty in aircraft weight estimates at the preliminary design stage, the primary parameter for cost esti-mations. Despite the availability and repeatability of results obtained through a CER, the use of the cost estimator’s own expert judgement is a useful part of analyses, especially as errors in formula-based cost estimation of up to 770% have been reported [154].

CERs in the sector of aircraft engine cost estimation are also available, such as those de-veloped by the RAND corporation for military engine programs [167]. The same regression techniques as for airframe are applied, however, the CER descriptor variables will be parame-ters such as turbine entry temperature, thrust rating or shaft horsepower [159].

It is worth noting that many of the sources for acquisition cost CERs rely on data obtained from military aircraft, highlighting the need to determine how applicable the models are for com-mercial projects. Finizie notes in a comparison between contractor and navy cost methods that contractor engines can cost 25% less than navy engines based on their respective estimation methods [168].

Manufacturing Process Cost Models

MPCM models support a bottom-up design process, which assess each component and the processes required for its manufacture, building up to an estimation of the total aircraft cost. A MPCM model may be alternatively known as an activity based cost method (ABC), as cost is comprised of the activities required for manufacture. Many studies consider its application to composite components which can require a large number of processes to manufacture. The Advanced Composite Cost Estimating Model (ACCEM) creates a methodology to estimate the recurring costs of fabrication of composite parts [169]. Cost is comprised of three modules:

factory labour standards estimation, support function estimation, and cost projections. The cost of a component is built up based on the processes required to manufacture it. Similarly, Gutowski et al. [170] outline a model for predicting the cost of advanced composite components by building up a set of tasks. The time total taken for these tasks may be used to predict the cost based on a cost per hour value. Castagne et al. [171] break down the cost of manufacturing a component into associated material, fabrication, and assembly costs. Such methods apply to the more detailed cost estimation of an advanced development stage, rather than the general top-down estimations of the concept phase that are associated with the PCMs of the previous section, although regression models may still be used.

The bottom-up style of cost estimation is best suited to projects at a more advanced stage of development, where cost details are known. This can limit their usefulness in design projects seeking to limit costs from an early stage, as the details necessary for the estimation are un-known. A MPCM estimation is also prone to underestimating costs, as it is inevitable that certain factors will either not be foreseen or are difficult to estimate (such as the cost of overrunning deadlines) [166]. The use of a high fidelity model will not be suitable at the preliminary design stage, as it would require many assumptions of the aircraft configuration that would introduce unnecessary errors into the estimate.

Combined Methods

Both of the summarised methods have advantages and drawbacks that mean their applicability is dependent on the stage of development. Newnes et al. identify that cost estimation software users would prefer options for both parametric and more detailed bottom-up design estimation models [69]. At the early conceptual design stage the detail required for a MPCM cost esti-mation is unavailable, ruling out such an estiesti-mation procedure. However, the applicability of conventional PCM estimation tools is limited when considering novel aircraft, especially for the publicly available tools such as the relationships presented by Raymer [116].

Scanlan et al propose a hybrid procedure that can be expanded as development progresses from the conceptual design phase to the detail design phase [172]. The aircraft is represented as an exemplar which contains all the parameters for a detailed design of the aircraft. At the conceptual design stage this structure is defined using default characteristics which can be de-fined as development progresses and detailed parameters become known. Design uncertainty at the early stage is represented by a cost uncertainty which reduces as more parameters are defined.

It is difficult to make an accurate cost estimate for a novel aircraft at the early design stage using either a PCM or MPCM. A combined method is nonetheless useful as research progress, as a cost estimate can be refined once further design detail becomes available. This research will make use of a PCM in reflection of the preliminary stage of development. However, refining the cost estimate is a necessary aspect of reducing uncertainty in the design and increasing the accuracy of an economic viability analysis. The goal of a cost estimate with respect to this research is to narrow down the region in the sensitivity analysis where a novel aircraft is

6. Acquisition Cost Estimation

expected to lie. This will necessitate the use of more accurate cost predictions where possible and once they may be suitably applied.