Uncertainty analysis

Sensitivity analysis helps identification of major cost drivers in the design pa-rameters. However, uncertainty or variation in the costing data can also affect the aircraft acquisition cost. For example, the cost of aircraft structure de-pends upon the exact cost of raw material and any variation (or uncertainty) in the raw material cost will lead to a change in the overall aircraft cost. It is important to quantify this uncertainty in order to have confidence that the overall cost falls in a certain range of values or to estimate the probability of the cost being less than a given value.

Monte Carlo method is used for quantifying the effect of “costing data uncertainty” on the costs in the acquisition cost model. The uncertainty in the costing data is represented as probability distribuations and Monte Carlo sampling method generates random variables from these given probability distributions. It is to be noted that Monte Carlo sampling might leave large regions of the design space unexplored, especially for less number of sampling points. The acquisition cost model is evaluated for each sample point and this is repeated “n” times for a Monte Carlo simulation (where “n” is the number of observations), which produces n-values each representing a possible value for the products total cost.

Figure 4.14: Cumulative probability distribution

The uncertainty in the raw material costing information was modelled as triangular distribution with +/- 10% variation from the initial value. Monte Carlo simulation is run 1000 times and every time the acquisition cost model is recalculated with a new number randomly selected from the triangular

distribution. Monte Carlo simulations run on the model provided the mean value of the total cost at £37941.53 with a standard deviation of £1760.97.

The cumulative probabilty distribution and probability frequency distribu-tion are as shown in Figure 4.14 and Figure 4.15, respectively. The cumu-lative distribution function graph shows that it is 70% likely that the total cost will be less than £39000 and 95% likely that the total cost will be less than £42000. Also, if the frequency distribution approximated as a normal distribution which means that there is 95% probability that the cost will lie in the range £34419.59 to £41463.47 (two standard deviations of the mean) and there is 68% probability that the cost will lie in the range £36180.36 to

£39702.50 (one standard deviation of the mean).

Figure 4.15: Probability density distribution

4.5 Summary

A cost model capable of calculating the acquisition costs from aircraft specifi-cations is presented. The model improves on the shortcomings of the previous costing models and systems as follows:

ˆ explicit product definition as input so that any changes to the design are reflected in the cost model

ˆ hierarchical tree structure that reflects the actual physical structure of the aircraft to allow easy and intuitive navigation

ˆ object oriented approach with libraries of materials and processes for easy integration into the cost model

ˆ risk analysis along with visualisation of costs and their uncertainties

These characteristics make the acquisition cost model easily auditable and understood by the users/designers, which is important if cost modelling is to come into prominence within the engineering community. Also, the knowl-edge representation techniques utilised in the cost model allow optimal se-lection of materials or manufacturing processes based on cost. Finally, mod-elling uncertainty attached with design parameters and costing information in order to represent cost as distributions rather than discrete values en-ables decision making during conceptual design by recognition of most cost sensitive design parameters and understanding of the effects of uncertainties at different levels of abstraction in the cost model. Thus, the risk analysis methods incorporated into the generic hierarchical acquisition cost model

with explicit product definition as input provides an elegant, flexible and comprehensive costing environment.

Life cycle cost includes acquisition costs as well as maintenance and repair costs. In order to estimate the operational costs, a simulation model is developed which is described in chapter 5.

Simulation Model

In this chapter, the simulation model capable of estimating the operation and maintenance costs for a fleet of aircraft taking into account the aircraft implicit product definition, mission characteristics, and the logistics data is presented. The reasons for choosing the simulation package are outlined before explaining the developed model. The affect of aircraft performance on mission efficiency is explained before describing the process of evaluat-ing aircraft performance usevaluat-ing aerodynamic and performance analysis. The simulation model makes use of a modular approach which is explained in section 5.4. Then, the theory behind the simulation model is described in detail, with emphasis on mission scheduling and pre-flight inspection, mission and maintenance simulation along with description of a few modules selected from the simulation model. It is difficult to display the details of the whole model as the model is quite large; however, the portions of the model shown in this section convey the theoretical background of the model. Finally, a case study is presented and a short summary of the section is given.

5.1 Software selection

The characteristics that are identified as the requirements for the simulation model are

ˆ Modularity: to indicate ease of maintenance of the model.

ˆ Ease of deployment: to integrate with other software applications, es-pecially DecisionPro acquisition cost model.

ˆ Transparency: for ease of understanding.

The Extend Industry simulation package has been selected because it satisfies the requirements for this study and because of its flexible, open architecture which allows new objects to be developed and incorporated into the packages library easily for model building. The library objects provided as part of the Extend package are flexible enough to enable a large degree of customisation to be made without having to resort to developing new objects in its own programming language, MoDL.