Change impact on a product and its redesign process: a tool for knowledge capture and reuse

Abstract

Change propagates, potentially affecting many aspects of a design and requiring much rework to implement. This article introduces a cross-domain approach to decompose a design and identify possible change propagation linkages, complemented by an interactive tool that generates dynamic checklists to assess change impact. The approach considers the information domains of requirements, functions, components, and the detail design process. Laboratory experiments using a vacuum cleaner suggest that cross-domain modelling helps analyse a design to create and capture the information required for change prediction. Further experiments using an electronic product show that this information, coupled with the interactive tool, helps to quickly and consistently assess the impact of a proposed change.

Appendix

This section describes the algorithm developed to assess the likelihood of change propagation from any set of initiating components to any other components that are directly or indirectly linked. The algorithm is based on an extension of the CPM proposed by Clarkson et al. (2004); for clarity that method is summarised before describing the enhancement.

1.1 Change propagation starting from a single component

The Change Propagation Method (CPM) allows the likelihood of change propagation between components captured in an ISF model to be calculated. To apply CPM, each dependency between two components must be specified in terms of the likelihood of change propagating through that linkage. The algorithm then accounts for the fact that propagation from one component to another can occur through several routes. For instance, considering Fig. 12, change may not propagate directly from component A (LCD) to B (Microcontroller) because no dependency between these components exists. However, change may propagate from A to B through several indirect paths.

Fig. 12

DSM view of the AUTOBELL component layer shown in Fig. 2, supplemented by estimated likelihood of change propagating between each pair of components. Direction of each dependency is from the element labelled in the column to the element labelled in the row

The calculation of combined propagation likelihood P(A → B) considering two possible paths A → H → I → B and A → H → J → B is explained here to illustrate.

First, the probability of change propagating through each path is calculated by multiplying the independent probabilities of change propagating through each step:

$$ P({A \rightarrow B})_{A\rightarrow H\rightarrow I\rightarrow B} = P(A \rightarrow H) \times P(H \rightarrow I) \times P(I \rightarrow B) = P_1 $$

(1)

$$ P({A \rightarrow B})_{A\rightarrow H\rightarrow J\rightarrow B} = P(A \rightarrow H) \times P(H \rightarrow J) \times P(J \rightarrow B) = P_2 $$

(2)

Possible propagations of change through these two routes are not independent events, because some steps are common. Therefore the two probabilities are combined as:

$$ P({A \rightarrow B})_{[A \rightarrow H\rightarrow I \rightarrow B] \cup [A \rightarrow H \rightarrow J \rightarrow B]} = P_1 + P_2 - (P_1 \times P_2) = 1 - ((1-P_1) \times (1-P_2)) $$

(3)

In the CPM algorithm, this computation is generated dynamically to take account of all possible routes between the two components of interest. The routes are identified using depth-first search, fanning out from the initiating component until the destination component is reached. A given search path is stopped if it is found to contain a cycle (Clarkson et al. (2004) exclude this case as being unrealistic), or if a maximum number of steps is exceeded (to ensure computational tractability). Clarkson et al. (2004) use a convergence argument to suggest a limit of 3 or 4 steps. This theoretical argument has since been supported by the empirical work of Pasqual and de Weck (2011), whose case work on a software system in an aerospace company indicated that changes very rarely propagate beyond four steps and never beyond five steps.

1.2 Calculating the likelihood of change in multiple sources propagating

The CPM algorithm, as summarised above, only allows estimation of change effects when a single component acts as initiator. This is a significant limitation because, in reality, change is often initiated in multiple components concurrently. In the approach reported in this article, a change to a function typically requires redesign of several components which interact to embody that function.

The CPM algorithm was thus extended to allow the combined likelihood of propagation to be estimated when change is initiated in multiple components concurrently.

To calculate the likelihood of change from two sources propagating to cause change in any given component, a function f was developed to combine the two relevant single-initiating-component likelihood values, x and y. Qualitative reasoning was used to determine that the function should fulfil the following criteria (where x and y can have values between 0 and 1):

$$ 0 \leq f (x,y) \leq 1 $$

(4)

$$ f (x,y) \leq x + y $$

(5)

$$ f (x,y) \geq {\text{max}}(x,y) $$

(6)

$$ f (x,y) = f(y,x) $$

(7)

$$ f(f (x,y),z) = f(x,f(y,z)) $$

(8)

The rationale for these conditions is as follows. The first condition ensures that the probability of change in a component remains between 0 and 1. The second condition ensures that the overall likelihood of change does not exceed the sum of the two individual values. The third condition ensures that the overall value is always greater than each of the individual likelihoods. The fourth and fifth conditions ensure the result is independent of the sequence of combination.

Many functions could satisfy all these conditions. The function used in the CMSA tool is:

$$ f (x,y) = {\text{min}}(1, ({x^2 + y^2})^{0.5}) $$

(9)

If there are more than two values to be combined, that is, more than two initiating components, the function is applied to the first two values, then the result is combined with the third value using the same approach, and so forth.