# Reasoning about Confidence in Goal Satisfaction
## 1 Introduction  
Consider requirements analysis in a healthcare setting, where a hospital intends to use a real-time wait time estimation system that informs patients of expected waiting times. An analyst builds a goal model capturing design alternatives for the system-to-be. For the analysis, the analyst gathers data such as the manual effort required, and the frequency of tasks, in order to decide how to estimate wait times. However, reliable data, such as the average time it takes to carry out a task manually, are often unavailable, so they have to be estimated on the basis of data available from a similar context, or even guessed on the basis of experience or first principles. The quality of the data used in the decision process may hence influence heavily the confidence the analyst and stakeholders have in the chosen solution for the problem at hand. In this paper, we are interested in estimating that confidence during the goal analysis process, which then influences decision making. Data availability for goal reasoning is a major challenge, especially in early phases of requirements and design analysis. New system design alternatives may not have been exposed to experimentation and performance testing. This results in uncertainties in the evaluation of these alternatives and, through propagation, in the satisfaction values of high-level goals. Moreover, ignoring the reliability level of sources from which data was collected may lead to uninformed decisions and inaccurate evaluations of high-level goals. [PERSON] et al. [1] introduced an elaborate, well-developed framework for decision making in the presence of uncertainty, which uses probability distribution techniques in the context of cost/benefit analysis. However, although mathematically sound, this framework is relatively complex and unaffordable in many situations where data is scarce orunavailable. Other proposed approaches, reviewed later in this paper, suffer from the same complexity and data availability concerns. This paper aims to propose a light-weight reasoning mechanism that can cope with incomplete data and is readily adoptable in requirements engineering and decision-making practices. The mechanism determines the _confidence level_ of the satisfaction of a given goal can be computed from confidence level values of leaf goals through propagation rules. For example, data collected from a pilot project operationalizing a leaf goal is more robust and of higher quality than purely estimated data acquired by front-end analysts. Accordingly, a higher or lower confidence value of the goal satisfaction value shall be assigned to leaf nodes, and then propagated to higher-level goals. The main objective of this work is to propose a _Data Quality Tagging and Propagation Mechanism_ that enables the tagging of data with a certain quality level, and the propagation of the quality level to assign confidence values to the satisfaction of higher-level goals and actors in a goal model. The data quality level varies based on the reliability of the source from which the data was collected. The approach qualifies the goal satisfaction levels by reflecting the data quality levels of leaf goals and their parents, leading to a more realistic view of goal evaluation in the presence of uncertainty. The confidence levels propagated to top-level goals and actors should influence decision making by having analysts better trust higher-confidence solutions, or by having them look for additional evidence or more reliable data. Although the ideas introduced herein can apply to many goal-oriented modeling languages, one specific language is used to present and formalize our proposal. We use the _Goal-oriented Requirement Language_ (GRL) because GRL is part of an international standard (User Requirements Notation--URN), enables the modeling of stakeholders and their goals, supports indicators for quantitative reasoning, supports contribution relationships, as well as evaluation strategies and propagation algorithms.