Recent advances in animal welfare science used judgement bias, a type of cognitive bias, as a means to objectively measure an animal's affective state. It is postulated that animals showing heightened expectation of positive outcomes may be categorised optimistic, while those showing heightened expectations of negative outcomes may be considered pessimistic. This study pioneers the use of a portable, automated apparatus to train and test the judgement bias of dogs. Dogs were trained in a discrimination task in which they learned to touch a target after a tone associated with a lactose-free milk reward and abstain from touching the target after a tone associated with water. Their judgement bias was then probed by presenting tones between those learned in the discrimination task and measuring their latency to respond by touching the target. A Cox's Proportional Hazards model was used to analyse censored response latency data. Dog and Cue both had a highly significant effect on latency and risk of touching a target. This indicates that judgement bias both exists in dogs and differs between dogs. Test number also had a significant effect, indicating that dogs were less likely to touch the target over successive tests. Detailed examination of the response latencies revealed tipping points where average latency increased by 100% or more, giving an indication of where dogs began to treat ambiguous cues as predicting more negative outcomes than positive ones. Variability scores were calculated to provide an index of optimism using average latency and standard deviation at cues after the tipping point. The use of a mathematical approach to assessing judgement bias data in animal studies offers a more detailed interpretation than traditional statistical analyses. This study provides proof of concept for the use of an automated apparatus for measuring cognitive bias in dogs.