This paper presents an algorithm for discovering conjunction rules with high reliability from data sets. The discovery of conjunction rules, each of which is a restricted form of a production rule, is well motivated by various useful applications such as semantic query optimization and automatic development of a knowledge base. In a discovery algorithm, a production rule is evaluated according to its generality and accuracy since these are widely accepted as criteria in learning from examples. Here, reliability evaluation for these criteria is mandatory in distinguishing reliable rules from unreliable patterns without annoying the users. However, previous discovery approaches have either ignored reliability evaluation or have only evaluated the reliability of generality, and consequently, tend to discover a huge number of rules. In order to circumvent these difficulties we propose an approach based on a simultaneous estimation. Our approach discovers the rules that exceed pre-specified thresholds for generality and accuracy with high reliability. A novel pruning method is employed for improving time efficiency without changing the discovery outcome. The proposed approach has been validated experimentally using 21 benchmark data sets from the UCI repository.