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This paper describes a study of a mathematical model of the impact of an equipment irregularity on trouble detection and the quality of customer service in a telephone network. The essence of the model is that the holding time of any piece of equipment may be altered if it develops a fault. Customer service is shown to be less sensitive to increases in holding time than decreases. Trunk and some types of other irregularities, characterized by holding times shorter than usual, are seen to affect service more severely than certain common control equipment irregularities, characterized by longer than usual holding times. Analytical and numerical techniques for studying the model are described. Results are presented for the various classes of equipment irregularities. The predicted effects are especially important in the area of recognizing and locating network faults and agree with practical experience.