An architecture style defines a commonly occurring pattern of the structural organization of components and connectors such that the impact of the pattern on the different non functional attributes is known. It is possible to make a qualitative assessment of whether a specific style is conducive to the non functional attribute of performance based on the knowledge and experience in the use of the style. It is necessary however, that such a qualitative judgment be substantiated by a quantitative estimate obtained using a systematic performance analysis approach, since architecture styles are likely to be used in domains where application performance will play a critical role in ensuring its widespread use. Recognizing this need, several research efforts have focused on the development of quantitative performance analysis approaches for general purpose software architectures as well as for architecture styles. A notable drawback of the existing approaches is that they do not consider failures of components and connectors and hence provide optimistic performance estimates. In this paper we present a performability analysis approach for a pipeline architecture style which accounts for unreliable components. The performance estimate provided by the proposed approach is more realistic than what can be provided by the prevalent approaches. We illustrate the potential of the approach with an industrial case study of a Document Analysis system.