Statistical Quality Control and Reliability Analysis Using the Birnbaum-Saunders Distribution with Industrial Applications

Quality improvement has been an important aspect considered by companies since the last century. However, today it is even more relevant in business and industry, particularly for production and service companies. Statistical quality control is the quantitative tool for quality improvement. The Gaussian distribution was the main ingredient of this quantitative tool, but nowadays new distributions are being considered, some of them taking into account asymmetry. The Birnbaum-Saunders model is one of these distributions and has recently received considerable attention because of its interesting properties and its relationship with the Gaussian distribution. Since its origins and applications in material science, the Birnbaum-Saunders distribution has found widespread uses in several areas, including quality control, with now well-developed methods that allow in-depth analyses. In this work, statistical quality control and reliability tools based on the Birnbaum-Saunders distribution are introduced. Implementation of those tools is presented using the R software. For the internal quality of companies, control charts for attributes and variables, as well as their multivariate versions and capability indices, are presented, discussed and illustrated with real data. For external quality, acceptance sampling plans are also presented and discussed. The main aspects of reliability, sometimes defined as ‘quality over time”, is discussed using the Birnbaum-Saunders distribution, illustrating them with data on nanotechnologies.