M. Crujeiras and A.Mart ́ınez Calvo (2016). Information processing from inspections of quality management. 122 European Study Group with Industry

http://www.math-in.net/122esgi/sites/math-in.net.122esgi/files/122ESGI.pdf

 

In Crujeiras et al (2016), the authors considered the problem of audit prediction. They proposed a tool, iAuditoria, for conducting audits and/or inspections from a checklist previously established by the user. The goal of this tool is, once a series of audits have been performed, try to predict the outcome of the next audit at the item level. This will allow following the evolution of the system in such a way that the user can identify critical items and act to prevent failures of mistakes.

 

The authors in Crujeiras et al. (2016) considered some collections of items may have the feature that the evolution of item value sequences are interrelated. Thus, they propose a statistical predictive approach based on Markov chains to model the evolution of items in the data set with this feature. The original categorical sequences are sequences of audit value corresponding to different items.  The Markov property must be tested, along with the order of the chain (one–step, two–steps,...) and homogeneity in time is tested to make sure that the data set fulfill the assumptions of the method. The parsimonious high-order multivariate Markov chain model along with the parameter estimation method in Ching et al. (2008) are then applied to predict the next audit. With the help of the high-order multivariate Markov chain model and the parameter estimation method, the audit value can be estimated by solving a linear programming problem which is much easier to be handled.​
 

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W. Ching, M. Ng and E. Fung (2008). Higher-order Multivariate Markov Chains and Their Applications, Linear Algebra and Its Applications, 428(2–3):492-507.

 

https://www.sciencedirect.com/science/article/pii/S0024379507002169