Applications of the EM Algorithm to the Analysis of Life Length Data

Abstract

The parameters of the life length distribution of a given component are to be estimated. The observations on which inference is to be based are field data which are incomplete in some fashion. Thus, for example, the reported life length may include a period of unknown duration during which the component is not in use, the life length distribution may be affected by an unobserved environmental factor or the component may be part of a larger system, and failure mode analysis reveals only the module containing the failed component, not its identity. It is shown how the EM algorithm can be used to calculate the maximum likelihood estimates of the parameters of interest in these instances. The methodology is applied to some data on the life lengths of electronic components used in the telecommunications industry, yielding values that are similar to those obtained from complete observations on comparable components.

Expectation-maximization algorithms for learning a finite mixture of univariate survival time distributions from partially specified class values

“…In the same ways that using unlabeled data leads to more reliable statistical knowledge when only few labeled data are given (Zhu and Goldberg, 2009), with partially supervised learning we can expect to take advantage of partially labeled data when only few labeled and unlabeled data are given. In the area of reliability engineering, learning failure time models from partially labeled data have been studied since the 1980's (Usher and Hodgson, 1988;Usher and Guess, 1989;Guess et al, 1991;Lin and Guess, 1994;Ramon et al, 1995;Park, 2005;Flehinger et al, 1996Flehinger et al, , 1998. In the field of machine learning however only few studies have been done regarding partially supervised learning for face recognition (Cour et al, 2009(Cour et al, , 2011 and finite mixture modeling (Ambroise and Govaert, 2000).…”

“…Such process of losing specified information about the origin is called masking (Usher and Hodgson, 1988;Usher and Guess, 1989;Guess et al, 1991;Lin and Guess, 1994;Ramon et al, 1995;Park, 2005;Flehinger et al, 1996Flehinger et al, , 1998. It is a special case of coarsening (Heitjan and Rubin, 1991;Gill et al, 1997), that is applied to nominal data.…”

“…In the area of reliability engineering, mixtures of failure time distributions with masked data have been studied since the 1980's (Miyakawa, 1984;Usher and Hodgson, 1988;Usher and Guess, 1989;Guess et al, 1991;Lin and Guess, 1994;Ramon et al, 1995;Park, 2005;Flehinger et al, 1996Flehinger et al, , 1998. In failure time analysis of machines, information that a failure of a specific component caused the system failure at time t implies that the other components have not been failed until t or have survived longer than t in other words.…”

Expectation-maximization algorithms for learning a finite mixture of univariate survival time distributions from partially specified class values

“…In the same ways that using unlabeled data leads to more reliable statistical knowledge when only few labeled data are given (Zhu and Goldberg, 2009), with partially supervised learning we can expect to take advantage of partially labeled data when only few labeled and unlabeled data are given. In the area of reliability engineering, learning failure time models from partially labeled data have been studied since the 1980's (Usher and Hodgson, 1988;Usher and Guess, 1989;Guess et al, 1991;Lin and Guess, 1994;Ramon et al, 1995;Park, 2005;Flehinger et al, 1996Flehinger et al, , 1998. In the field of machine learning however only few studies have been done regarding partially supervised learning for face recognition (Cour et al, 2009(Cour et al, , 2011 and finite mixture modeling (Ambroise and Govaert, 2000).…”

“…When δ ik = 1 for some k, we obtain a partial label for the ith sample, which means precise information about the origin of the ith sample is missing. Such process of losing specified information about the origin is called masking (Usher and Hodgson, 1988;Usher and Guess, 1989;Guess et al, 1991;Lin and Guess, 1994;Ramon et al, 1995;Park, 2005;Flehinger et al, 1996Flehinger et al, , 1998. It is a special case of coarsening (Heitjan and Rubin, 1991;Gill et al, 1997), that is applied to nominal data.…”