The effect of loss functions on empirical Bayes reliability analysis

• Main Authors: Camara Vincent A. R., Tsokos Chris P.
• Format: Article
• Language: English
• Published: Hindawi Limited 1998-01-01
• Series: Mathematical Problems in Engineering
• Subjects: Reliability; Wiebull and gamma underlying failure models; Empirical Bayes estimates; Integrated mean square error; Relative efficiency
• Online Access: http://www.hindawi.net/access/get.aspx?journal=mpe&volume=4&pii=S1024123X98000969
• ISSN: 1024-123X; 1563-5147

<p>The aim of the present study is to investigate the sensitivity of empirical Bayes estimates of the reliability function with respect to changing of the loss function. In addition to applying some of the basic analytical results on empirical Bayes reliability obtained with the use of the &#8220;popular&#8221; squared error loss function, we shall derive some expressions corresponding to empirical Bayes reliability estimates obtained with the Higgins&#8211;Tsokos, the Harris and our proposed logarithmic loss functions. The concept of efficiency, along with the notion of integrated mean square error, will be used as a criterion to numerically compare our results.</p> <p>It is shown that empirical Bayes reliability functions are in general sensitive to the choice of the loss function, and that the squared error loss does not always yield the best empirical Bayes reliability estimate.</p>