Abstract
This paper estimates component reliability from masked series-system life data, viz, data where the exact component causing system failure might be unknown. We extend the results of Usher & Hodgson (1988) by deriving exact maximum likelihood estimators (MLE) for the general case of a series system of 3 exponential components with independent masking. Their previous work shows that closed-form MLE are intractable, and they propose an iterative method for the solution of a system of 3 Nonlinear likelihood equations. They do not, however, prove convergence for their iterative method. As such, we show how this system of Nonlinear equations can be replaced by a single quartic equation, whose solution is straight-forward. Since it does not depend upon the convergence of numerical solution algorithms, the results are exact. Though the resulting estimators are somewhat lengthy & cumbersome to find manually, they can be written as a straightforward computer code. The calculations can then be easily performed on a personal computer. This method for reducing the likelihood equations to simpler-to-solve forms can be extended readily to a higher number of components. In many cases for more than 3 components it is easier while for others it is more complicated; even in the more complicated cases, this simplification makes the problems much more tractable.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 631-635 |
| Number of pages | 5 |
| Journal | IEEE Transactions on Reliability |
| Volume | 42 |
| Issue number | 4 |
| DOIs | |
| State | Published - Jan 1 1993 |
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All Science Journal Classification (ASJC) codes
- Safety, Risk, Reliability and Quality
- Electrical and Electronic Engineering
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Exact Maximum Likelihood Estimation Using Masked System Data. / Lin, Dennis K.J.; Usher, John S.; Guess, Frank M.
In: IEEE Transactions on Reliability, Vol. 42, No. 4, 01.01.1993, p. 631-635.Research output: Contribution to journal › Article
TY - JOUR
T1 - Exact Maximum Likelihood Estimation Using Masked System Data
AU - Lin, Dennis K.J.
AU - Usher, John S.
AU - Guess, Frank M.
PY - 1993/1/1
Y1 - 1993/1/1
N2 - This paper estimates component reliability from masked series-system life data, viz, data where the exact component causing system failure might be unknown. We extend the results of Usher & Hodgson (1988) by deriving exact maximum likelihood estimators (MLE) for the general case of a series system of 3 exponential components with independent masking. Their previous work shows that closed-form MLE are intractable, and they propose an iterative method for the solution of a system of 3 Nonlinear likelihood equations. They do not, however, prove convergence for their iterative method. As such, we show how this system of Nonlinear equations can be replaced by a single quartic equation, whose solution is straight-forward. Since it does not depend upon the convergence of numerical solution algorithms, the results are exact. Though the resulting estimators are somewhat lengthy & cumbersome to find manually, they can be written as a straightforward computer code. The calculations can then be easily performed on a personal computer. This method for reducing the likelihood equations to simpler-to-solve forms can be extended readily to a higher number of components. In many cases for more than 3 components it is easier while for others it is more complicated; even in the more complicated cases, this simplification makes the problems much more tractable.
AB - This paper estimates component reliability from masked series-system life data, viz, data where the exact component causing system failure might be unknown. We extend the results of Usher & Hodgson (1988) by deriving exact maximum likelihood estimators (MLE) for the general case of a series system of 3 exponential components with independent masking. Their previous work shows that closed-form MLE are intractable, and they propose an iterative method for the solution of a system of 3 Nonlinear likelihood equations. They do not, however, prove convergence for their iterative method. As such, we show how this system of Nonlinear equations can be replaced by a single quartic equation, whose solution is straight-forward. Since it does not depend upon the convergence of numerical solution algorithms, the results are exact. Though the resulting estimators are somewhat lengthy & cumbersome to find manually, they can be written as a straightforward computer code. The calculations can then be easily performed on a personal computer. This method for reducing the likelihood equations to simpler-to-solve forms can be extended readily to a higher number of components. In many cases for more than 3 components it is easier while for others it is more complicated; even in the more complicated cases, this simplification makes the problems much more tractable.
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UR - http://www.scopus.com/inward/citedby.url?scp=0027842108&partnerID=8YFLogxK
U2 - 10.1109/24.273596
DO - 10.1109/24.273596
M3 - Article
AN - SCOPUS:0027842108
VL - 42
SP - 631
EP - 635
JO - IEEE Transactions on Reliability
JF - IEEE Transactions on Reliability
SN - 0018-9529
IS - 4
ER -