Bayes estimation of prediction intervals for a power law process

We propose a maintenance policy for new equipment on a repair-refund maintenance strategy in this paper and derive the optimal lease period from the lessor’s perspective based on independent and identical distribution of historical failure data which obey power law process. The cost model of a full refund and a proportional refund is studied, and the corresponding optimal leasing period is determined by reducing the expected total cost rate to the largest extent. We use a numerical example to illustrate the proposed cost model and analyze the sensitivity of related parameters. Furthermore, we show that the proportional refund policy is preferable than a full refund to the lessor. Finally, according to the simulation outcome, the proposed methods are effective and instructions for lessor in regard to equipment lease are provided.

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Intrinsic Bayes factor approach to a test for the power law process

Journal of Statistical Planning and Inference ◽

10.1016/s0378-3758(98)00181-5 ◽

1999 ◽

Vol 77 (2) ◽

pp. 195-220 ◽

Cited By ~ 6

Author(s):

Rama T. Lingham ◽

S. Sivaganesan

Keyword(s):

Power Law ◽

Bayes Factor ◽

Power Law Process ◽

Intrinsic Bayes Factor

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Power Law Process

Wiley StatsRef: Statistics Reference Online ◽

10.1002/9781118445112.stat02201 ◽

2014 ◽

Author(s):

Steven E. Rigdon

Keyword(s):

Power Law ◽

Power Law Process

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Reliability inferences of modulated power-law process #i

IEEE Transactions on Reliability ◽

10.1109/24.994901 ◽

2002 ◽

Vol 51 (1) ◽

pp. 23-26 ◽

Cited By ~ 4

Author(s):

K. Muralidharan

Keyword(s):

Power Law ◽

Power Law Process

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BAYESIAN RELIABILITY APPROACH TO THE POWER LAW PROCESS WITH SENSITIVITY ANALYSIS TO PRIOR SELECTION

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539313500046 ◽

2013 ◽

Vol 20 (01) ◽

pp. 1350004

Author(s):

CARLOS A. MOLINARES ◽

CHRIS P. TSOKOS

Keyword(s):

Maximum Likelihood ◽

Power Law ◽

Real Data ◽

Random Variable ◽

Intensity Function ◽

Rate Of Change ◽

Bayesian Estimate ◽

Squared Error Loss Function ◽

Power Law Process ◽

Prior Selection

The intensity function is the key entity to the power law process, also known as the Weibull process or nonhomogeneous Poisson process. It gives the rate of change of the reliability of a system as a function of time. We illustrate that a Bayesian analysis is applicable to the power law process through the intensity function. First, we show using real data, that one of the two parameters in the intensity function behaves as a random variable. With a sequence of estimates of the subject parameter we proceeded to identify the probability distribution that characterizes its behavior. Using the commonly used squared-error loss function we obtain a Bayesian reliability estimate of the power law process. Also a simulation procedure shows the superiority of the Bayesian estimate with respect to the maximum likelihood estimate and the better performance of the proposed estimate with respect to its maximum likelihood counterpart. As well, it was found that the Bayesian estimate is sensitive to a prior selection.

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