A critical look at some point-process models for repairable systems

A Model-Driven Approach for the Failure Data Analysis of Multiple Repairable Systems Without Information on Individual Sequences

“…In particular, assuming that the observations are time truncated, the proposed approach provides estimates of the (unconditional) distributions of the interarrival times that are quite close to those provided by other authors [2], [12] who implicitly assumed that the observations are failure-truncated, so that the each data set represents the entire population of the -th interarrival time. Thus, if the observations were really time-truncated (as this paper suggests), the probability distributions provided in [2] and [12] would be seriously misleading, because these distributions no longer refer to the entire population of the -th interarrival time (as assumed in [2] and [12]), but only to that part of the population that can be observed before the truncation time .…”

“…To our knowledge, the only approach that aims to provide a physical interpretation to the bus-motor failure process is that proposed by Newby [12]. In the bus-motor application, the model by Newby [12] assumes that the hazard rate of each data set has a 3-parameter power law behaviour, with common shape parameter, and uncommon scale and location parameters, where the location parameter represents the virtual age of the system just after repair , i.e., it is a measure of accumulating age.…”

“…In the bus-motor application, the model by Newby [12] assumes that the hazard rate of each data set has a 3-parameter power law behaviour, with common shape parameter, and uncommon scale and location parameters, where the location parameter represents the virtual age of the system just after repair , i.e., it is a measure of accumulating age. Newby's model lies between the non-homogeneous Poisson process (NHPP) and the renewal process; it reduces to a renewal process when all the virtual ages are equal to 0, and it becomes an NHPP (assuming minimal repairs) when the virtual age is just equal to the system age at the time of failure .…”

A review on reliability models with covariates

“…Newby [55] asserts that AHM applications are restricted by an identifiability problem. Theoretical limitations leads to identification problems while estimating parameters of the model [56]. Due to that this model is not identifiable, the observation of explanatory variables does not add anything to the knowledge obtained from the event data [55].…”

“… An additive assumption often leads to estimated hazard less than zero, as a result it is not a realistic and reasonable assumption  This model cannot handle tied values (which have likelihood zero under the continuous random variable assumption)  The model cannot handle failure times equal to zero  This model can only be used in a phenomenological way to measure the magnitude of the jump in the hazard, and models for the which makes use of explanatory variables are unlikely to produce satisfactory estimators of the parameters [56] 2.1.5 Mixed (Additive-Multiplicative) Model To enhance modelling capability about covariates, the mixed model considers the hazard of an asset/ individual, which contains both a multiplicative and an additive component [57,58]. The additive-multiplicative hazard model specifies that the hazard for the counting process associates with a multidimensional covariate process = ( , ) .…”