# A GRP model that also considers the Preventive Maintenance Efficiency

R

#### Reliable.Outlier

As you know, Preventive Maintenance (PM) will reduce the real age to a virtual age for repairable systems (for example a car).

Think of 10,000km PM actions for a car: suppose filters, brakes, tyres renewed. All sensor outputs are controlled and all related adjustments are redone. Engine & transmission are inspected. Briefly let?s say that your car had an extensive preventive maintenance (PM). So after this extensive PM, real age is still 10,000km; however virtual age is <10,000km.

For a while a read what ever I found from resources about GRP models that are HPP, NHPP, GRP Kijima Type 1 and GRP Kijima type 2.

As I understood none of them includes the extensive PM times into its model. The 3 Variables are Weibull parameters (scale+shape) and efficiency of repair (q).

So my questions are:
1) Is there any model that consider the extensive PM also. I don?t know but maybe there can be 2 q parameters in a such model: 1 for corrective maintenance efficiency after a failure; 1 for periodical preventive maintenance efficiency. Can you give me the scientific common name of the model you know for me to search on it

While trying to understand the reliability characteristics of a complex repairable system, it is much more realistic to consider the PM effects also.

Best regards

B

#### Buratino

Hello there,
Well as my knowledge, there isn't a model that combines PM and CM (corrective maintenance). But in fact many authors considers 2 parallel process : 1 PM failure process with maintenance efficiency q_p and CM failure process with maintenance efficiency q_c. That is to say, for a data set that records both PM and CM actions times, one can model PM process with GRP Kijima type I ( or others), CM process with NHPP, or GRP type I, or type II... The problem is to calibrate or estimate model parameters because we have 2 set of parameters for CM and PM process. You can start to search for the work of Laurent Doyen for exemple. In addition, an analogue term for GRP/Kijima model is Virtual Age model or especially Arithmetic Reduction of Age (ARA) model.
Hope this helps!

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