A summary of research outcomes:

Research team of Waseda University Grant for Special Research Projects (2014B-443) consisted of the following members:

Principal researcher: Dr Yu Hayakawa, Waseda University

Research collaborator: Dr Richard Arnold, Victoria University of Wellington

Research collaborator: Dr Stefanka Chukova, Victoria University of Wellington

Research collaborator: Ms Ting Ying Chen, Waseda University

(undergraduate and masters student)

In our research plan submitted for this grant, we stated that the main focus is on the modeling of the warranty costs based on the generalised alternating renewal (GAR) process of type 1 (renewal operating times followed by geometric repair times) and the GAR of type 2 (geometric operating times followed by geometric repair times) under both the non-renewing and renewing free replacement policies. We also obtain numerical results by employing simulation methods. 

We report that we have made good progress on this project and on some related projects as well.

Dr Richard Arnold attended the 6^th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling held in Sapporo and visited the School of International Liberal Studies (SILS), Waseda University in August 2014.  Yu Hayakawa visited Victoria University of Wellington from 23 February 2015 to 11 March 2015, with which both Drs Richard Arnold and Stefanka Chukova are affiliated.  Throughout the period of this grant, we worked together on the project described above and a few other related topics described below.  We also worked on the project with Dr Sarah Marshall, Auckland University of Technology, who joined the team in December 2014.

1)    We model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free replacement warranties.  We study two models which are based on the generalised alternating renewal process of type 1 (renewal operating times followed by geometric repair times – GAR I) and that of type 2 (geometric operating times followed by geometric repair times – GAR II) under both the non-renewing and renewing free replacement policies. We derive new results on GAR I & II with a finite time horizon. 

Some results are in the manuscripts [1] & [5].  The manuscript [1] was presented by Yu Hayakawa at the 6^th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014, August 2014, Sapporo, Japan).  The manuscript [5] will be presented by Yu Hayakawa at The Ninth International Conference on Mathematical Methods in Reliability (MMR 2015) in Tokyo on 1-4 June 2015.

Dr Stefanka Chukova delivered an invited talk on this project at the  International Statistical Institute Regional Statistics Conference 2014 (ISI-RSC 2014) held in Kuala Lumpur, Malaysia, on 16-20 November 2014.  The talk title was "Warranty cost analysis: geometric operational and repair times."

Dr Sarah Marshall will present some results on this project at the 27th European Conference on Operational Research held in Glasgow, United Kingdom, 12-15th July 2015.  The talk title will be “Modelling warranty costs using geometric repair times.”

Ms Ting Ying Chen created some graphs to summarise simulation results for this project.

We are working on extended versions of the manuscripts [1] & [5] by incorporating the simulation results under both non-renewing and renewing warranty replacement policies using GAR I and GAR II.  Also we are working on a numerical procedure related to some results included in the manuscript [1]. 

2)    We have constructed a model for correlated failures in multicomponent systems where failed components are repaired.  Our results are in the manuscript [2].  This manuscript was presented by Dr Richard Arnold at the 6^th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014) in August 2014.  An expanded version of the paper has been accepted for publication in the Journal of Risk and Reliability [4].

3)    We apply finite mixture methods to group units into fuzzy clusters, in order to model the joint distribution of failure times and severities.  This work is in the manuscript [3].  This manuscript was presented by Dr Richard Arnold at the 6^th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014) in August 2014.

4)    We develop inference procedures for multicomponent systems where the system is viewed as being made up of independent overlapping subsystems that we had previously published. We introduce a new type of grouping of subunits which allow for common cause failures, i.e., all the components within a subunit failure simultaneously.  We extend our results and a paper on this project [6] is close to completion.