（代表者） 国際学術院 国際教養学部 教授 早川　有
（連携研究者） Victoria University of Wellington Associate Professor Richard Arnold
（連携研究者） Victoria University of Wellington Reader Stefanka Chukova
（連携研究者） School of International Liberal Studies, Waseda University Research Associate Yuuki Rikimaru

1)    We model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free repair warranties.  We assume that the repair time for rectifying the claims is non-zero and the repair cost is a function of the length of the repair time.  To accommodate the ageing of the product and repair equipment, we use a decreasing geometric process to model the consecutive operational times and an increasing geometric process to model the consecutive repair times.  We identify and study the alternating geometric process (AGP), which is an alternating process with cycles consisting of the item’s operational time followed by the corresponding repair time.  We derive new results for the AGP in finite horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under a non-renewing free repair warranty (NRFRW), a renewing free repair warranty (RFRW) and a restricted renewing free repair warranty (RRFRW(n)).  Properties of the model are demonstrated using a simulation study.

Together with Dr Sarah Marshall, Auckland University of Technology, we wrote a paper on the results of this project and it was made a technical report (Research Report Series (ISSN:1174-2011), #18-1, Victoria University of Wellington School of Mathematics and Statistics (http://sms.victoria.ac.nz/Main/ResearchReportSeries) (2018)).  We submitted this paper to a joint conference: APARM2018 & QR2MSE2018.  We will present this paper at this conference in August 2018.

2)    We present a model for the delayed reporting of faults: multiple non-fatal faults are accumulated and then simultaneously reported and repaired.  The reporting process is modelled as a stochastic process dependent on the underlying stochastic process generating the faults.

We have worked on the cases of multiple faults types, planned preventative maintenance and customer rush.  A manuscript has been written on the results and we plan to extend it by adding simulation studies and submit it to an international peer reviewed journal this year.