System maintenance cost dependent on life cycle under renewing warranty policy

A number of optimal maintenance policies have been proposed and studied based on several types of warranty policies. As the criteria for optimality, the expected cost rate per unit time during the life cycle of the system is quite often used by many authors. However, the expected cost rate may depend on the length of life cycle and so the definition of life cycle plays a significant role in optimizing the maintenance policy. This paper considers a system maintenance policy during the post-warranty period under the renewing warranty policy and the life cycle is defined from the user's perspective. The life cycle starts with the installment of a new system and ends when the system is replaced by a new one at the expense of the user. In many renewing warranty models, the life cycle is defined as the lifelength of the new system installed initially, which is quite different from our definition. The expected cost rate per unit time is evaluated based on the life cycle newly defined and is compared with the existing results.