Warranty cost analysis: Increasing warranty repair times

Abstract

In this study, we model the warranty servicing costs under nonrenewing and renewing free repair warranties. We assume nonzero increasing repair times with the warranty cost depending on the length of the repair time. An increasing geometric process is used to model the consecutive repair times. We introduce the generalised alternating renewal process, which is an alternating process with cycles consisting of an item's operational time followed by the corresponding repair time. We derive analytical results for a generalised alternating renewal process with a finite time horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under the nonrenewing free repair warranty and renewing free repair warranty. Properties of the model are demonstrated through a simulation study and through the application to warranty claims data from an automotive manufacturer.

Warranty cost analysis with an alternating geometric process

“…If the warranty expires during an operational period, the cost of the following repair is not covered by the warrantor and the cycle is incomplete. Similar to Chukova and Hayakawa 1,2 and Marshall et al, 7 we assume that the cost of the i th repair has the form…”

“…In these examples, we determine the corresponding scale parameter θ and variance Var ( X 1 ) for given k and E ( X 1 ) . 7,18 Table 2 provides some examples of parameter values used in the following numerical examples.…”

“…The hypothesis tests outlined by Lam 14 (§4.2, pp.101–104) were applied to the operational times and repair times for these two vehicles, and the results are shown in Table 4. For details of these tests, refer to Lam 14 or Marshall et al 7 For both operational and repair times, when testing for a GP, the null hypothesis is not rejected ( P U T , P U D , P V T , P V D > 0 . 05 ) , and when testing for an RP, the null hypothesis is rejected by at least one of the tests for each vehicle ( P L < 0 . 05 or P R < 0 . 05 ). These results indicate that a GP is a suitable model for the operational and repair times for both vehicles.…”

“…4 For details on models with non-zero repair times, see previous studies. [5][6][7][8][9][10][11][12][13] The main goal of this article is to study a generalisation of the aforementioned results in Chukova and Hayakawa 1,2 to more realistically account for product ageing, that is, the operational times are stochastically decreasing and the repair times are stochastically increasing. We use the geometric process (GP) to model the stochastically increasing and decreasing times (see Lam 14 for an overview of the GP).…”

Bi-objective optimization of non-periodic preventive maintenance strategy by considering time value of money

“…One of the effective methods to reduce the probability of failures during the warranty and post-warranty periods is performing preventive maintenance (PM) which controls the degradation process and becomes more important when the servicing cost is high [8]. Although performing PM leads to lower repair cost, it imposes extra cost on the system [9]. The cost of preventive maintenance over the warranty period can be paid by either the manufacturer or the buyer.…”