Using accelerated life tests data to predict warranty cost under imperfect repair

- A warranty cost prediction framework based on ALT data is proposed.
- Variability of ALT data and field stress is considered simultaneously.
- Large sample approximation is used to enhance the computational efficiency.
- Markov chain Monte Carlo is used to obtain the samples for prediction.
- Imperfect repair is assumed for the warranty coverage.
- The consideration of variability is necessary to avoid underestimation of the warranty cost.

For new products that have not been put on the market, manufacturers usually want to predict the warranty cost to forecast its influence on future profit. In the test phase of new products, accelerated life tests (ALT) are commonly used to predict the lifetime under use condition. In this paper, we present a framework to predict the warranty cost and risk under one-dimensional warranty by analyzing ALT experimental data. Two sources of variability are considered to make inferences of predicted warranty cost: the uncertainty of estimated parameters from ALT data and the variation in field conditions. Under these assumptions, the expected warranty cost and warranty risk is computed by Markov chain Monte Carlo (MCMC) sampling based on the approximated lifetime distribution. We assume that the warranty guarantees imperfect repairs. The framework could be easily repeated for ALT data based on log-location-scale lifetime distributions and both constant-stress and step-stress ALT data. Compared with original Monte Carlo (MC) simulation, the proposed method provides comparable prediction accuracy with significantly less computational effort. A numerical example with sensitivity analysis is given to illustrate the effectiveness of the proposed methods.