Maintenance optimization for second‐hand products following periodic imperfect preventive maintenance warranty period

The maintenance policy for a product's life cycle differs for second‐hand and new products. Although several maintenance policies for second‐hand products exist in the literature, they are rarely investigated with reference to periodic inspection and preventive maintenance action during the warranty period. In this research, we study an optimal post‐warranty maintenance policy for a second‐hand product, which was purchased at age x with a fixed‐length warranty period. During the warranty period, the product is periodically inspected and maintained preventively at a prorated cost borne by the user, while any product failure is only minimally repaired by the dealer. After the warranty expires, the product is self‐maintained by the user for a fixed‐length maintenance period and the costs incurred during this time are fully borne by the user. At the end of the maintenance period, the product is replaced with a product of the user's choice. This study is focused on the determination of an optimal length for the maintenance period after the warranty expiration. As a criterion for the optimality, we adopt the long‐run mean cost during the second‐hand product's life cycle from the user's perspective. Finally, our results are analyzed numerically for sensitive analysis of several relevant factors, assuming that the failure distribution follows a Weibull distribution.     

基于SPEI及游程理论的云贵地区1960-2014年干旱时空变化特征

基于云贵地区49个气象站点1960-2014年的逐月气象数据,计算得到云贵地区季尺度及年尺度的标准化降水蒸散发指数序列,结合游程理论及经验正交（EOF）等方法,揭示云贵地区干旱的时空变化特征.研究结果表明：（1）云贵地区气候呈现逐渐变干的趋势,且年尺度和季尺度在21世纪初均出现由湿转干的迹象.（2）同一干旱历时条件下,不同等级干旱发生的频率不同,等级越小发生频率越高,反之亦然.同一等级的干旱发生频率随干旱历时长度的增加而减小.（3）在历时2~5个月的干旱事件中,云南省的干旱重现期均小于贵州省,即云南省发生干旱事件较贵州省频繁.27°N以北地区的干旱重现期较长,干旱事件发生频率较小.（4）对云贵地区近55 a的SPEI进行经验正交（EOF）分析知,EOF展开第1模态反映的是季风系统控制下的云贵地区旱涝一致性变化情况,21世纪后,云贵地区普遍处于干旱状态;EOF展开第2模态反映的是受乌蒙山阻隔,东西两侧干旱呈现反相位变化的空间分布特征.该研究对于认识和把握区域气候干旱趋势与规律,提高区域干旱预警能力,保证粮食安全和生态经济稳定有重要的现实意义.