# Research and Evaluation Method for Echelon Usage of Double-Life Equipment Considering Calendar Life
## 1 Introduction  
The double-life equipment studied in this paper [1, 2] refers to disposable equipment with calendar life, working life, or other life limitations, which will be used many times in the whole life cycle according to the different tasks undertaken, in which the calendar life decreases with the change of calendar time [3, 4] (the difference in the reduction of calendar life caused by the working environment is not considered for the time being), and the working life will decrease according to the different use and consumption of the tasks undertaken. In order to give full play to the economic benefits of the equipment [5], it is necessary to control the use of the equipment so that the working life and calendar life are consumed and used at the same time. Due to the long life cycle of double-life equipment, the waste of life often does not occur immediately, and the problem is not easy to detect. The reasonable use control of equipment and the orderly use of reasonable life distribution are the premise to avoid the problem of life waste. For example, too little use causes the problem of working life waste, too much use causes the problem of working life reaching the specified life in advance, and improper use causes the problem of the working life of a large amount of equipment reaching the specified life at the same time. The so-called working life echelon usage [6] refers to the equipment's working life in ascending or descending order. The arrangement of the working life of the equipment is in a step shape. The working life echelon usage of equipment is usually used to control the use of the equipment to ensure orderly use and avoid life waste. For the usage and controldecision of double-life equipment [7], it is more complex and difficult to control the use of equipment because of the need to take care of two life indicators at the same time. The current usage and control method has several main problems:  
1. Considering working life and calendar life indicators at the same time, and how to give consideration to both indicators;
2. When the unit task quantity is determined, how to determine the controllable range of working life and whether there is equipment beyond the controllable range;
3. What distribution of working life is the strongest resistance to the impact of working life caused by changes in the external environment;
4. How to evaluate the equipment life reserve in the unit. For example, a unit has 10 pieces of equipment. When the calendar life or working life of the equipment reaches its end, the equipment needs to be scrapped. Each task requires the use of multiple pieces of equipment. In order to avoid the problem of life waste and the simultaneous retirement of multiple pieces of equipment, the use of equipment should be controlled. As shown in Figure 1, two life echelon usages are marked in the control method of the ladder chart. The diagonal column is the working life, and the blank column is the calendar life. The column chart is arranged from small to large according to the working life, so that the column chart of the calendar life is not necessarily a ladder chart. If the unit task quantity is determined, how can the controllable range of life be determined? It is obvious from the figure that the calendar life of equipment No.3 is too much, and the calendar life of equipment No.7 is too little. The working life of equipment No.3 can be consumed in the same proportion as the calendar life by reducing the usage. The reduced working time of equipment No. 3 will be consumed by other equipment, and may not be consumed. Assume that the current equipment in Figure 1 is within the controllable range, and the unit task volume and other indicators change, resulting in the change to the controllable range. The distribution status of the equipment life distribution can still be within the controllable range.