For the convenience of study and practical operation, the assumptions are as follows.

1) The situation studied in this paper is to set a certain number of decoys around the target according to camouflage requirements to improve the survival ability of the target.

2) According to the newly formulated Johnson Criterion, the reconnaissance level is divided into four levels: discovery, distinction, identification, and confirmation. Once a target is identified, it means it is destroyed in information warfare, that is, the recognition rate of the target is equal to its destruction rate [11] .

3) According to the combat technology performance of decoys, the enemy’s existing reconnaissance equipment cannot distinguish between our target and decoys [12] [13] .

The more decoys are configured, the higher the survival probability of targets and the better camouflage effect. However, the more decoys are required, the more time, manpower, and material resources are needed; The fewer configurations are needed, the fewer decoys are required, and the less time, manpower, and material resources are needed. But, the less the survival probability of the target is improved, the lower the effectiveness of the display falsity. Therefore, we can establish a cost-effectiveness ratio model for determining the configuration quantity of decoys.

The cost-effectiveness ratio is the ratio of output benefits to input costs. Developed countries’ armies have long attached great importance to the study and calculation of cost-effectiveness in the military field. During World War I, the British army pioneered the “Lancaster equation” for optimizing the deployment of infantry combat forces. During World War II, the armies of the United States and Britain used military operations research to plan the deployment of air defense forces and maritime transportation. After the war, they applied this method to various aspects, such as selecting national security strategies, developing strategies for weapons and equipment, optimizing the structure of military forces, and reforming policies and systems for military personnel. The calculation of this cost-effectiveness ratio is not just a simple number, it reflects the scientific management concepts of quantitative analysis, cost accounting, detail management, process control, etc. It is an effective method to improve the efficiency of the military field from the accurate management of the whole process of input to output [11] .

The cost-effectiveness model can be expressed as follows:

$\eta =\frac{E}{C}$

Among them: $\eta$ represents the cost-effectiveness ratio; E representing the benefits generated; C represents the cost consumed.

In the configuration quantity model of decoy based on cost-effectiveness ratio, the product of the increase in the survival probability of the target and the cost of the target is used as the generated benefit. The probability of a disguised target being detected and identified by enemy reconnaissance is $P_T$, that is, the probability of a target being destroyed by the enemy is $P_T$, the probability of a decoy that has imperfect camouflage being destroyed by the enemy is $P_F=k\ast P_T$, the ratio of the probability of a target being destroyed to the probability of a decoy being destroyed is $k$, the cost of a target is $V_T$, the configuration quantity of decoy is $n$, the cost of a decoy is $V_F$.

When decoys are not configured, the survival probability of targets is $P_{TS}$:

$P_{TS}=1-P_T$

After configuring n decoys, the probability of the target being destroyed is ${P^{\prime }}_T$:

The situation and corresponding probability of the target being identified and destroyed by enemy reconnaissance are $n+1$ as follows.

The probability of the first reconnaissance target being identified and destroyed by the enemy is:

$\frac{P_T}{n+1}$

The destroyed probability that the target is diecovered and identified after the enemy discovers a target and the target is not identified as a decoy is:

$\frac{n\left(1-P_F\right)}{n+1}\times \frac{P_T}{n}\text{=}\frac{P_T\left(1-P_F\right)}{n+1}$

The destroyed probability that the target is diecovered and identified after the enemy discovers two targets and the target is not identified as decoy is:

$\frac{n\left(1-P_F\right)}{n+1}\times \frac{\left(n-1\right)\left(1-P_F\right)}{n}\times \frac{P_T}{n-1}\text{=}\frac{P_T{\left(1-P_F\right)}^2}{n+1}$

$\cdots$

The destroyed probability that the target is diecovered and identified after the enemy discovers $n$ targets and the target is not identified as decoy is:

$\frac{n\left(1-P_F\right)}{n+1}\times \frac{\left(n-1\right)\left(1-P_F\right)}{n}\times \frac{\left(n-2\right)\left(1-P_F\right)}{n-1}\times \cdots \times \frac{1-P_F}{2}\times P_T=\frac{P_T{\left(1-P_F\right)}^n}{n+1}$

The destroyed probability of the target:

$\begin{array}{c}{P^{\prime }}_T=\frac{P_T}{n+1}+\frac{P_T\left(1-P_F\right)}{n+1}+\frac{P_T\left(1-P_F\right)}{n+1}+\cdots +\frac{P_T{\left(1-P_F\right)}^n}{n+1}\\ =\frac{P_T}{n+1}\left({\left(1-P_F\right)}^0+{\left(1-P_F\right)}^1+{\left(1-P_F\right)}^2+\cdots +{\left(1-P_F\right)}^n\right)\\ =\frac{P_T}{n+1}\times \frac{1-{\left(1-P_F\right)}^{n+1}}{P_F}\\ =\frac{1-{\left(1-k{P}_T\right)}^{n+1}}{k\left(n+1\right)}\end{array}$

The survival probability of the target:

${P^{\prime }}_{TS}\left(n\right)=1-\frac{1-{\left(1-k\times P_T\right)}^{n+1}}{k\times \left(n+1\right)}$

The benefits generated by configuring $n$ decoys are:

$E\left(n\right)=\left({P^{\prime }}_{TS}\left(n\right)-P_{TS}\right)\times V_T$

The probability that the configured decoy will be destroyed $P_F$ is:

${P^{\prime }}_F=1-\left(1-P_T\right)\times {\left(1-k\times P_T\right)}^n-{P^{\prime }}_T$

The cost for each decoy $V_F$ is:

$V_F=V_F\times {P^{\prime }}_T$

$\eta =\frac{E}{C}=\frac{\left(P_T-\frac{1-{\left(1-P_F\right)}^{n+1}}{k\times \left(n+1\right)}\right)\times V_T}{n\times V_F\times {P^{\prime }}_T}$

Assuming the probability of a target is identified and destroyed is P_T = 20%, the cost is V_T = 6 million, the ratio of the destroyed probability of decoy to the destroyed probability of target is $k=1.5$, and the cost is V_F = 200000. The corresponding relationship table and curve graph between the cost-effectiveness ratio $\eta$ and the configuration quantity of decoy $n$ obtained by substitution calculation are as follows Table 1 and Figure 1 .

According to the calculation results, when the configuration quantity of decoys is 6, the cost-effectiveness ratio is less than 1; that is, the generated benefits are less than the cost of consumption. At this time, we call 5 as the critical value of the configuration quantity of decoys $n^{\prime }$. According to the calculation results of the cost-effectiveness ratio, the number of decoys should not be greater than 5, otherwise the gains will outweigh the losses.

For the data in the hypothesis, the probability of target being identified and destroyed is P_T = 20%, V_T = 6 million, the ratio of decoy’ destroyed probability to target’ destroyed probability is $k=1.5$, and the cost is V_T = 6 million. Change a certain value one by one, keep other numerical variables unchanged, and analyze its impact on the critical value of the configuration quantity of decoys.

Let P_T change within a reasonable range, V_T = 6 million, $k=1.5$, V_F = 200000 remain unchanged, the relationship P_T with the critical value of the configuration quantity of decoys $n^{\prime }$ and its cost-effectiveness ratio $\eta$ is shown in the Table 2 below.

Let V_T change within a reasonable range, P_T = 20%, $k=1.5$, V_F = 200000 remain unchanged, the relationship V_T with the critical value of the configuration quantity of decoys $n^{\prime }$ and its cost-effectiveness ratio $\eta$ is shown in the Table 3 below.

Let $k$ change within a reasonable range, P_T = 20%, V_T = 6 million, V_F = 200000 remain unchanged, the relationship $k$ with the critical value of the configuration quantity of decoys $n^{\prime }$ and its cost-effectiveness ratio $\eta$ is shown in the Table 4 below.

Let V_F change within a reasonable range, P_T = 20%, V_T = 6 million, $k=1.5$ remain unchanged, the relationship V_F with the critical value of the configuration quantity of decoys $n^{\prime }$ and its cost-effectiveness ratio $\eta$ is shown in the Table 5 below.

Statistics are made on the appearing number of critical value of the configuration quantity of decoys $n^{\prime }$ in the data, as shown in the following Table 6 .