One of the ways to increase the reliability of the system is redundancy allocation to the system. The standby redundancy is divided into three categories, cold, hot, and warm, depending on the environmental conditions in which they are placed in standby mode. The cold standby redundancy is inactive in standby mode, and the possibility of its failure in this mode is considered zero. A hot standby redundancy is active in standby mode and has the same failure rate as active system components. A warm standby redundancy is also active in standby mode, but it is not subjected to the same stress as the active system components as a hot standby redundancy. In this article, we investigate the reliability of stress-strength in k out of n:G system in an H-Weibull model equipped with three types of standby redundancy and we get results about the time to add the standby component to this system. The baseline distribution function of the model is H, which is the distribution of the stress system. The contents of this article are categorized as follows. In the second part, in the general case, we will calculate the reliability of stress-strength in a k out of n:G system in an H-Weibull model equipped with a standby redundancy in H-Weibull models. In addition, we obtain a closed form for the stress-strength reliability of these systems under the exponential baseline distribution in the three standby states of cold, hot, and hot. In the third part, we study the time and cost of adding the standby component to this system. In this section, by introducing the cost function, we obtain the optimal time to add the standby component of the system with the aim of simultaneously reducing the costs and increasing the reliability of the stress-strength model under different values of the model parameters. In the last part, the conclusion of the content of the article is presented. Material and Methods In this paper, we present the general case for adding a standby component to a k out of n:G stress-strength system. Then, in the H-Weibull model, we investigate the reliability behavior of stress-strength in this system. A k out of n:G system is active, whenever at least k components out of n components are active. Consider a k out of n:G system with independent identically distributed (i.i.d) Y₁ ،...، Yn with distribution function G. Assume that the components of the above system are independent of each other putting into a common random stress Z with cumulative distribution function H and random variables Z and Yi for i = 1 ،...، n. In this case, the stress-strength reliability of this system is given as R(n. k) = P(ZYn-k+1n), where Yi:n, is i th order statistic in the random sample Y₁ ،...، Yn. Suppose that the random variable X is the lifetime of a standby redundant with the distribution function F in normal environmental conditions and with the cumulative distribution function F(γ(t)) in the standby state, where γ(t) is any ascending function meeting two requirements for every t > 0, γ(0) = 0 and γ(t) ≤t. On the other hand, the ascending function w(t) is the transformed age of the standby redundant, from the standby state to the normal condition applying to every t > 0 in two conditions w(0) = 0 and w(t) ≤t. The hot and cold ready add-ons are special modes of the above model and are obtained when w(t) = γ(t) = 0 and w(t) = γ(t) = t, respectively. Letk out of n:G mentioned stress-strength system equipped with the standby redundant with lifetime X. Here, the standby redundancy enters the system operation after observing the (n-k-m+1)th failure among the system components, where m = 0...n-k, and the system until the failure of the (m + 1)th component out of m+k remaining components is kept active. Results and Conclusion In this article, the importance of the time allocation of the standby redundant to the k-out-of-n:G stress-strength system and its effect on the stress-strength reliability and costs in the H-Weibull model are investigated. Also, the behavior of the cost function based on the H-Weibull model parameters is studied. The optimal time to add the standby component to the system performance in a k-out-of-n:G stress-strength system in the H-Weibull model is presented. Based on the results of this article, the adding time of the standby component with the aim of increasing the stress-strength reliability is dependent on the parameters of H-Weibull model, and the time changes by changing these parameters. On the other hand, the time to add the standby component to the stress-strength system in the model with the aim of increasing the stress- strength reliability and reducing the system costs simultaneously, in addition to the system parameters is dependent on the number of system components and the value of k. In any case, we can conclude that for large values of n and k, the optimal time to add is m = 0 and for small values of k and large n, this value is usually m=n k and based on the distance between the values of n and k from each other, the value of m will be changeable. [ABSTRACT FROM AUTHOR]