## 1 Introduction  
Reliability estimation is a popular research topic that has recently received much attention. Many studies focus on the stress-strength system with two components, which can be regarded as two random variables \(X\) and \(Y\), representing strength and stress. Its reliability is \(R=P(X>Y)\). For this kind of system, extensive research has been carried out. Many scholars have discussed the estimation of this reliability under certain distributions, such as [PERSON] and [PERSON] [1], [PERSON] et al. [2], [PERSON] et al. [3], [PERSON] et al. [4], etc. In the theory of reliability, the multicomponent stress-strength system is an extension of the classical stress-strength system, which contains one stress component and \(k\) independent strength components. The system will remain stable if at least \(s\) of the \(k\) strength values exceed the stress value. For instance, a bridge with \(k\) vertical cables that represent the strength of the structure is just a multicomponent stress-strength system. It will remain stable if the stress brought on by wind, high traffic volume, etc., does not exceed the values of at least \(s\) of its \(k\) strength components. Another example is an eight-cylinder vehicle engine, which operates as long as at least four of the eight cylinders are firing. For \(k\) strengths that are exposed to one stress, strengths \(X_{1},\ X_{2},\...,\ X_{k}\) are independent random variables with the same cumulative distribution function (CDF) \(F_{X}(y)\), and stress \(Y\) (independent of \(X_{1},\ X_{2},\...,\ X_{k}\)) is a random variable with the CDF \(F_{Y}(y)\). Then, the multicomponent stress-strength reliability (MSSR) can be described as  
\[ \begin{split} R_{s,k}&=P[\text{at least $s$ of $(X_{1},X_{2},\ldots,X_{k})$ exceed Y}]\\ &=\sum_{m=s}^{k}\left(\begin{array}{c}k\\ m\end{array}\right)\int_{-\infty}^{+\infty}[1-F_{X}(y)]^{m}[F_{X}(y)]^{k-m}dF_{ Y}(y).\end{split}  \tag{1}\]  
The estimation of the MSSR has been widely studied under complete sample data, where different distributions have been used. For example, [PERSON] [5] studied the maximum likelihood estimation and asymptotic confidence interval of the MSSR based on generalized exponential distribution. [PERSON] et al. [6] discussed the classical estimation of the MSSR based on generalized inverted exponential distribution. [PERSON] and [PERSON] [7] derived the estimation of the MSSR based on the Marshall-Olkin Bivariate Weibull distribution using frequentist and Bayesian methods. The Bayesian estimators were developed using [PERSON]'s approximation and Markov Chain Monte Carlo techniques. [PERSON] and [PERSON] [8] discussed the estimation of the MSSR based on the Bivariate Kumaraswamy distribution in a similar way. Censoring is an effective tool that is often used in lifetime tests. In practical experiments, censoring plays an important role when there are not enough test units or when data for all test units cannot be collected because of the lack of time and resources. Type-I and Type-II censoring attract a lot of attention due to their mathematical simplicity. In Type-I censoring, if a pre-determined time is reached, the test will be stopped, whereas in Type-II censoring, if a pre-determined number of units fail, the test will be stopped. However, both censoring schemes may be inappropriate if the experimenter needs to intermittently remove units. Thus, progressive Type-II censoring is considered a better option and has been widely used in recent years. In this censoring, the intermittent removal of units is allowed. In addition, it saves time and expenses to a certain extent. Progressive Type-II censoring in a lifetime test is as follows. Assume that \(M\) units are tested in the experiment. When the first failure \(x_{1}\) happens, \(R_{1}\) units are randomly removed. When the second failure \(x_{2}\) happens, \(R_{2}\) units are randomly removed, and so on. Finally, when the \(m^{\text{th}}\) failure \(x_{m}\) happens, the remaining \(R_{m}\) active units are all removed. Note that \(M=R_{1}+R_{2}+...+R_{m}+m\).