## 2 Related Works  
In this section, the existing literature on designing partially accelerated test (PAT) plans including life test and degradation test are reviewed. Several previous studies have attempted to determine the optimal testing procedures for PATs. Most studies focused on the planning of the PALT [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. In addition, these studies also considered constant stress (CS) loading [2; 3; 4; 5; 6; 7] and step stress (SS) loading [2; 8; 9; 10; 11; 12; 13; 14]. To design the test plans, the number of stress variables, degradation model, optimization criterion, and the decision variable were mainly considered along with the stress loading method [15; 16]. In terms of failure distributions, exponential [2], lognormal [8], Gompertz [5; 9], Weibull (or inverse Weibull) [3; 6; 10; 12; 13; 14], logistic [4; 11], and Burr XII [7] were adopted.  
In PATs, since the lowest accelerated stress level is fixed with the normal use condition, no or few failures in the test samples are observed under test conditions including accelerated stress levels. However, in the case of degradation tests, reliability information such as degradation data can be obtained under the use and accelerated test conditions. Therefore, the PAT concept is more suitable for PADTs than PALTs [1; 17].  
Studies of PADT plans have been performed under CS loading [17] and SS loading [1]. A two-phase planning strategy for the design of CS-PADT plans that minimizes the Avar of the estimated \(q\)th quantile of the lifetime distribution was proposed [17]. In addition, practical SS-PADT planning with three stress levels was suggested [1]. However, almost all of the previous studies on the design of PALT and PADT plans have only considered a single stress variable. Thus, in this paper, practical PSSADT plans with two stress variables were developed.  
Table 1 summarizes the literature on the design of PAT plans. In addition, decision variables were also considered as sample proportions were allocated to the allocation ratio (\(\pi\)), stress level (\(s\)), stress change time (SCT), and SCT based on the number of failures (SCF).  
In addition to the design of optimal PAT plans, studies that estimated the parameters of probability distribution and compared performances of the estimators have been conducted. The MLEs and Bayesian estimators and credible intervals of the Weibull parameters were obtained to analyze the competing risks model in the PALTs under progressively type-I hybrid censoring [18]. [PERSON] et al. [19] analyzed performances of the estimators in the SS-PALTs under type-I and type-II progressive hybrid censoring. [PERSON] et al. [20] concentrated on the estimation of inverse Weibull parameters under progressive type-II censoring. [PERSON] and [PERSON] [21] introduced a competing risk model with the SS-PADT plan under type-I progressively hybrid censoring. [PERSON] and [PERSON] [22] and [PERSON] et al. [23] considered parameters estimations of two-parameters linear exponential [22] and Weibull-exponential distribution [23] with the CS-PALTs under progressively type-II censoring.  
The WP degradation model is one of the stochastic processes for modeling of degradation pattern over time. The WP degradation model is often applied for degradation test planning and degradation analyses [1, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]. Recently, degradation data analysis and remaining useful life estimation approaches based on Wiener process were reviewed [33]. [PERSON] [34, 35] applied the weighted-sum approach for four bi-objective vehicle routing problems and worker allocation problems with integer and mixed-integer programming. As seen above, studies have focused on PADT analysis, few studies on the design of PADT have not been published.