###### Abstract
[10] considered a simple step-stress life test in the presence of exponentially distributed competing risks with Type-II censored data. Ref. [11] considered a simple step-stress model based on a complete sample that follows the Weibull distribution and derived the maximum likelihood estimation and Bayesian estimation. Ref. [12] provided a comprehensive exploration of accelerated life models and discussed the theoretical foundations of the models. To better extrapolate the lifetime under normal use conditions, partially accelerated life test (PALT) was developed. It divides all products into groups and test each in normal and accelerated environments. Two sorts of prevalent PALTs are known as the constant stress partially accelerated life tests (CSPALTs) and the step stress partially accelerated life tests (SSPALTs). CSPALTs set different groups of units under use and stress condition respectively. By comparison, SSPALTs start with normal conditions and switch to accelerated conditions if the unit does not cease to function before a prefixed point in time \(\tau\). The specific illustration of the differences between the two PALTs are displayed in Figure 2. Many researchers have studied PALTs, ref. [13] considered the CSPALTs with type-I censoring under Weibull distribution and minimized the asymptotic variance of the maximum likelihood estimators. Ref. [14] developed a SSPALT under adaptive type-II progressive hybrid censoring scheme with test items following the inverted Lomax distribution and obtained the maximum likelihood estimation of the model parameters. Censoring is another strategy of important use that can significantly reduce the test time and cost. It involves knowing only parts of all the units' exact failure times while the other units are removed or lost from the experiment before they fail. This helps experimenters save time and reduce costs. There exist numerous censoring schemes (CSs), with the prevalent ones being Type-I and Type-II censoring. For the former, the experiment concludes after a predetermined duration, and for the latter, the test stops upon a specific number of unit failures. Moreover, a broader, more adaptable, and efficient approach known as progressive Type-II censoring was introduced into practical problems by [15]. In this censoring scheme (CS), suppose there are \(n\) units undergoing a lifetime test, and \(R=(R_{1},R_{2},\cdots,R_{m})\) represents some predetermined CS. Immediately following the initial failure, a random elimination of \(R_{1}\) units is made from the \(n-1\) units which are still functioning. Then \(R_{2}\) units are withdrawn from those \(n-2-R_{1}\) still working ones. This process is repeated until the \(m\)th failure takes place, at which instant the experimenter eliminates all of the \(n-m-R_{1}-R_{2}-\cdots-R_{m-1}\) remaining units, then this test concludes. Researchers have done a lot of work on these CSs. In [16], CSPALTs using adaptive progressively Type I censored samples are taken into account and the estimation of  
Figure 2: A schematic diagram of CSPALT (**a**) and SSPALT (**b**). model parameters are derived using maximum likelihood, maximum product and Bayesian method. Ref. [17] considered different methodologies for estimating the parameters of the gamma distribution using progressive Type-II censored data, and further present an optimal progressive censoring plan using three optimality criteria. As for general progressive Type-II censoring (referenced in [15], Chapter 1.5, page 9), it is a more general and flexible form of the progressive Type-II censoring, which allows the experimenters to lose the first \(r\) observations (which means they only know the number but without exact time of the failures) before they start to perform the progressive censoring. Consequently, the censoring scheme evolved into \((R_{r+1},R_{r+2},\cdots,R_{m})\), signifying that censoring initiates upon the \((r+1)\)th failure. The entire procedure is explained in Figure 3. Many scholars have discussed this type of CS. For example, ref.