Table 1 Classical optimal design model of CSALT and extended researches

Test purpose

To estimate the pth quantile y _p (0) of lifetime under normal stress

To estimate multiple quantiles [20,21,22]; for acceptance of product [23, 24]; to select the optimal product [25]; to estimate the quantile of the different products under normal stress [26]; to estimate the other parameters [27,28,29,30]

Test forms

Type of test censoring

Type-I censoring

Failure censored [23, 25, 31, 32]; time failure mixed censored [33]

Data collection method

Continuous testing

Periodic testing [34,35,36,37,38,39]

Strategy for testing the samples

All samples are put in from the start.

Sequential test method [40,41,42,43]

Number of stress levels

Singe stress level

Double or multiple stress levels [44,45,46,47,48,49,50,51,52,53,54,55]

Statistical models

Failure mode

Single failure mode

Multiple failure modes [28, 29]

Types of life distribution

Weibull/lognormal distribution

Two parameter exponential distribution [56]; Rayleigh distribution [36]; Burry type XII [38]; nonparametric method [27, 57]

Parameters relating to stress

Location parameter of location- scale distribution

Location and scale parameter of location-scale distribution [24, 58]

Form of stress-life relationship

Linear function

Polynomial [26] /nonparametric [27]

Data form

Life data

Group data [34,35,36,37,38,39]

Data analysis method

MLE

Unbiased estimation [56]; Bayesian [40, 59, 60]

Optimal design models of test plan

Optimization objective

Minimize the asymptotic variance of estimated y _p (0)

Multi-objective [20,21,22, 26, 27, 61,62,63,64,65,66,67,68]; cost [68]; test time [65, 66]; D-optimal [28, 29, 48, 69]; minimax [70]; robustness [21, 64]; highest stress [71]; others [27, 30]

Design Variables

Stress level

Minimum stress

Intermediate stress [27, 57, 65,66,67,68, 72, 73]

Allocation of sample size

Proportion in which samples are allocated to the lowest stress level.

Proportion in which samples are allocated to the intermediate stress level [27, 57, 65,66,67,68, 72, 73]

Allocation of test time

Not optimized

Optimize test time allocated to each stress level [65, 66, 68]

Constraints

Total sample size

Large sample size

Limited sample size [74]

Total test time

Specify the censoring time allocated to each stress level

Specify the total test time [68]

Space between stress levels

Unconstrained/Equal difference

Unequal difference [21, 27, 34, 36, 57, 63, 64, 66,67,68, 70, 72, 73]

Allocation of sample size

Unconstrained/equal allocation/Specified proportion

Minimize the expected number of failures [27, 39, 57, 66,67,68, 74]

Allocation of test time

Equal

Un-equal [65, 66, 68]

Other

/

Acceleration factor [49]; probability of failure at each stress level [65, 67, 72, 73], etc.