On designing step-stress partially accelerated life tests under failure-censoring scheme

Abstract

In this article the maximum likelihood estimates of the model parameters under step-stress partially accelerated life tests (SSPALT) are obtained assuming the Weibull distribution with Type-II censored data. Also, the confidence bounds of the parameters are obtained. In addition, optimum step stress test plans are developed. The optimum test plan determines the optimal stress change point that minimizes the generalized asymptotic variance of the maximum likelihood estimators for the model parameters. That is, improving the quality of the statistical inference.

Planning of Partially Accelerated Degradation Test with Two Stress Variables for Practical Lifetime Estimation

“…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].…”

“…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 addition, decision variables were also considered as sample proportions were allocated to the allocation ratio (π), stress level (s), stress change time (SCT), and SCT based on the number of failures (SCF). [3] ALT (1) Constant Weibull Avar π, s Srivastava and Mittal [4] ALT (1) Constant Logistic Avar π Anwar and Islam [5] ALT (1) Constant Gompertz Avar π, s Ismail [6] ALT (1) Constant Weibull Avar π Srivastava and Mittal [7] ALT (1) Constant Burr XII Avar π Bai et al [8] ALT 1Step Lognormal Avar SCT Ismail [9] ALT 1Step Gompertz Avar SCT Aly and Ismail [10] ALT 1Step Weibull Avar SCT Srivastava and Mittal [11] ALT 1Step Logistic Avar SCT Hassan and Al-Thobety [12] ALT 1Step Inverse Weibull Avar SCF Ismail [13] ALT 1Step Weibull Avar SCT…”

Reliability analysis under constant-stress partially accelerated life tests using hybrid censored data from Weibull distribution

“…PALTs have been considered under Type-I and Type-II censoring schemes by numerous authors, for example, see Goel [18], DeGroot and Goel [12], Bhattcharyya and Soejoeti [9], Bai and Chung [7], Bai et al [8], Abdel-Ghaly et al [1], Abdel-Ghaly et al [2], Abdel-Ghaly et al [3], Abdel-Ghani [4], Abdel-Ghani [5], Ismail [21], Aly and Ismail [6], Ismail and Sarhan [25], Ismail et al [20] and Ismail [23].…”

Likelihood and Bayesian estimations for step-stress life test model under Type-I censoring

“…Most of literature performed on PALT considered the classical approach to estimate the parameters of interest, for example, see Goel [16], Bhattacharyya and Soejoeti [11], Bai and Chung [7], Bai et al [8], Attia et al [6], Abdel-Ghaly et al [2], Madi [29], Abdel-Ghani [3], Aly and Ismail [5], Ismail and Sarhan [25], Ismail [23], Ismail and Abu-Youssef [24], Ismail [21][22] and Abd-Elfattah et al [1].…”