Optimal Design of Reliability Acceptance Sampling Plan Based on Data Obtained from Partially Accelerated Life Test (PALT)

Abstract

In this paper, constant–stress partially accelerated life tests (PALT) are considered for a product with the assumption that the lifetime of the product follows Weibull distribution with known shape parameter and unknown scale parameter. Based on data obtained using Type-II censoring, the maximum likelihood estimates (MLEs) of the Weibull parameters and acceleration factor are obtained assuming linear and Arrhenius relationships with the lifetime characteristics and stress. Exact distributions of the MLEs of the parameters of Weibull distribution are also obtained. Optimal acceptance sampling plans are developed using both linear and Arrhenius relationships. Some numerical results are also presented to illustrate the resulted test plans.

Optimal Variable Acceptance Sampling Plan under Progressive Type-II Censoring for Mixture Distribution: Applications in Breast Cancer Data

“…They focused on determining the optimal allocation of sample proportion to both conditions by minimizing the generalized asymptotic variance of MLEs of the acceleration factor and model parameters. Meanwhile, Kumar et al (2020) designed an optimal ASP for Weibull distribution under PALT based on the type-II censoring scheme. They have considered two different life-stress relationships, namely, linear relation and Arrhenius.…”

“…In this section, MLE of the unknown parameters ϑ and ϕ of the mixture distribution ERMD is derived, where units are tested under PALT based on progressive type-II censoring. The conditional likelihood function for observed data under PALT is given by (see Kumar et al, 2020)…”

“…Solving the simultaneous equations ( 70) and ( 71) for b 0 and b 1 , we get estimators for b 0 and b 1 respectively, as (see Kumar et al, 2020)…”

Optimal design of reliability acceptance sampling plan based on constant‐stress accelerated life testing considering the uncertainty of accelerated factor

“…where P(𝐶|𝐷) is the probability of 𝐶 under the given 𝐷. Based on Equation (11), the risk constraint equations of both sides under the condition that AF is a constant can be expressed as…”

“…Therefore, combining ASP with the ALT techniques, an accelerated acceptance sampling plan (AASP) can be designed to effectively solve the problem of long test time, large sample size, and high cost in traditional reliability demonstration tests. Several studies on the design of AASPs have reported with different focuses on lifetime distributions (e.g., Exponential distribution, 5 Weibull distribution, 6 and Lognormal distribution 7 ), ALT types (e.g., constant‐stress accelerated life testing (CSALT) 8 and step‐stress accelerated life testing 9 ) and censoring schemes (e.g., time‐censoring, 9 failure‐censoring, 10 and sequential truncation 11 ). Among them, the CSALT with time‐censoring is more widely used in reliability demonstration tests, 12 and a lot of products’ lifetimes follow the lognormal distribution that plays an important role in statistically predicting the lifetime of mechanical products 13 .…”