Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

Abstract

A novel adaptive multiple dependent state sampling plan (AMDSSP) was designed to inspect products from a continuous manufacturing process under the accelerated life test (ALT) using both double sampling plan (DSP) and multiple dependent state sampling plan (MDSSP) concepts. Under accelerated conditions, the lifetime of a product follows the Weibull distribution with a known shape parameter, while the scale parameter can be determined using the acceleration factor (AF). The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive. An economic design of the proposed sampling plan was also considered for the ALT. A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number (ASN) and total cost of inspection (TC) under both producer's and consumer's risks. Numerical results are presented to support the AMDSSP for the ALT, while performance comparisons between the AMDSSP, the MDSSP and a single sampling plan (SSP) for the ALT are discussed. Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions. The AMDSSP also had a higher operating characteristic (OC) curve than both the existing sampling plans. Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

Modified DS <i>np</i> Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

“…The Weibull distribution is often employed in statistical quality control studies [16][17][18][19]28]. Because of its flexibility and closed shape, the Weibull distribution serves as the most popular choice to model the data lifespan.…”

“…Since the acceptance or rejection of current lots depends on previous and current lots, the MDS sampling plan is intended for a continuous production process whereby lots are sent for serial inspection, which reduces the sample size. Several researchers have adopted MDS sampling plans to develop a more efficient acceptance sampling plan [16][17][18][19]. Many researchers created designs to apply MDS sampling in the area of control charts, such as Aslam et al [20] who provided the X chart using MDS sampling based on a double control limit.…”