A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

The design of a new adaptive version of the multiple dependent state (AMDS) sampling plan is presented based on the time truncated life test under the Weibull distribution. We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans. A warning sign for acceptance number was proposed to increase the probability of current lot acceptance. The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk. A simulation study was presented to support the proposed sampling plan. A comparison between the proposed and existing sampling plans, namely multiple dependent state (MDS) sampling plans and a modified multiple dependent state (MMDS) sampling plan, was considered under the average sampling number and operating characteristic curve values. In addition, the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan. The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.     

System reliability for non-repairable multi-state series–parallel system using fuzzy Bayesian inference based on prior interval probabilities

In this article, the fuzzy concepts are applied in analysis of the system reliability problem. The fuzzy number is used to construct the fuzzy reliability of the non-repairable multi-state series–parallel system (NMSS). The fuzzy failure rate function is represented by an exponential fuzzy number. By using this innovative approach, the fuzzy system reliability of NMSS is created. In order to analyse this fuzzy system reliability, the fuzzy Bayesian point estimate of fuzzy system reliability is made by the conventional Bayesian formula. And, the posterior fuzzy system reliability of NMSS is developed by Bayesian inference with fuzzy probabilities. Finally, the performance of the method is measured by the mean square error of fuzzy Bayesian point estimate for the fuzzy system reliability of NMSS.     

Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

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.