Binomial-Based Attribute Sampling: Formulating
Multiple-Dependent State Plans Based On The Extended Odd Exponential Distribution For Truncated Life Tests

Rehab Alsultan^1,*

¹Department of Mathematics, College of Sciences, Umm Al-Qura University, Makkah, Saudi Arabia

Email: rasultan@uqu.edu.sa

Abstract

This paper develops a Multiple Dependent State Sampling Plan (MDSSP) based on the Extended Odd Exponential Generalized Exponential (EOEGE– E) distribution for truncated life tests. The proposed methodology determines the optimal sampling plan by minimizing the required sample size while satisfying predetermined producer’s and consumer’s risk requirements. An optimization algorithm is developed to obtain the optimal plan parameters for different combinations of the termination ratio, quality ratio, and consumer’s risk. A comprehensive numerical study is conducted to investigate the effects of the design parameters on the optimal sampling plans and their operating characteristics. The results show that the proposed methodology produces feasible and stable sampling plans over a wide range of design set- tings. In general, the required sample size decreases as the quality ratio and termination ratio increase, whereas more stringent consumer protection re- quires larger sample sizes. The proposed methodology is illustrated using a real COVID–19 mortality dataset. The EOEGE–E distribution is first fit- ted to the data using the maximum likelihood method, and goodness-of-fit analyses confirm its suitability for modeling the observed lifetime data. The fitted distribution is then employed to construct the proposed MDSSP. Comparative studies demonstrate that the proposed sampling plan consistently re- quires fewer inspected units than both the conventional Single Sampling Plan (SSP) and the Weibull-based MDSSP while maintaining the prescribed pro- ducer’s and consumer’s risk requirements. The proposed MDSSP provides an efficient and economical inspection procedure for truncated life testing and represents a practical alternative for reliability analysis and industrial quality control.

Keywords: Acceptance sampling; Multiple dependent state sampling plan; Truncated life test; Extended Odd Exponential Generalized Exponential distribution; Operating characteristic function; Consumer’s risk; Producer’s risk

1.       Introduction

Acceptance sampling is one of the most widely adopted statistical quality control techniques for making decisions on submitted production lots without conducting complete inspection [11]. Instead of examining every manufactured item, a decision regarding lot acceptance or rejection is made based on the quality characteristics observed in a representative sample. This approach substantially reduces inspection cost, testing time, and operational effort while maintaining an acceptable balance between producer’s and consumer’s risks. Since the pioneering work of [20], acceptance sampling has become an indispensable component of industrial quality assurance and has found extensive applications in manufacturing, electronics, pharmaceuticals, biomedical engineering, and reliability assessment [12].

For highly reliable or expensive products, destructive life testing is often impractical because it requires waiting until all test units fail. Consequently, truncated life tests have become an attractive alternative by terminating the experiment at a predetermined time and making acceptance decisions based only on the observed failures before the truncation time.