Scheming of reliability sampling plans with some lifetime distributions based on percentiles estimation using intervened Poisson characteristics

Abstract

In industry, the practice of determining the performance of a product by intervening with the normal working conditions of the manufacturing process is an acceptable method. When reliability is a key quality factor, the reliability single sampling plan is generally used to optimise sample size and estimate time characteristics. The application of Intervened Poisson Distribution (IPD) and some of the lifetime distributions are used in this article to implement a reliability sampling plan. The IPD can be used as a model for counting the defective items in an appropriate situation and the defectiveness will be determined with the help of lifetime distributions. The minimum sample size required to accept a lot and the estimation of the true percentile time of the accepted lots according to the magnitude of the intervention parameter can be found using IPD associated with the Rayleigh Distribution (RD), Exponentiated Rayleigh Distribution (ERD) and Inverse Rayleigh Distribution (IRD). The minimum sample size is necessary to ensure the specified life percentile is obtained under a consumer risk. The operating characteristic (OC) values and estimated percentile time of an accepted lot are presented.

Keywords:

• Intervened poisson distribution
• operating characteristic value
• minimum sample size
• consumer risk
• percentile time
• producer risk

Acknowledgments

The authors are grateful to Bharathiar University, Coimbatore for providing necessary facilities to carry out this research work. The authors thank the anonymous reviewers for valuable comments, which contributed to the improvement in the presentation of the paper. Asif T Thottathil is thankful to UGC, New Delhi, India for providing financial support in the scheme of Maulana Azad National Fellowship (UGC-Ref. No.:4287/(CSIR-UGC NET JUNE 2019)).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data Availability statement

The authors confirm that the data supporting the findings of the study in Section Inverse Rayleigh Distribution (IRD) are available within the article ‘Statistical investigation of the fatigue life of deep-groove ball bearings’ by Lieblein, J., and Zelen, M. (1956) and its supplementary materials.

Additional information

Notes on contributors

Pradeepa Veerakumari Kumarasamy

Pradeepa Veerakumari Kumarasamy is working as Assistant Professor in Statistics at Bharathiar University, Coimbatore. Her research area of expertise is Statistical Quality Control, designing and simulation of acceptance sampling procedures and deep insight on reliability involving lifetime time distributions with percentile estimation.

Asif T. Thottathil

Asif T Thottathil is a Research Fellow pursuing the course at the Department of Statistics, Bharathiar University, Coimbatore for the award of Ph. D., Degree in Statistics. He has selected for award of fellowship by University Grants Commissions (UGC) under the scheme of Maulana Azad National Fellowship for Minority Students - 2019-20. His field of specialisation is Statistical Quality Control and Reliability.