Home Design of Optimal Reliability Acceptance Sampling Plans for Exponential Distribution
Article
Licensed
Unlicensed Requires Authentication

Design of Optimal Reliability Acceptance Sampling Plans for Exponential Distribution

  • Mahesh Kumar EMAIL logo and Ramyamol P C
Published/Copyright: April 15, 2016
Become an author with De Gruyter Brill

Abstract

In this paper, an attempt is made to derive the most efficient economic reliability sampling plans for accepting a lot containing identical units having exponentially distributed lifetime with parameter θ. We consider two types of sampling plans, namely, (a) sequential sampling plan (t1,t2) and (b) repetitive group sampling plan (n,t1,t2). Under plan (a), the lot is rejected when the time between successive failures (Yr) is less than t1, and accepted when Yrt2. The testing will continue for t1Yr<t2. Also we formulate an optimization problem that minimizes the total expected testing cost. Under plan (b), four different criteria are used to derive the sampling plan. The optimization problem formulated under each criterion is solved using a genetic algorithm to obtain the plan parameters (n,t1,t2). Several numerical examples are discussed to illustrate our plans. In addition, a real example is also considered to demonstrate our plan. Finally, we compare the cost of our plan with that of an existing plan in the literature. Our plan has significant potential to reduce the testing cost by about 50%.

The authors wish to express their thanks to the editor and the reviewer for their suggestions to improve the presentation and quality of the paper.

References

1 A. I. Al-Omari, Acceptance sampling plan based on truncated life tests for three parameter kappa distribution, Econ. Qual. Contr. 29 (2014), 1, 53–62. 10.1515/eqc-2014-0006Search in Google Scholar

2 M. Aslam, Double acceptance sampling based on truncated life-tests in Rayleigh distribution, Eur. J. Sci. Res. 17 (2007), 605–611. Search in Google Scholar

3 M. Aslam and C.-H. Jun, A group acceptance sampling plan for truncated life test having Weibull distribution, J. Appl. Stat. 36 (2009), 1021–1027. 10.1080/02664760802566788Search in Google Scholar

4 M. Aslam and C.-H. Jun, A group acceptance sampling plans for truncated life tests based on the inverse Rayleigh and log-logistic distributions, Pakistan J. Statist. 25 (2009), 1–13. 10.1515/eqc.2010.008Search in Google Scholar

5 M. Aslam, C.-H. Jun, A. J. Fernandez, M. Ahmad and M. Rasool, Repetitive group sampling plan based on truncated tests for Weibull models, Res. J. Appl. Sci. Engrg. Technol. 7 (2014), 1917–1924. 10.19026/rjaset.7.483Search in Google Scholar

6 M. Aslam, S. T. A. Niaki, M. Rasool and M. S. Fallahnezhad, Decision rule of repetitive acceptance sampling plans assuring percentile life, Sci. Iranica 19 (2012), 879–884. 10.1016/j.scient.2012.02.012Search in Google Scholar

7 M. Azam, M. Aslam, S. Balamurali and A. Javaid, Two stage group acceptance sampling plan for half normal percentiles, J. King Saud Univ. Sci. 27 (2015), 239–243. 10.1016/j.jksus.2015.03.009Search in Google Scholar

8 S. Balamurali and M. Usha, Optimal design of variable chain sampling plan by minimizing the average sample number, Int. J. Manufac. Engrg. 3 (2013), 1–10. 10.1155/2013/751807Search in Google Scholar

9 D. J. Bartholomew, The sampling distribution of an estimate arising in life testing, Technometrics 5 (1963), 361–374. 10.1080/00401706.1963.10490104Search in Google Scholar

10 R. F. Drenick, The failure law of complex equipment, J. Soc. Indust. Appl. Math. 8 (1960), 680–689. 10.1137/0108051Search in Google Scholar

11 B. Epstein, Truncated life tests in the exponential case, Ann. Math. Statist. 25 (1954), 3, 555–564. 10.1214/aoms/1177728723Search in Google Scholar

12 B. Epstein and M. Sobel, Life testing, J. Amer. Statist. Assoc. 48 (1953), 486–502. 10.1080/01621459.1953.10483488Search in Google Scholar

13 C.-H. Jun, S. Balamurali and S.-H. Lee, Variable sampling plans for Weibull distribution lifetimes under sudden death testing, IEEE Trans. Reliab. 55 (2006), 53–58. 10.1109/TR.2005.863802Search in Google Scholar

14 C.-H. Jun, L. Hyeseon, S.-H. Lee and S. Balamurali, A variables repetitive goup sampling plan under failure-censored reliability tests for Weibull distribution, J. Appl. Stati. 37 (2010), 453–460. 10.1080/02664760802715914Search in Google Scholar

15 R. R. Kantam, K. Rosaiah and G. Srinivas Rao, Acceptance sampling plans based on life tests: Log-logistic model, J. Appl. Stat. 28 (2001), 121–128. 10.1080/02664760120011644Search in Google Scholar

16 H. A. Noughabi, Testing exponentiality based on the likelihood ratio and power comparison, Ann. Data Sci. 2 (2015), 195–204. 10.1007/s40745-015-0041-0Search in Google Scholar

17 F. Proschan, Theoretical explanation of observed decreasing failure rate, Technometrics 5 (1963), 315–383. 10.1080/00401706.1963.10490105Search in Google Scholar

18 G. S. Rao, A group acceptance sampling plans for lifetimes following a generalized exponential distribution, Econ. Qual. Contr. 24 (2009), 75–85. 10.1515/EQC.2009.75Search in Google Scholar

19 R. E. Sherman, Design and evaluation of a repetitive group sampling plan, Technometrics 7 (1965), 11–21. 10.1080/00401706.1965.10490222Search in Google Scholar

20 T. R. Tsai and S. J. Wu, Acceptance sampling based on truncated life test for generalized rayleigh distribution, J. Appl. Stat. 33 (2006), 595–600. 10.1080/02664760600679700Search in Google Scholar

21 C.-W. Wu, M. Aslam, J. C. Chen and C.-H. Jun, A repetitive group sampling plan by variables inspection for product acceptance determination, Eur. J. Indust. Engrg. 9 (2015), 308–326. 10.1504/EJIE.2015.069340Search in Google Scholar

22 C.-H. Yen, C.-H. Chang and M. Aslam, Repetitive variable acceptance sampling plan for one-sided specification, J. Stat. Comput. Simul. 85 (2015), 1102–1116. 10.1080/00949655.2013.862791Search in Google Scholar

Received: 2015-8-25
Revised: 2015-12-11
Accepted: 2016-3-26
Published Online: 2016-4-15
Published in Print: 2016-6-1

© 2016 by De Gruyter

Downloaded on 24.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/eqc-2015-0005/html
Scroll to top button