# Design of Optimal Reliability Acceptance Sampling Plans for Exponential Distribution

Design of Optimal Reliability Acceptance Sampling Plans for Exponential Distribution 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 ( t 1 , t 2 ) \${(t_1,t_2)}\$ and (b) repetitive group sampling plan ( n , t 1 , t 2 ) \${(n,t_1,t_2)}\$ . Under plan (a), the lot is rejected when the time between successive failures ( Y r ) \${(Y_r)}\$ is less than t 1 , and accepted when Y r ≥ t 2 \${Y_r\ge t_2}\$ . The testing will continue for t 1 ≤ Y r < t 2 \${t_1\le Y_r< t_2}\$ . 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 , t 1 , t 2 ) \${(n,t_1,t_2)}\$ . 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%. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

# Design of Optimal Reliability Acceptance Sampling Plans for Exponential Distribution

, Volume 31 (1) – Jun 1, 2016
14 pages

/lp/de-gruyter/design-of-optimal-reliability-acceptance-sampling-plans-for-ESym3aVE3h
Publisher
de Gruyter
ISSN
0940-5151
eISSN
1869-6147
DOI
10.1515/eqc-2015-0005
Publisher site
See Article on Publisher Site

### Abstract

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 ( t 1 , t 2 ) \${(t_1,t_2)}\$ and (b) repetitive group sampling plan ( n , t 1 , t 2 ) \${(n,t_1,t_2)}\$ . Under plan (a), the lot is rejected when the time between successive failures ( Y r ) \${(Y_r)}\$ is less than t 1 , and accepted when Y r ≥ t 2 \${Y_r\ge t_2}\$ . The testing will continue for t 1 ≤ Y r < t 2 \${t_1\le Y_r< t_2}\$ . 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 , t 1 , t 2 ) \${(n,t_1,t_2)}\$ . 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%.

### Journal

Economic Quality Controlde Gruyter

Published: Jun 1, 2016

### References

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