Single and Double Acceptance Sampling Plans Based on the Time Truncated Life Tests for the Compound Weibull-Exponential
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RESEARCH ARTICLE
Single and Double Acceptance Sampling Plans Based on the Time Truncated Life Tests for the Compound Weibull-Exponential Distribution Canan Hamurkarog˘lu1
•
A. Yig˘iter2
•
N. Danacıog˘lu3
Accepted: 18 September 2020 The Indian Society for Probability and Statistics (ISPS) 2020
Abstract Acceptance sampling plans are one of the important statistical tools in production sector. While the producers want the protection of the quality of the products and minimum variability between them, the consumers expect the products to satisfy the quality characteristics. It is worth to mention that the acceptance sampling plans protect both the interest of the producers and the consumers. For some products, the life time might be an important quality characteristic. In this case, the satisfaction of the quality control of the products can be controlled using a suitable life time test based on the acceptance sampling plans for the life time of the products. In the industry, the acceptance sampling plans based on the life time test of the product life are called as reliability. The fact that it is almost impossible to inspect all the products due to the limitations of both cost and time, the acceptance sampling plans are used based on a truncated life time test with a censoring scheme. In this study, optimal plan parameters are obtained for single and double acceptance sampling plans when the life time of a product follows compound Weibull-Exponential distribution. Keywords Acceptance sampling plans Truncated life time test Producer’s risk Consumer’s risk Compound Weibull-Exponential distribution
& A. Yig˘iter [email protected] 1
Department of Actuary and Risk Management, Faculty of Business Administration, Karabu¨k University, Karabu¨k, Turkey
2
Department of Statistics, Faculty of Science, Hacettepe University, Ankara, Turkey
3
Department of Statistics, Faculty of Science, Sinop University, Sinop, Turkey
123
Journal of the Indian Society for Probability and Statistics
1 Introduction Acceptance sampling plans include the process of deciding whether to accept the products in a production unit. Quality levels of the products are very important for both producers and consumers. It is almost impossible to inspect all of the products due to restrictions regarding cost, time and formation of the damaged products during inspection and etc. Therefore, the decision on the quality of the product is taken based on random sample selected from the lot. Acceptance sampling plans can be single, double, multiple or sequential plans. Although single acceptance sampling plans (SASP) are preferred due to their application simplicity, double acceptance sampling plans (DASP) provide psychological confidence for both producer and consumer. In SASP, the lot is rejected if the number of failures is equal or greater than a pre-determined acceptance number and it is accepted if the opposite is the case. DASPs are used either to reduce sample size or producer’s risk. If a decision cannot be taken from the firs
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