Skip to main content
SpringerLink
Log in

Designing acceptance sampling plans based on the lifetime performance index under gamma distribution

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Acceptance sampling is popular in industries to determine whether a submitted lot should be accepted or not. Various sampling plans have been developed under the assumption that the quality characteristic of a product follows a normal distribution. However, lifetime data generally follows a non-normal distribution, such as exponential, gamma, or Weibull distribution in many applications. Therefore, this paper considers a product lifetime with a gamma distribution and develops two acceptance sampling plans, single sampling plan (SSP) and resubmitted sampling plan (RSP), based on the lifetime performance index. The plan parameters are obtained based on the two-point condition on the operating characteristic (OC) curve, which aims to satisfy the desired quality levels and the allowable risks by the producer and the consumer concurrently. The procedure of the proposed plans and tables of plan parameters are prepared for making decisions on product acceptance determination.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Arizono I, Kanagawa A, Ohta H, Watakabe K, Tateishi K (1997) Variable sampling plans for normal distribution indexed by Taguchi’s loss function. Nav Res Logist 44:591–603

    Article  Google Scholar 

  2. Aslam M, Jun CH, Lio YL, Ahmad M, Rasool M (2011) Group acceptance sampling plans for resubmitted lots under Burr-type XII distributions. Journal of the Chinese Institute of Industrial Engineers 28(8):606–615

    Article  Google Scholar 

  3. Aslam M, Wu CW, Azam M, Jun CH (2013) Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items. Appl Math Model 37(3):667–675

    Article  MathSciNet  Google Scholar 

  4. Aslam M, Wu CW, Azam M, Jun CH (2014) Mixed acceptance sampling plans for product inspection using process capability index. Qual Eng 26(4):450–459

    Article  Google Scholar 

  5. Das NG, Mitra SK (1964) The effect of non-normality on sampling inspection. Sankhya 26A:169–176

    MATH  Google Scholar 

  6. Govindaraju K, Ganesalingam S (1997) Sampling inspection for resubmitted lots. Communications in Statistics - Simulation and Computation 26(3):1163–1176

    Article  Google Scholar 

  7. Hamaker HC (1979) Acceptance sampling for percent defective by variables and by attributes. J Qual Technol 11(3):139–148

    Article  Google Scholar 

  8. Hogg RV, Mckean JW, Craig AT (2005) Introduction to Mathematical Statistics, 6th edn. Prentice-Hall, Upper Saddle River, NJ

    Google Scholar 

  9. Hong CW, Lee WC, Wu JW (2012) Computational procedure of performance assessment of lifetime index of products for the Weibull distribution with the progressive first-failure-censored sampling plan. Journal of Applied Mathematics, Article ID 717184:1–13

    MATH  Google Scholar 

  10. Hsu BM, Shu MH, Wang TC (2020) Variables adjustable multiple dependent state sampling plans with a loss-based capability index. Int J Adv Manuf Technol 107(5-6):2163–2175

    Article  Google Scholar 

  11. Jennett WJ, Welch BL (1939) The control of proportion defective as judged by a single quality characteristic varying on a continuous scale. Suppl J R Stat Soc 6(1):80–88

    Article  Google Scholar 

  12. Kao JHK (1971) MIL-STD-414: sampling procedures and tables for inspection by variables for percent defective. J Qual Technol 3(1):28–37

    Article  Google Scholar 

  13. Kurniati N, Yeh RH, Wu CW (2015) A sampling scheme for resubmitted lots based on one-sided capability indices. Quality Technology & Quantitative Management 12(4):501–515

    Article  Google Scholar 

  14. Lee AHI, Wu CW, Wang ZH (2018) The construction of a modified sampling scheme by variables inspection based on the one-sided capability index. Comput Ind Eng 122:87–94

    Article  Google Scholar 

  15. Lee HM, Wu JW, Lei CL, Hung WL (2011) Implementing lifetime performance index of products with two-parameter exponential distribution. Int J Syst Sci 42(8):1305–1321

    Article  MathSciNet  Google Scholar 

  16. Lee WC (2010) Assessing the lifetime performance index of gamma lifetime products in the manufacturing industry. Proc Inst Mech Eng B J Eng Manuf 224(10):1571–1579

    Article  Google Scholar 

  17. Lehmann EL, Scheffe H (1950) Completeness, similar regions and unbiased estimates. Sankhya 10:305–340

    MathSciNet  MATH  Google Scholar 

  18. Liu SW, Lin SW, Wu CW (2014) A resubmitted sampling scheme by variables inspection for controlling lot fraction nonconforming. Int J Prod Res 52(12):3744–3754

    Article  Google Scholar 

  19. Mahalingam U, Balamurali S (2019) Economic design of quick switching sampling system for resubmitted lots. Communications in Statistics– Theory and Methods 48(16):4019–4033

    Article  MathSciNet  Google Scholar 

  20. Montgomery DC (1985) Introduction to statistical quality control. John Wiley & Sons, New York

    MATH  Google Scholar 

  21. Nelson W (1980) Accelerated life testing-step-stress models and data analyses. IEEE Trans Reliab 29(3):103–108

    Article  Google Scholar 

  22. Owen DB (1964) Control of percentages in both tails of the normal distribution. Technometrics 6(4):377–387

    Article  Google Scholar 

  23. Owen DB (1967) Variables sampling plans based on the normal distribution. Technometrics 9(3):417–423

    Article  MathSciNet  Google Scholar 

  24. Stephens MA (1974) EDF statistics for goodness of fit and some comparisons. J Am Stat Assoc 69(374):730–737

    Article  Google Scholar 

  25. Seifi S, Nezhad MSF (2017) Variables sampling plan for resubmitted lots based on process capability index and Bayesian approach. Int J Adv Manuf Technol 88(9-12):2547–2555

    Article  Google Scholar 

  26. Tong LI, Chen KS, Chen H (2002) Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution. International Journal of Quality & Reliability Management 19:812–824

    Article  Google Scholar 

  27. Wang ZH, Wu CW (2019) Improved inspection scheme with a loss-based capability index. Int J Adv Manuf Technol 104(1-4):1321–1331

    Article  Google Scholar 

  28. Wu CW, Aslam M, Chen JC, Jun CH (2015a) A repetitive group sampling plan by variables inspection for product acceptance determination. Eur J Ind Eng 9(3):308–326

    Article  Google Scholar 

  29. Wu CW, Aslam M, Jun CH (2012) Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk. Eur J Oper Res 217(3):560–566

    Article  Google Scholar 

  30. Wu CW, Chen JC, Wu TH (2015b) A flexible sampling scheme for variables inspection with loss consideration. J Stat Comput Simul 85(18):3766–3777

    Article  MathSciNet  Google Scholar 

  31. Wu CW, Liu SW (2018) A new lot sentencing approach by variables inspection based on process yield. Int J Prod Res 56(12):4087–4099

    Article  Google Scholar 

  32. Wu CW, Liu SW, Chen JT, Lin JJ (2019) Design and construction of a variables switch-based sampling system for product acceptance determination. Int J Adv Manuf Technol 101(9-12):2643–2652

    Article  Google Scholar 

  33. Wu CW, Pearn WL (2008) A variables sampling plan based on Cpmk for product acceptance determination. Eur J Oper Res 184(2):549–560

    Article  Google Scholar 

  34. Wu JW, Lee HM, Lei CL (2007) Computational testing algorithmic procedure of assessment for lifetime performance index of products with two-parameter exponential distribution. Appl Math Comput 190:116–125

    MathSciNet  MATH  Google Scholar 

  35. Yen CH, Chang CH (2009) Designing variables sampling plans with process loss consideration. Communications in Statistics— Simulation and Computation 38(8):1579–1591

    Article  MathSciNet  Google Scholar 

Download references

Availability of data and material

The authors confirm that the data supporting the findings of this study are available within the article (and/or) its supplementary materials. The raw data that support the findings of this study are available from the corresponding author, upon a reasonable request.

Code availability

Not applicable.

Funding

This work was partially supported by the Ministry of Science and Technology of Taiwan under Grant No. MOST 106-2628-E-007-009-MY3.

Author information

Authors and Affiliations

  1. Department of Industrial Management, Chung Hua University, Hsinchu, Taiwan

    Amy H. I. Lee

  2. Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan

    Chien-Wei Wu & Cheng-Hsuan Liu

  3. College of Management, National Chin-Yi University of Technology, Taichung, Taiwan

    Shih-Wen Liu

Authors
  1. Amy H. I. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chien-Wei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shih-Wen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cheng-Hsuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Amy H. I. Lee was responsible for writing and organizing the suitable structure of content. The corresponding author Chien-Wei Wu has been responsible for planning and curating the main scope of this study. He was also responsible for the derivation of mathematical model. Shih-Wen Liu was responsible for the programming and analyzing and the confirmation of solved data. Cheng-Hsuan Liu was responsible for conducting sensitivity test of plan parameters and implementing the case study.

Corresponding author

Correspondence to Chien-Wei Wu.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, A.H.I., Wu, CW., Liu, SW. et al. Designing acceptance sampling plans based on the lifetime performance index under gamma distribution. Int J Adv Manuf Technol 115, 3409–3422 (2021). https://doi.org/10.1007/s00170-021-07299-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-021-07299-6

Keywords

Search

Navigation