Skip to main content
SpringerLink
Log in

Computational testing algorithmic procedure of assessment for lifetime performance index of Pareto products under progressive type I interval censoring

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

Process capability indices had been widely used to evaluate the process performance to the continuous improvement of quality and productivity. When the lifetime of products possesses a one-parameter Pareto distribution, the larger-the-better lifetime performance index is considered. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also investigated. We use this estimator to develop the new hypothesis testing algorithmic procedure in the condition of known lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

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

Similar content being viewed by others

References

  • Aggarwala R (2001) Progressive interval censoring: some mathematical results with applications to inference. Commun Stat Theory Methods 30:1921–1935

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson DR, Sweeney DJ, Williams TA (1990) Stat Bus Econ. West Publishing Company, Saint Paul

    Google Scholar 

  • Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods and applications. Birkhäuser, Boston

    Book  Google Scholar 

  • Epstein B, Sobel M (1953) Life-testing. J Am Stat Assoc 48:486–502

    Article  MathSciNet  MATH  Google Scholar 

  • Gail MH, Gastwirth JL (1978) A scale-free goodness of fit test for the exponential distribution based on the Gini statistic. J R Stat Soc B 40:350–357

    MathSciNet  MATH  Google Scholar 

  • Hong CW, Wu JW, Cheng CH (2008) Computational procedure of performance assessment of lifetime index of Pareto lifetime businesses based on confidence interval. Appl Soft Comput 8:698–705

    Article  Google Scholar 

  • Kane VE (1986) Process capability indices. J Qual Technol 18:41–52

    Google Scholar 

  • Keller G, Warrack B, Bartel H (1994) Statistics for management and economics. Duxbury Press, Belmont, CA

  • Lee WC, Wu JW, Hong CW (2009) Assessing the lifetime performance index of products with the exponential distribution under progressively type II right censored samples. J Comput Appl Math 231:648–656

    Article  MathSciNet  MATH  Google Scholar 

  • Lee HM, Wu JW, Lei CL (2013) Assessing the lifetime performance index of exponential products with step-stress accelerated life-testing data. IEEE Trans Reliab 62:296–304

    Article  Google Scholar 

  • Meyer PL (1965) Introductory probability and statistical applications. Addison-Wesley, Reading

    Google Scholar 

  • Montgomery DC (1985) Introduction to statistical quality control. Wiley, New York

    MATH  Google Scholar 

  • Nigm AM, Al-Hussaini E, Jaheen ZF (2003) Bayesian one-sample prediction of future observations under Pareto distribution. Stat Theor Appl Stat 37:527–536

    MathSciNet  MATH  Google Scholar 

  • Sanjel D, Balakrishnan N (2008) A Laguerre polynomial approximation for a goodness-of-fit test for exponential distribution based on progressively censored data. J Stat Comput Simul 78:503–513

    Article  MathSciNet  MATH  Google Scholar 

  • Tong LI, Chen KS, Chen HT (2002) Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution. Int J Qual Reliab Manag 19:812–824

    Article  Google Scholar 

  • Wu SF (2010) Interval estimation for the two-parameter exponential distribution under progressive censoring. Qual Quant 44:181–189

    Article  Google Scholar 

  • Wu SJ, Lin YP, Chen YJ (2006) Planning step-stress life test with progressively type-I group-censored exponential data. Stat Neerl 60:46–56

    Article  MathSciNet  MATH  Google Scholar 

  • Wu SJ, Lin YP, Chen ST (2008) Optimal step-stress test under type I progressive group-censoring with random removals. J Stat Plan Inference 138:817–826

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author wish to thank an associate editor and referees for their careful reading and valuable suggestions so that the article is more readable and applicable. The author’s research was supported by The National Science Council NSC101-2118-M-032-003- and Ministry of Science and Technology MOST 103-2118-M-032-004-MY2 and MOST 105-2118-M-032-005-MY2 in Taiwan, ROC.

Author information

Authors and Affiliations

  1. Department of Statistics, Tamkang University, Tamsui, Taipei, 25137, Taiwan, ROC

    Shu-Fei Wu

  2. National Taipei University of Business Office of Institutional Research, Taipei, Taiwan, ROC

    Jin-Yang Lu

Authors
  1. Shu-Fei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jin-Yang Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shu-Fei Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, SF., Lu, JY. Computational testing algorithmic procedure of assessment for lifetime performance index of Pareto products under progressive type I interval censoring. Comput Stat 32, 647–666 (2017). https://doi.org/10.1007/s00180-017-0717-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-017-0717-3

Keywords

Search

Navigation