Skip to main content
SpringerLink
Log in

Optimal Stress Screening strategies formulti‐component systems sold under warranty:The case of phase‐type lifetimes

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Environmental Stress Screening (ESS) is employed to reduce, if not eliminate, the occurrence of early field failures. This paper examines the necessary trade‐offs between the reduction in warranty costs and the increase in manufacturing costs associated with optimal stress screening strategies. A multi‐level ESS model is presented for a multi‐component electronic system. Screening can be performed at component, unit, and system levels. Components and connections are assumed to come from good and substandard populations and their time‐to‐failure distributions are modeled by mixed distributions. The majority of ESS models found in the literature assume that the time‐to‐failure distributions are exponential. The exponential distribution is used primarily to take advantage of its mathematical tractability. This paper generalizes previous work by modeling component and connection lifetimes with phase-type distributions. Phase‐type distributions offer the advantage of mathematical tractability as well as versatility in the family of distributions they can represent. To date there is no significant research into the impact that the selection of a lifetime distributions for modeling the failure process has on ESS decisions. In this paper, we evaluate screening strategies for several lifetime distributions. Numerical examples are provided to illustrate the effect of various model parameters on the optimal stress screening strategy.

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

Similar content being viewed by others

References

  1. S. Asmussen, O. Nerman and M. Olsson, Fitting phase-type distributions via the EM algorithm, Working Paper No. 1994:23, Department of Mathematics, Chalmers University of Technology, The University of Göteborg, 1994.

  2. D. Assaf and B. Levikson, Closure of phase-type distributions under operations arising in reliability theory, Ann. of Probability 10(1982)265-269.

    Article  Google Scholar 

  3. C.T. Baker, The Numerical Treatment of Integral Equations, Clarendon Press, 1977.

  4. D.J. Bartholomew, An approximate solution of the integral equation of renewaltheory, Journal of the Royal Statistical Society, Series B 25(1963)432-441.

    Google Scholar 

  5. L.A. Baxter, E.M. Scheur, D.J. McConalogue and W.R. Blischke, On the tabulation of the renewal function, Technometrics 24(1981)151-158.

    Article  Google Scholar 

  6. D.H. Chi and W. Kuo, Burn-in optimization under reliability and capacity restrictions, IEEE Transactions on Reliability 38(1989)193-198.

    Article  Google Scholar 

  7. W.K. Chien and W. Kuo, Optimal burn-in simulation on highly integrated circuit systems, IIE Transactions 24(1992)33-43.

    Article  Google Scholar 

  8. W.K. Chien and W. Kuo, Optimization of the burn-in times through redundancy allocation, 2nd Annual Industrial Engineering Research Conference Proceedings, 1993, pp. 579-583.

  9. W.K. Chien and W. Kuo, Modeling and maximizing burn-in effectiveness, IEEE Transactions on Reliability 44(1995)19-25.

    Article  Google Scholar 

  10. D.R. Cox, Renewal Theory, Wiley, London, 1962.

    Google Scholar 

  11. Z.S. Deligonul and S. Bilgen, Solution of the Volterra equation of renewal theory with the Galerkin technique using cubic splines, Journal of Statistical Computing and Simulation 20(1984)37-45.

    Article  Google Scholar 

  12. Environmental Stress Screening Guidelines for Assemblies, Institute of Environmental Sciences, Mount Prospect, IL, 1990.

  13. E.W. Frees and S.H. Nam, Approximating expected warranty costs, Management Science 34(1988) 1441-1448.

    Article  Google Scholar 

  14. O. Haggstrom, S. Asmussen and O. Nerman, EMPHT — A program for fitting phase type distributions, Working Paper, Chalmers University of Technology, The University of Göteborg, 1992.

  15. C.N. Huang, The numerical computation of renewal functions, Thesis, University of Texas at Austin, 1972.

  16. D.L. Jaquette, Approximations to the renewal function, Operations Research 20(1972)722-727.

    Article  Google Scholar 

  17. F. Jensen and N.E. Petersen, Burn-In, Wiley, Chichester, 1982.

    Google Scholar 

  18. M.A. Johnson, User's guide for MEFIT, A Fortran package for fitting mixtures of Erlang Distributions, Working Paper 90-004, Systems and Industrial Engineering Department, University of Arizona, 1990.

  19. M.A. Johnson and M.R. Taffe, Matching moments to phase-type distributions: Density function shapes, Stochastic Models 6(1990)283-306.

    Article  Google Scholar 

  20. M.A. Johnson and M.R. Taffe, Matching moments to phase-type distributions: Nonlinear programming approaches, Stochastic Models 6(1990)259-281.

    Article  Google Scholar 

  21. E.P. Kao, Computing the phase-type renewal and related functions, Technometrics 30(1988)87-93.

    Article  Google Scholar 

  22. W. Kuo and Y. Kuo, Facing the headaches of early failures: A state of the art review of burn-in decisions, Proceedings of the IEEE 71(1983)1257-1266.

    Article  Google Scholar 

  23. W. Kuo, Reliability enhancement through optimal burn-in, IEEE Transactions on Reliability 33(1984)145-156.

    Article  Google Scholar 

  24. A. Lang, Parameter estimation for phase-type distributions, Part 1: Fundamentals and existing methods, Technical Report 159, Oregon State University, 1994.

  25. A. Lang, Parameter estimation for phase-type distributions, Part II: Computational evaluation, Technical Report 160, Oregon State University, 1994.

  26. L.M. Leemis and M. Beneke, Burn-in models and methods: A review” IIE Transactions 22(1990) 172-180.

    Article  Google Scholar 

  27. Z.A. Lomnicki, A note on the Weibull renewal process, Biometrika 53(1966)375-381.

    Article  Google Scholar 

  28. W. Nelson, Accelerated Testing, Wiley, New York, 1990.

    Book  Google Scholar 

  29. M.F. Neuts, Probability distributions of phase-type, in: Liber Amicorum Prof. Emeritus H. Florin, Department of Mathematics, University of Louvain, Belgium, 1975, pp. 173-206.

    Google Scholar 

  30. M.F. Neuts, Renewal processes of phase-type, Naval Research Logistics Quarterly 25(1978)445-454.

    Article  Google Scholar 

  31. M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, 1981.

    Google Scholar 

  32. M.F. Neuts, Structured Stochastic Matrices of M G 1 Type and Their Applications, Marcel Dekker, New York, 1989.

    Google Scholar 

  33. D.G. Nguyen and D.N. Murthy, Optimal burn-in time to minimize costs for products sold under warranty, IIE Transactions 14(1982)167-174.

    Article  Google Scholar 

  34. C.A. O'Cinneide, On non-uniqueness of representations of phase type distributions, Stochastic Models 5(1989)247-259.

    Article  Google Scholar 

  35. C.A. O'Cinneide, Characterization of phase-type distributions, Stochastic Models 6(1990)1-57.

    Article  Google Scholar 

  36. H. Perlstein and J.W. Littlefield, ESS quantification for complex systems, The Journal of Environmental Sciences (1989)194-197.

  37. H. Perlstein and I. Bazovsky, Identification of early failures in ESS data, Proceedings of the Institute of Environmental Sciences (1989)194-197.

  38. H. Perlstein, J.W. Littlefield and I. Bazovsky, The quantification of Environmental Stress Screening, Proceedings of The Institute of Environmental Sciences(1987) 202-208.

  39. E.A. Pohl and D.L. Dietrich, Environmental Stress Screening strategies for complex systems: A 3 level mixed distribution model, Microelectronics and Reliability 35(1995)637-656.

    Article  Google Scholar 

  40. E.A. Pohl and D.L. Dietrich, Environmental Stress Screening strategies for multi-component systems with Weibull failure times and imperfect failure detection, Proceedings of Annual Reliability and Maintainability Symposium, 1995, pp. 223-232.

  41. F. Proschan, Theoretical explanation of observed decreasing failure rate, Technometrics 5(1963)375-383.

    Article  Google Scholar 

  42. R. Reddy and D.L. Dietrich, A two-level ESS model: A mixed distribution approach, IEEE Transactions on Reliability 43(1994)85-90.

    Article  Google Scholar 

  43. S. Ross, Approximations in renewal theory, Probability in the Engineering and Informational Sciences 1(1987)163-174.

    Article  Google Scholar 

  44. L. Schmickler, MEDA: Mixed Erlang distributions as phase-type representations of empirical distribution functions, Stochastic Models 8(1992)131-156.

    Article  Google Scholar 

  45. E. Smeitink and R. Dekker, A simple approximation to the renewal function, IEEE Transactions on Reliability 39(1990)71-75.

    Article  Google Scholar 

  46. W.L. Smith and M.R. Leadbetter, On the renewal function for the Weibull distribution, Technometrics 5(1963)393-396.

    Article  Google Scholar 

  47. R.M. Soland, A renewal theoretic approach to the estimation of future demand for replacement parts, Operations Research 16(1968)36-51.

    Article  Google Scholar 

  48. M. Spearman, Optimal maintenance policies for multicomponent systems with Weibull failure times, Unpublished Dissertation, Texas A&M, 1986.

  49. P.A. Tobias and D.C. Trindade, Applied Reliability, Van Nostrand Reinhold, New York, 1986.

    Google Scholar 

  50. G.S. Watson and W.T. Wells, On the possibility of improving the mean residual life of items by eliminating those with short lives, Technometrics 3(1961)281-298.

    Article  Google Scholar 

  51. J.S. White, Weibull renewal analysis, Proceedings of Aerospace Reliability and Maintainability Conference, 1964, pp. 639-657.

  52. M. Xie, On the solution of renewal-type integral equations, Communications in Statistics-Simulation 18(1989)281-293.

    Article  Google Scholar 

Download references

Authors
  1. E.A. Pohl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D.L. Dietrich
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pohl, E., Dietrich, D. Optimal Stress Screening strategies formulti‐component systems sold under warranty:The case of phase‐type lifetimes. Annals of Operations Research 91, 137–161 (1999). https://doi.org/10.1023/A:1018989404805

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018989404805

Keywords

Search

Navigation