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Interference theory of reliability: a review

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Abstract

The interference theory, which is the subject matter of this paper, has acquired an important place in reliability study of the systems. In it the system’s strength and stress working on it are taken into consideration for evaluation of its reliability. Two aspects of reliability problems are considered here viz. evaluation of system reliability from mathematical model of the system and inference of reliability. Under the former we have discussed some important interference or stress–strength (S–S) models along with the expression of reliability in each case. The models considered here are: for single component systems, when S–S are independent/correlated, when they have mixture of distributions, when more than one stress is working on a component i.e. a component may fail in different ways, when parameters of the distributions are random variables and for multi-components systems, the chain model, cold, warm and cascade redundancy with perfect and imperfect switches and when S–S are stochastic processes. In addition we have discussed some time dependent S–S models where along with S–S time is also taken into consideration and some maintenance (in particular repair) problems. For inference in interference models we have discussed parametric (classical and Bayesian), as well as non-parametric studies. The studies involving Monte-Carlo simulation for estimation of reliability and other characteristics are also presented. We have highlighted some studies of reliability growth models also.

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References

  • Abu-Salih MS, Shamseldin AA (1988) Bayesian estimation of P(X < Y) for a bivariate exponential distribution. Arab Gulf J Sci Res A 6(1):17–18

    MathSciNet  MATH  Google Scholar 

  • Ahmad KE, Fakhry ME, Jaheen ZF (1997) Empirical Bayes estimation of P(X \ge Y) and characterizations of burr-type X model. J Stat Plan Inference 64(2):297–308

    MathSciNet  MATH  Google Scholar 

  • Akman O, Sansgiry P, Minnotte MC (1999) On the estimation of reliability based on mixture of inverse Gaussian distribution applied statistical science IV. Nova Science Publishers, Hauppauge, pp 121–128

    Google Scholar 

  • Aldrisi MM (1987) A simulation approach for computing system reliability. Microelectron Reliab 27(3):463–467

    Google Scholar 

  • Ali MM, Pal M, Woo J (2012) Estimation of P (Y < X) in a four-parameter generalized gamma distribution. Aust J Stat 41(3):197–210

    Google Scholar 

  • Aminzadeh MS (1999) Estimation of P(Z < Y) for correlated stochastic time series models. Appl Math Comput 104:179–189

    MathSciNet  MATH  Google Scholar 

  • An ZW, Huang HZ, Lie Y (2008) A discrete stress–strength interference model based on unbiased generating function. Reliab Eng Syst Saf 93:1485–1490

    Google Scholar 

  • Awad AM, Azzam MM, Hamdan MA (1981) Some inference results on P(X < Y) in the bivariate exponential model. Commun Stat Theory Methods 10:2515–2525

    MathSciNet  Google Scholar 

  • Baklizi A (2008) Likelihood and Bayesian estimation of Pr(X < Y) using lower bound record values from the generalized exponential distribution. Comput Stat Data Anal 52:3468–3473

    MathSciNet  MATH  Google Scholar 

  • Barlow RE, Proschan F (1965) Mathematical theory of reliability. Wiley, New York

    MATH  Google Scholar 

  • Barlow RE, Scheuer EM (1966) Reliability growth during a development testing programme. Technometrics 8:53–60

    MathSciNet  Google Scholar 

  • Basu AP (1981) The estimation of P(Y < X) for distributions useful in life-testing. Naval Res Logist 28(2):383–392

    MATH  Google Scholar 

  • Basu AP, Ebrahimi N (1983) On the reliability of stochastic systems. Stat Probab Lett 1(5):265–267

    MathSciNet  MATH  Google Scholar 

  • Beg MA (1980a) Estimation of P(Y < X) for truncated parametric distribution. Commun Stat Theory Methods 9(3):327–345

    MathSciNet  Google Scholar 

  • Beg MA (1980b) On the estimation of P(Y < X) for the two parameter exponential distribution. Metrika 27:29–34

    MathSciNet  MATH  Google Scholar 

  • Beg MA (1980c) Estimation of reliability of cascade system. IEEE Trans Reliab R-29(5):429–430

    MathSciNet  Google Scholar 

  • Beg MA, Singh N (1979) Estimation of P(Y < X) for the Pareto distribution. IEEE Trans Reliab R-28(5):411–414

    Google Scholar 

  • Bhattacharyya GK, Johnson RA (1974) Estimation of reliability in multicomponent S–S model. J Am Stat Assoc 69(348):966–970

    MathSciNet  MATH  Google Scholar 

  • Bilikam JE (1985) Some stochastic stress–strength processes. IEEE Trans Reliab 34:269–274

    MATH  Google Scholar 

  • Birnbaum ZW (1956) On a use of the Mann–Whitney statistics. In: Proceedings of the third Berkeley symposium on mathematical statistics and probability, vol 1. University of California Press, Berkeley, pp 13–17

  • Birnbaum ZW, McCarty BC (1958) A distribution-free upper confidence bounds for Pr(Y < X) based on independent samples of X and Y. Ann Math Statist 29:558–562

    MathSciNet  MATH  Google Scholar 

  • Biswas S, Sriwastav GL (2006) Stochastic processes in demographic applications. New-Central-Book-Agency, Kolkata

    Google Scholar 

  • Biswas S, Sriwastav GL (2011) Mathematical statistics, a textbook. Narosa, New Delhi

    MATH  Google Scholar 

  • Bukoswski JV, Goble WM (2001) Verifying common-cause reduction rules for fault tolerant system via simulation using a stress–strength failure model. ISA Trans 40:183–190

    Google Scholar 

  • Chandra S, Owen DB (1975) On estimating the reliability of a component subject to several different stresses (strengths). Naval Res Logist 22(1):31–39

    MathSciNet  Google Scholar 

  • Chandra S, Owen DB (1977) On an estimator of the probability P(X1 < Y, X2 < Y,…, X n < Y). S Afr Stat J 11(2):149–154

    MathSciNet  MATH  Google Scholar 

  • Cheng KF, Chao A (1984) Confidence intervals for reliability from stress–strength relationship. IEEE Trans Reliab 33:246–249

    MATH  Google Scholar 

  • Church JD, Harris V (1970) The estimation of reliability from stress–strength relationship. Technometrics 12(1):49–54

    MATH  Google Scholar 

  • Delong ER, Sen PK (1981) Estimation of P (X < Y) based on Mann–Whitney statistics. Commun Stat Theory Methods A-10(10):963–981

    MathSciNet  Google Scholar 

  • Dhillon BS (1980a) Stress–strength reliability models. Microelectron Reliab 20(4):513–516

    Google Scholar 

  • Dhillon BS (1980b) Reliability growth: a survey. Microelectron Reliab 20(5):743–754

    Google Scholar 

  • Disney RL, Lipson L, Sheth NJ (1968) The determination of probability of failure by stress/strength interference theory. In: Proceedings of annual symposium on reliability, pp 417–422

  • Doloi C, Borah M, Sriwastav GL (2010) Cascade system with random attenuation factor. Indian Assoc Prod Qual Reliab 35(2):81–90

    Google Scholar 

  • Downton F (1973) The estimation of P(Y < X) in the normal case. Technometrics 15:551–558

    MathSciNet  MATH  Google Scholar 

  • Dutta K, Bhowal MK (1997) Imperfect switching with identical strength for a cold standby redundant system. Assam Stat Rev 11(1):137–147

    Google Scholar 

  • Dutta K, Bhowal MK (1998) Imperfect switching with identical stress for a cold standby redundant system. Presented at the 85th session of ISCA, Hyderabad, 3-7 Jan 1998

  • Dutta K, Bhowal MK (1999) A cascade reliability model for n-warm standby system. Assam Stat Rev 12(2):66–72

    Google Scholar 

  • Dutta K, Sriwastav GL (1986) An n-standby system with P (X < Y < Z). Indian Assoc Prod Qual Reliab Trans 12(1–2):95–97

    MathSciNet  Google Scholar 

  • Ebrahimi N, Ramallingam T (1993) Estimation of system reliability in Brownian stress–strength models based on sample paths. Ann Inst Stat Math 45(1):9–19

    MathSciNet  MATH  Google Scholar 

  • Enis P, Geisser S (1971) Estimation of the probability that Y < X. J Am Stat Assoc 66:162–168

    MathSciNet  MATH  Google Scholar 

  • Feinberg AA, Gibson GJ (1995) Accelerated reliability growth methodologies and models. In: Balakrishnan N (ed) Recent advances in life testing and reliability. CRC Press, London

    Google Scholar 

  • Ferguson TS (1973) A Bayesian analysis of some nonparametric problems. Ann Stat 1(2):209–230

    MathSciNet  MATH  Google Scholar 

  • Finkelstein JM (1983) A logarithmic reliability-growth model for single-mission system. IEEE Trans Reliab R-32(5):508–511

    Google Scholar 

  • Fries A, Sen A (1996) A survey of discrete reliability growth models. IEEE Trans Reliab 45(4):582–604

    Google Scholar 

  • Gnedenko BV, Beliaev LK, Solovev AD, Barlow RE (1969) Mathematical methods of reliability theory. Academic Press, New York

    MATH  Google Scholar 

  • Gogoi J, Borah M, Sriwastav GL (2010) An interference model with number of stresses a poisson process. Indian Assoc Prod Qual Reliab Trans 34(2):139–152

    Google Scholar 

  • Gopalan MN, Venkateswarlu P (1985) A reliability physical model for dissimilar two-unit standby system with single repair facility. Microelectron Reliab 25(1):17–23

    Google Scholar 

  • Govindarajulu Z (1967) Two-sided confidence limit for P(X < Y) based on normal samples of X and Y. Sankhya B-29:35–40

    MathSciNet  Google Scholar 

  • Govindarajulu Z (1968) Distribution free confidence bounds for P(X \ge Y). Ann Inst Stat Math 20:229–238

    MathSciNet  MATH  Google Scholar 

  • Gumbel EJ (1960) Bivariate Expon Distrib. J Am Stat Assoc 55:698–707

    MathSciNet  MATH  Google Scholar 

  • Gupta CG, Brown N (2001) Reliability studies of the skew-normal distribution and its application to a strength-stress model. Commun Stat Theory Methods 30:2427–2445

    MathSciNet  MATH  Google Scholar 

  • Halwaka P (1975) Estimation of the parameter p = P(X < Y < Z). Prace Nauk. Inst. Mat. Politechn. Wroclaw. No. 11, Ser. Stud. I Materialy No10 Problemy rachunku prawdopodobienstwa, pp 55–65 (in polish)

  • Hangal DD (1997) Note on estimation of reliability under bivariate Pareto stress–strength model. Stat Papers 38:453–459

    Google Scholar 

  • Harris CM, Singpurwalla ND (1968) Life distributions derived from stochastic hazard of functions. IEEE Trans Reliab R-17:70–79

    Google Scholar 

  • Heller RA, Donat RC (1967) Fatigue failure of a redundant structures. In: Structural fatigue in air-craft, ASTM STP 404. American Society for Testing Materials, Philadelphia, pp 55–66

  • Hilton HH, Fergen M (1960) Minimum weight analysis based on structural reliability. J Aerospace Sci 27(9):641–653

    MathSciNet  MATH  Google Scholar 

  • Hollander M, Korwar RM (1976) Nonparametric empirical bayes estimation of the probability that X < Y. Commun Stat Theory Methods 5:1369–1389

    MathSciNet  Google Scholar 

  • Hollander M, Proschan F (1984) Shock model. In: Krishnaiah PR, Sen PK (eds) Handbook of statistics. Elsevier, Amsterdam

    Google Scholar 

  • Hollander M, Wolf DA (1999) Nonparametric statistical methods, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Huang Z, Jin Y (2009) Extension of stress and strength interference theory for conceptual design-for-reliability. J Mech Des 131:1–10

    Google Scholar 

  • Huang K, Mi J, Wang Z (2012) Inference about reliability parameter with gamma strength and stress. J Stat Plan Inference 142(4):848–854

    MathSciNet  MATH  Google Scholar 

  • Ivshin VV (1998) On the estimation of the probabilities of a double linear inequality in the case of uniform and two-parameter exponential distribution. J Math Sci 88:819–827

    MathSciNet  Google Scholar 

  • Johnson RA (1988) Stress–strength models for reliability. In: Krishnaiah PR, Rao CR (eds) Handbook of statistics, vol 7. Elsevier, North Holland, pp 27–54

    Google Scholar 

  • Johnson RA (1992) Confidence estimation with discrete reliability growth models. J Stat Plan Inference 29(1–2):87–97

    Google Scholar 

  • Kakati MC, Sriwastav GL (1981) Accelerated life-testing under stress–strength model. Indian Assoc Prod Qual Reliab Trans 11(1-2):51–56

    Google Scholar 

  • Kapur KC (1975) Reliability bounds in probabilistic design. IEEE Trans Reliab R-24(3):193–195

    Google Scholar 

  • Kapur KC, Lamberson LR (1977) Reliability in engineering design. Wiley, New York

    Google Scholar 

  • Kelly GD, Kelly JA, Schucany WR (1976) Efficient estimation of P(Y < X) in the exponential case. Technometrics 18(3):359–361

    MathSciNet  Google Scholar 

  • Klein JP, Basu AP (1985) Estimating reliability for bivariate exponential distribution. Sankhya B-47:346–353

    MathSciNet  Google Scholar 

  • Kotz S, Lumelsk Y, Pensky M (2003) The stress–strength model and its generalizations: theory and applications. World Scientific, Hackensack

    MATH  Google Scholar 

  • Krishnamoorthy K, Mukherjee S, Huizhen G (2006) Interference on reliability in two parameter exponential stress–strength model. METRIKA. doi:10.1007/s00184-0074-7

  • Kundu D, Gupta RD (2005) Estimation fro generalized exponential distribution. Metrika 61:298–308

    MathSciNet  Google Scholar 

  • Leve HL (1965) Insufficiency of instantaneous strength determination for failure rate prediction. IEEE Trans Reliab R-34(2):77–83

    Google Scholar 

  • Lloyd DK, Lipow M (1962) Reliability: management, methods and mathematics. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Maheswari TSU, Rekha A, Raghavachar ACN (1992) Reliability of single strength under n-stresses. Microelectron Reliab 32(10):1475–1478

    Google Scholar 

  • Manders WP, Bader MG, Chou TW (1982) Monte Carlo simulation of the strength of composite fiber bundles. Fiber Sci Technol 17(3):183–204

    Google Scholar 

  • Mann HB, Whitney DR (1947) On a test whether one of two random variables is stochastically larger than the other. Ann Math Stat 18:50–60

    MathSciNet  MATH  Google Scholar 

  • Mann NR, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data. Wiley, New York

    MATH  Google Scholar 

  • Mazumder R (1970) Some estimates of reliability using interference theory. Naval Res Logist 17:159–165

    Google Scholar 

  • Moses F, Kinser DE (1967) Analysis of structural reliability. J Struct Div 93:147

    Google Scholar 

  • Nandi SB, Aich AB (1994) A note on confidence bounds for P (X \ge Y) in bivariate normal samples. Sankhya Ser B 56:129–136

    MathSciNet  MATH  Google Scholar 

  • Owen DB, Craswell KJ, Hanson DL (1964) Non-parametric upper confidence bounds for P (Y < X) and confidence limits for P (Y < X) when Y and X are normal. J Am Stat Assoc 59:906–924

    MathSciNet  MATH  Google Scholar 

  • Pandit SNN, Sriwastav GL (1975) Studies in Cascade Reliability-I. IEEE Trans Reliab 24(1):53–56

    Google Scholar 

  • Pandit SNN, Sriwastav GL (1976) On a generalized geometric distribution and cascade reliability. Sankhya Ser B 38(Pt.I):68–71

    MATH  Google Scholar 

  • Pandit SNN, Sriwastav GL (1978) Studies in cascade reliability-II. IEEE Trans Reliab R-27(4):653–658

    Google Scholar 

  • Patowary AN, Hazarika J, Sriwastav GL (2011) Reliability growth models with interference. Assam Stat Rev 25(2):101–121

    Google Scholar 

  • Paul RK, Uddin MB (1997) Estimation of reliability of stress–strength model with non-identical component strengths. Microelectron Reliab 37(6):923–927

    Google Scholar 

  • Pensky M (2002) Estimation of probabilities of linear inequalities for independent elliptic random vectors. Sankhya 65(2):91–106

    MathSciNet  Google Scholar 

  • Pham-Gia T, Almhana J (1995) The generalized gamma distribution: its hazard rate and stress–strength model. IEEE Trans Reliab 44:392–397

    Google Scholar 

  • Pham-Gia T, Turkkan N (2007) The joint predictive-posterior method in the Bayesian analysis of stress–strength reliability. Int J Reliab Qual Saf Eng 14(1):29–47

    MathSciNet  Google Scholar 

  • Pieruschka E (1963) Principles of reliability. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Pulcini G (2001) An exponential reliability-growth model in multi-copy testing program. IEEE Trans Reliab 50(4):365–373

    MathSciNet  Google Scholar 

  • Raghavachar ACN, Rao BK, Chargulu NCHP (1983) Survival functions under stress attenuation in cascade reliability. OPSEARCH 20(4):207–224

    Google Scholar 

  • Raghavachar ACN, Rao BK, Pandit SNN (1984) Stress and strength Markov models of the system reliability. Sankhya Ser B 46:147–156

    MathSciNet  Google Scholar 

  • Rajput KK, Islam AU (2008) A brief survey of reliability growth models. Anvikshiki 8:128–136

    Google Scholar 

  • Rao GS, Kantam RRL (2010) Estimation of reliability in multi-component stress–strength model: log–logistic distribution. Electron J Appl Stat Anal 3(2):75–84

    Google Scholar 

  • Rekha A, Shyam Sunder T (1997) Survival function under strength attenuation of a system for exponential distribution. Assam Stat Rev 11(2):148–152

    Google Scholar 

  • Rekha A, Raghavachar ACN, Rao BK (1988) Cascade reliability with log-normal and Weibull distributions. Assam Stat Rev 2(1):46–52

    Google Scholar 

  • Rekha A, Mahaeswari TSU, Raghavachar ACN, Rao BK (1992) Survival function under strength attenuation of a system for exponential distribution. Assam Stat Rev 6(1):66–70

    Google Scholar 

  • Rezaei S, Tahmasbi R, Mahmoodi M (2010) Estimation of P [Y < X] for generalized Pareto distribution. J Stat Plan Inference 140(2):480–494

    MathSciNet  MATH  Google Scholar 

  • Robert NH (1964) Mathematical methods in reliability. McGraw-Hill, New York

    Google Scholar 

  • Samaniego FJ (2007) Estimation based on autopsy data from stress–strength experiments. Qual Technol Quant Manag 4(1):1–15

    MathSciNet  Google Scholar 

  • Sathe YS, Shah SP (1981) Estimating P(X \ge Y) for the exponential distribution. Commun Stat Theory Methods A-10(1):39–47

    MathSciNet  Google Scholar 

  • Sen PK (1960) On some convergence properties of U-statistic. Calcutta Stat Assoc Bull 10:1–8

    MATH  Google Scholar 

  • Sen PK (1967) A note on asymptotically distribution-free confidence intervals for P(X < Y) based on two independent samples. Sankhya Ser A 29:95–102

    MathSciNet  MATH  Google Scholar 

  • Sen A, Bhattacharyya GK (1995) A reliability growth model under inherent and assignable-cause failures. In: Balakrishnan N (ed) Recent advances in life testing and reliability. CRC Press, London, pp 295–318

    Google Scholar 

  • Sengupta S, Mukhuti S (2008) Unbiased estimation of P (X \ge Y) for exponential population using order statistics with application in ranked set sampling. Commun Stat Theory Methods 37(6):898–916

    MATH  Google Scholar 

  • Shooman ML (1968) Probabilistic reliability: an engineering approach. McGraw-Hill, New York

    Google Scholar 

  • Singh N (1980) On the estimation of P (X1 < Y < Y2). Commun Stat Theory Methods 19(15):1551–1561

    Google Scholar 

  • Singh N (1981) MVUE of P(X < Y) for multivariate normal populations: an application to S–S models. IEEE Trans Reliab R.30(2):192–193

    Google Scholar 

  • Sriwastav GL (1978) A reliability growth model. IEEE Trans Reliab 27(5):306–307

    MATH  Google Scholar 

  • Sriwastav GL (1988) Reliability estimation in stress–strength model with ancillary information. Assam Stat Rev 2(1-2):16–20

    Google Scholar 

  • Sriwastav GL (1992) A cascade reliability model with imperfect switching. Assam Stat Rev 6(2):110–115

    Google Scholar 

  • Sriwastav GL (1996) Reliability of n-standby system: stress–strength mixtures of n-exponential distribution. Assam Stat Rev 17(1):49–55

    Google Scholar 

  • Sriwastav GL (2003) A discrete time dependent stress–strength model. Assam Stat Rev 17(2):153–158

    Google Scholar 

  • Sriwastav GL (2004) Warm standby with imperfect switching in S–S model. Assam Stat Rev 18(2):158–168

    Google Scholar 

  • Sriwastav GL (2005) A stress–strength standby system with repair. Assam Stat Rev 19(2):129–136

    Google Scholar 

  • Sriwastav GL, Dutta K (1984) Standby redundant system with imperfect switching in S–S model. Presented at the 54th annual session of the national academy of sciences, Gwalior

  • Sriwastav GL, Dutta K (1985) Markov-chain in S–S model for a redundant system. Indian Assoc Prod Qual Reliab Trans 10(1-2):79–85

    MATH  Google Scholar 

  • Sriwastav GL, Dutta K (1986) An n-standby system with different types of failures in S–S model. Presented at Indian science congress association, Delhi

  • Sriwastav GL, Dutta K (1988) A time dependent S–S model with redundancy. Presented at Indian science congress association, Pune

  • Sriwastav GL, Dutta K (1989) Warm standbys in stress–strength model. Indian Assoc Prod Qual Reliab Trans 14(1, 2):83–89

    MathSciNet  MATH  Google Scholar 

  • Sriwastav GL, Kakati MC (1980) A stress–strength model with random parameters. Q R J 7(2):69–71

    Google Scholar 

  • Sriwastav GL, Kakati MC (1981a) A stress–strength model with redundancy. Indian Assoc Prod Qual Reliab Trans 6(1):21–27

    MATH  Google Scholar 

  • Sriwastav GL, Kakati MC (1981b) Correlated stress–strength model for multi-component system. In: National conference on quality and reliability, IIT, Bombay

  • Sriwastav GL, Kakati MC (1981c) Reliability estimates of two parameter exponential distribution. Math Forum IV(1):47–56

    Google Scholar 

  • Sriwastav GL, Kakati MC (1982) A two-component standby stress–strength model where strengths of the components are correlated. Q R J 9(3):115–116

    Google Scholar 

  • Sriwastav GL, Pandit SNN (1978) Markov chain with taboo states and reliability: naval research logistic. Quarterly 25(4):653–658

    MATH  Google Scholar 

  • Stancampiano PA (1978) Simulation approaches to probabilistic structural design at component level. Clear Eng 50(1):123–129

    Google Scholar 

  • Stumpf H, Schwartz P (1993) A Monte-Carlo simulation of the stress-rupture of seven-fiber micro-composites. Compos Sci Technol 49(3):251–263

    Google Scholar 

  • Surles JG, Padgett WJ (1998) Inference for P (Y < X) in the burr type X model. J Appl Stat Sci 7:225–238

    MATH  Google Scholar 

  • Surles JG, Padgett WJ (2001) Inference for reliability and stress–strength for a scaled burr type X distribution. Lifetime Data Anal 7:187–200

    MathSciNet  MATH  Google Scholar 

  • Tong H (1974) A note on the estimation of P(Y < X) in the exponential case. Technometrics 16:625

    MathSciNet  MATH  Google Scholar 

  • Tong H (1975) Letters to the editor. Technometrics 16(4):625

    Google Scholar 

  • Tong H (1977) On the estimation of P(Y < X) for exponential families. IEEE Trans Reliab R-26(1):54–55

    Google Scholar 

  • Tumolillo TA (1974) Method for calculating reliability function for systems subjected to random stress. IEEE Trans Reliab R-23:256–262

    MathSciNet  Google Scholar 

  • Uddin MB, Pandey M, Ferdous J, Bhuiyan MR (1993) Estimation of reliability in a multicomponent stress–strength model. Microelectron Reliab 33(13):2043–2046

    Google Scholar 

  • Ury HK (1972) On the distribution free confidence bound for P(Y < X). Technometrics 14(3):577–581

    MATH  Google Scholar 

  • Weiss HK (1956) Estimation of reliability growth in a complex system with a poisson-type failure. Oper Res 4:532–545

    Google Scholar 

  • Wilcoxon F (1945) Individual comparisons by ranking method. Biometr Bull 1:80–83

    Google Scholar 

  • Xie L, Wang J (2009) Load–strength interference failure rate model. Int J Reliab Qual Saf Eng 16(3):249–260

    Google Scholar 

  • Xie L, Zhou J, Hao C (2004) System-level load–strength interference based reliability modeling of k-out-of-n system. Reliab Eng Syst Saf 84:311–317

    Google Scholar 

  • Xie X, Zhou J, Wang Y, Wang X (2005) Load–strength order statistics interference models for system reliability evaluation. Int J Perform Eng 1(1):23–36

    Google Scholar 

  • Xie L, Wu N, Qlan W (2010) A probabilistic fatigue life estimation approach for complex structure and component. Int J Reliab Qual Saf Eng 17(6):553–564

    Google Scholar 

  • Yang MCK, Mo TC (1985) Distribution free confidence bounds for P(Y < X) of an r-out-of-k system. IEEE Trans Reliab 34:499–503

    MATH  Google Scholar 

  • Yu QQ, Govindarajulu Z (1995) Admissibility and minimaxity of the UMVU estimator of P (X < Y). Ann Stat 23:598–607

    MathSciNet  MATH  Google Scholar 

  • Zaremba SC (1965) Note on the Wilcoxon–Mann–Whitney statistic. Ann Math Stat 36:1058–1060

    MathSciNet  MATH  Google Scholar 

  • Zhang H, Chandrangsu T, Ramussen KJR (2010) Probabilistic study of the strength of steel scaffold system. Struct Saf 32(6):393–401

    Google Scholar 

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Acknowledgments

This work is a part of UGC Major Research Project (Sc.), and the authors are thankful to UGC (India) for providing financial assistance for the same. The authors are also thankful to referee for very constructive comments which helped in improving the paper.

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  1. Department of Statistics, Dibrugarh University, Dibrugarh, 786 004, Assam, India

    A. N. Patowary, J. Hazarika & G. L. Sriwastav

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  1. A. N. Patowary
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Patowary, A.N., Hazarika, J. & Sriwastav, G.L. Interference theory of reliability: a review. Int J Syst Assur Eng Manag 4, 146–158 (2013). https://doi.org/10.1007/s13198-013-0162-9

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