Abstract
The number of hours of sleep gained by means of a soporific (sleep-inducing preparation) will generally vary from person to person. With the help of statistics we would like to make a statement on the average gain in the number of hours of sleep. We must also test whether the gain in the duration of sleep is statistically significant. Analyses of this type require not only knowledge of statistical methods but also a thorough familiarity with the field of study, because to determine the unique effects of specified causes we must be able to sort out the more important factors contributing to the phenomenon examined. These factors can be of a psychological or physical nature. In our example confidence in the medication and in the physician, as well as the physician’s attitude, are factors in the first category; charges in the diet, and in the daily routine belong to the second. To eliminate two influences of the first type, neither the physician assessing the therapy result nor the patient must know whether a soporific or a placebo is administered. This type of study is called a double blind trial.
If in the analysis of survival times in medicine or technology some objects are still alive at the end of the study their exact survival times are incomplete. These are called censored observations or censored times. More on this and on the comparison of survival distributions—see also pages 206, 210 and 235—is provided in the book by Lee (1980) with computer programs for 5 two sample tests and a k sample test [Chapter 5 and Appendix B, with both Peto and Peto’s tests: logrank test and generalized Wilcoxon test].
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References
[8:2] Chapter 2 [8:2a] Medical statistics
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[8:2b] Sequential test plans
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[8:2c] Bioassay
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Brock, N., and Schneider, B.: Pharmakologische Charakterisierung von Arzneimitteln mit Hilfe des Therapeutischen Index. Arzneim.-Forschg. 11 (1961), 1–7
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Finney, D. J.: Statistical Methods in Biological Assay. 2nd ed. London 1964 (3rd edition Macmillan 1979)
Gaddum, J. H.: Simplified mathematics for bioassay. J. Pharmacy and Pharmacology 6 (1953), 345–358.
Gaddum, J. H.: Bioassay and mathematics. Pharmacol. Rev. 5 (1953), 87–134
Golub, A., and Grubbs, F. E.: Analysis of sensitivity experiments when the levels of stimulus cannot be controlled. J. Amer. Statist. Assoc. 51 (1956), 257–265
Hubert, J. J.: Bioassay. (Kendall/Hunt Publ. Co.; pp. 164) Dubuque, Iowa 1980
International Symposium on Biological Assay Methods. (Ed.: R. H. Regamey) (Karger, pp. 262) Basel, New York 1969
Kärber, G.: Ein Beitrag zur kollektiven Behandlung pharmakologischer Reihenversuche. Archiv für experimentelle Pathologie und Pharmakologie 162 (1931), 480–483
Kaufmann, H.: Ein einfaches Verfahren zur Auswertung von Überlebenskurven bei tödlich verlaufenden Erkrankungen. Strahlentherapie 130 (1966), 509–527
Kimball, A. W., Burnett, W. T., Jr., and Doherty, D. G.: Chemical protection against ionizing radiation. I. Sampling methods for screening compounds in radiation protection studies with mice. Radiation Research 7 (1957), 1–12
King, E. P.: A statistical design for drug screening. Biometrics 19 (1963), 429–440
Lazar, Ph.: Les essais biologiques. Revue de Statistique Appliquée 16 (No. 3, 1968), 5–35
Litchfield, J. T., Jr., and Wilcoxon, F.: A simplified method of evaluating dose-effect experiments. J. Pharmacol. Exptl. Therap. 96 (1949), 99–113
Little, R. E.: The up-and-down method for small samples with extreme value response distributions. Journal of the American Statistical Association 69 (1974), 803–806
McArthur, J. W., and Colton, T. (Eds.): Statistics in Endocrinology. Proc. Conf., Dedham, Mass., Dec. 1967. (MIT Press, pp. 476) Cambridge, Mass. 1970
Oberzill, W.: Mikrobiologische Analytik. Grundlagen der quantitativen Erfassung von Umwelteinwirkungen auf Mikroorganismen. (Carl, 519 pages) Nürnberg 1967
Olechnowitz, A. F.: Ein graphisches Verfahren zur Bestimmung von Mittelwert und Streuung aus Dosis-Wirkungs-Kurven. Arch. exp. Veterinärmed. 12 (1958), 696–701
Petrusz, P., Diczfalusy, E., and Finney, D. J.: Bioimmunoassay of gonadotrophins. Acta endocrinologica 67 (1971), 40–62
Schneider, B.: Probitmodell und Logitmodell in ihrer Bedeutung für die experimentelle Prüfung von Arzneimitteln. Antibiot. et Chemother. 12 (1964), 271–286
Stammberger, A.: Über ein nomographisches Verfahren zur Lösung der Probleme des Bio-Assay. Biometr. Zeitschr. 12 (1970), 35–53 (see also pages 351–361)
Ther, L.: Grundlagen der experimentellen Arzneimittelforschung. (Wiss. Verlagsges., 439 pages) Stuttgart 1965. pp. 74–112
Vølund, A.: Multivariate bioassay. Biometrics 36 (1980), 225–236
Warner, B. T.: Method of graphical analysis of 2 + 2 and 3 + 3 biological assays with graded responses. J. Pharm. Pharmacol. 16 (1964), 220–233
Waud, D. R.: On biological assays involving quantal responses. J. Pharmacol. Exptl. Therap. 183 (1972), 577–607
[8:2d] Statistics in engineering
Amstadter, B. L.: Reliability Mathematics. (McGraw-Hill, pp. 320) New York 1970
Bain, L. J., and Thoman, D. R.: Some tests of hypotheses concerning the three-parameter Weibull distribution. J. Amer. Statist. Assoc. 63 (1968), 853–860 [see also Technometrics 14 (1972), 831–840, 16 (1974), 49–56, 17 (1975), 369–374, 375–380 19 (1977), 323–331, 20 (1978), 167–169, and 21 (1979), 233–237]
Barlow, R. E., Fussell, J. B., and Singpurwalla, N. D. (Eds.): Reliability and Fault Tree Analysis; Theoretical and Applied Aspects of System Reliability and Safety Assessment, Society for Industrial and Applied Mathematics, Philadelphia, 1975, pp. 927
Barlow, R. E., and Proschan, F.: Mathematical Theory of Reliability. (Wiley; pp. 265) New York 1965
Beard, R. E., Pentikäinen, T., and Pesonen, E.: Risk Theory. The Stochastic Basis of Insurance. 3rd ed. (Chapman and Hall; pp. 230) London 1984
Beightler, C. S., and Shamblin, J. E.: Sequential process control. Industrial Engineering 16 (March-April 1965), 101–108
Berrettoni, J. N.: Practical applications of the Weibull distribution. ASQC Convention (Cincinnati, Ohio, USA) Transactions 1962, pp. 303–323
Bingham, R. S., Jr.: EVOP for systematic process improvement. Industrial Quality Control 20 (Sept. 1963), 17–23
Bowker, A. H., and Lieberman, G. J.: Engineering Statistics. Englewood Cliffs, N.J. 1961
Box, G. E. P.: Multi-factor designs of first order. Biometrika 39 (1952), 49–57.
Box, G. E. P.: The exploration and exploitation of response surfaces: some general considerations and examples. Biometrics 10 (1954), 16–60.
Box, G. E. P.: Evolutionary operation: a method for increasing industrial productivity. Applied Statistics 6 (1957), 3–23.
Box, G. E. P.: A simple system of evolutionary operation subject to empirical feedback. Technometrics 8 (1966), 19–26
Box, G. E. P., and Draper, N. R.: A basis for the selection of a response surface design. J. Amer. Statist. Assoc. 54 (1959), 622–654 [see also 70 (1975), 613–617].
Box, G. E. P., and Draper, N. R.: Evolutionary Operation. A Statistical Method for Process Improvement. (Wiley, pp. 237) New York 1969; Übers., Das EVOP-Verfahren. (Oldenbourg; 268 pages) München 1975
Box, G. E. P., and Hunter, J. S.: Multifactor experimental designs for exploring response surfaces. Ann. Math. Statist. 28 (1957), 195–241.
Box, G. E. P., and Hunter, J. S.: Experimental designs for the exploration and exploitation of response surfaces. In V. Chew (Ed.), Experimental Designs in Industry. New York 1958, pp. 138–190.
Box, G. E. P., and Hunter, J. S.: Condensed calculations for evolutionary operations programs. Technometrics 1 (1959), 77–95.
Box, G. E. P., and Hunter, J. S.: A useful method for model-building. Technometrics 4 (1962), 301–318
Box, G. E. P., and Lucas, H. L.: Design of experiments in non-linear situations. Biometrika 46 (1959), 77–90
Box, G. E. P., and Wilson, K. B.: On the experimental attainment of optimum conditions. J. Roy. Statist. Soc., Ser. B 13 (1951), 1–45 [see also Biometrika 62 (1975), 347–352]
Box, G. E. P., and Youle, P. V.: The exploration and exploitation of response surfaces: an example of the link between the fitted surface and the basic mechanism of the system. Biometrics 11 (1955), 287–323 [see also Technometrics 18 (1976), 411–417]
Brewerton, F. J.: Minimizing average failure detection time. J. Qual. Technol. 2 (1970), 72–77
Brooks, S. H.: A comparison of maximum seeking methods. Operations Research 7 (1959), 430–457
Brooks, S. H., and Mickey, M. R.: Optimum estimation of gradient direction in steepest ascent experiments. Biometrics 17 (1961), 48–56
Burdick, D. S., and Naylor, T. H.: Response surface methods in economics. Rev. Internat. Statist. Inst. 37 (1969), 18–35
Cohen, A. C., Jr.: Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples. Technometrics 7 (1965), 579–588
Cox, D. R., and Oakes, D. O.: Analysis of Survival Data. (Chapman and Hall; pp. 200) London 1984
D’Agostino, R. B.: Linear estimation of the Weibull parameters. Technometrics 13 (1971), 171–182
Davies, O. L.: Design and Analysis of Industrial Experiments, London 1956, Chapter 11
Dean, B. V., and Marks, E. S.: Optimal design of optimization experiments. Operations Research 13 (1965), 647–673
Dhillon, B. S., and Singh, C.: Engineering Reliability. New Techniques and Applications. (Wiley; pp. 339) New York 1981
Drnas, T. M.: Methods of estimating reliability. Industrial Quality Control 23 (1966), 118–122
Dubey, S. D.: On some statistical inferences for Weibull laws. Naval Res. Logist. Quart. 13 (1966), 227–251.
Dubey, S. D.: Normal and Weibull distribution. Naval Res. Logist. Quart. 14 (1967), 69–79.
Dubey, S. D.: Some simple estimators for the shape parameter of the Weibull laws. Naval Res. Logist. Quart. 14 (1967), 489–512.
Dubey, S. D.: Some percentile estimators for Weibull parameters. Technometrics 9 (1967), 119–129.
Dubey, S. D.: On some permissible estimators of the location parameter of the Weibull and certain other distributions. Technometrics 9 (1967), 293–307
Duckworth, W. E.: Statistical Techniques in Technological Research: An Aid to Research Productivity. (Methuen, pp. 303) London 1968
Duncan, A. J.: Quality Control and Industrial Statistics. 4th ed. (Irwin; pp. 1047) Homewood, Ill 1974
Durr, A. C.: Accurate reliability prediction. Reliability Engineering 3 (1982), 475–485
Eagle, E. L.: Reliability sequential testing. Industrial Quality Control 20 (May 1964), 48–52
Ferrell, E. B.: Control charts for log-normal universes. Industrial Quality Control 15 (Aug. 1958), 4–6
Freudenthal, H. M., and Gumbel, E. J.: On the statistical interpretation of fatigue tests. Proc. Roy. Soc., Ser A 216 (1953), 309–332 [see also Technometrics 19 (1977); 87–93]
Fussell, J. B. and Burdick, G. R.: Nuclear Systems Reliability Engineering and Risk Assessment, Society for Industrial and Applied Mathematics, Philadelphia, 1977, pp. 849
Gheorghe, A.: Applied Systems Engineering. (Wiley; pp. 342) New York 1983
Goldberg, H.: Extending the Limits of Reliability Theory. (Wiley; pp. 263) New York 1981
Goldman, A. S., and Slattery, T. B.: Maintainability. A Major Element of System Effectiveness. (Wiley; pp. 282) New York 1964
Gottfried, P., and Roberts, H. R.: Some pitfalls of the Weibull distribution. Ninth Symp. on Reliability and Quality Control, pp. 372–379, San Francisco, Calif. (Jan. 1963)
Gross, A. J., and Clark, Virginia, A.: Survival Distributions. Reliability Applications in the Biomedical Sciences. (Wiley; pp. 331) New York 1975
Gryna, F. M., Jr., McAfee, N. J., Ryerson, C. M., and Zwerling, S.: Reliability Training Text. (Institute of Radio Engineers) New York 1960
Guild, R. D. and Chipps, J. D.: High reliability systems by multiplexing. Journal of Quality Technology 9 (1977), 62–69
Hahn, G. J.: Some things engineers should know about experimental design. Journal of Quality Technology 9 (1977), 13–20
Harter, H. L.: A bibliography of extreme-value theory. International Statistical Review 46 (1978), 279–306
Harter, H. L., and Dubey, S. D.: Theory and tables for tests of hypotheses concerning the mean and the variance of a Weibull population. ARL Tech. Rep. No. 67–0059 (Aerospace Research Laboratories. pp. 393), Wright-Patterson Air Force Base, Ohio 1967
Henley, E. J., and Kumamoto, H.: Reliability Engineering and Risk Assessment. (Prentice-Hall; pp. 568) New York 1980
Hill, W. J., and Hunter, W. G.: A review of response surface methodology: a literature survey. Technometrics 8 (1966), 571–590 [see also 15 (1973), 113–123 and 301–317 as well as Biometrics 31 (1975), 803–851]
Hillier, F. S.: Small sample probability limits for the range chart. J. Amer. Statist. Assoc. 62 (1967), 1488–1493.
Hillier, F. S.: X- and R-chart control limits based on a small number of subgroups. J. Qual. Technol. 1 (1969), 17–26 [see also N. I. Gibra, J. Qual. Technol. 7 (1975), 183–192]
Honeychurch, J.: Lambda and the question of confidence. Microelectronics Reliability 4 (1965), 123–130
Hunter, W. G., and Kittrel, J. R.: Evolutionary operation: a review. Technometrics 8 (1966), 389–397
Johns, M. V., Jr., and Lieberman, G. J.: An exact asymptotically efficient confidence bound for reliability in the case of the Weibull distribution. Technometrics 8 (1966), 135–175
Johnson, L. G.: Theory and Technique of Variation Research. (Elsevier, pp. 105) Amsterdam 1964
Kabe, D. G.: Testing outliers from an exponential population. Metrika 15 (1970), 15–18 [see also J. Likes, 11 [1966], 46–54 and L. R. Lamberson, AIIE Transact. 6 (1974), 327–337]
Kao, J. H. K.: A graphical estimation of mixed parameters in life testing of electron tubes. Technometrics 1 (1959), 389–407 [see U. Hjorth 22 (1980), 99–107]
Kapur, K. C., and Lamberson, L. R.: Reliability in Engineering Design. (Wiley; pp. 586) New York 1977
Kaufman, A., Grouchko, D., and Cruon, R.: Mathematical Models for the Study of the Reliability of Systems, (Academic Press, pp. 221) New York 1977
Kenworthy, I. C.: Some examples of simplex evolutionary operation in the paper industry. Applied Statistics 16 (1967), 211–224
Kiefer, J. C.: Optimum experimental designs. J. Roy. Statist. Soc., Ser. B 21 (1959), 272–319
Knowler, L. A., Howell, J. M., Gold, B. K., Coleman, E. P., Moan, O. B., and Knowler, W. C.: Quality Control by Statistical Methods. (McGraw-Hill, pp. 139) New York 1969
Kumar, S., and Patel, H. I.: A test for the comparison of two exponential distributions. Technometrics 13 (1971), 183–189 [see also 15 (1973), 177–182, 183–186]
Lawless, J. F.: Confidence interval estimation for the Weibull and extreme value distributions. Technometrics 20 (1978), 355–364 [see also 365–368]
Lie, C. H., Hwang, C. L., and Tillman, F. A.: Availability of maintained systems. A. state-of-the-art survey. AIIE Transactions 9, No. 3 (1977), 247–259
Lieblein, J., and Zelen, M.: Statistical investigation of the fatigue life of deep-groove ball bearings. J. Res. Nat. Bur. Stds. 57 (Nov. 1956), 273–319 [see also Technometrics 14 (1972), 693–702]
Little, R. E., and Jebe, E. H.: Statistical Design of Fatigue Experiments. (Applied Science Publishers; pp. 280) London 1975
Lloyd, D. K., and Lipow, M.: Reliability: Management, Methods and Mathematics. (Prentice-Hall; pp. 528) Englewood Cliffs, N.J. 1962 (2nd edition 1977)
Lowe, C. W.: Industrial Statistics. Vol. 2. (Business Books Ltd., pp. 294) London 1970, Chapter 12
Mann, Nancy R.: Tables for obtaining the best linear invariant estimates of parameters of the Weibull distribution. Technometrics 9 (1967), 629–645 [see also 10 (1968), 231–256, 15 (1973), 87–101, 16 (1974), 49–56, 17 (1975), 361–368, 22 (1980), 83–97 and 567–573]
Mann, Nancy R., Schafer, R. E., and Singpurwalla, N. D.: Methods for Statistical Analysis of Reliability and Life Data. (Wiley; pp. 564) New York 1974
Martz, H. F., and Waller, R. A.: Bayesian Reliability Analysis. (Wiley; pp. 745) New York 1982
McCall, J. J.: Maintenance policies for stochastically failing equipment: a survey. Management Science 11 (1965), 493–524
Morice, E.: Quelques modèles mathématiques de durée de vie. Revue de Statistique Appliquée 14 (1966), No. 1, 45–126; Errata 14 (1966), No. 2, 99–101.
Morice, E.: Quelques problèmes d’estimation relatifs à la loi de Weibull. Revue de Statistique Appliquée 16 (1968), No. 3, 43–63
Morrison, J.: The lognormal distribution in quality control. Applied Statistics 7 (1958), 160–172
Myhre, J. M., and Saunders, S. C.: Comparison of two methods of obtaining approximate confidence intervals for system reliability. Technometrics 10 (1968), 37–49
Nelson, L. S.: Tables for a precedence life test. Technometrics 5 (1963), 491–499.
Nelson, L. S.: Weibull probability paper. Industrial Quality Control 23 (1967), 452–455
Nelson, W.: A statistical test for equality of two availabilities. Technometrics 10 (1968), 594–596 [see also pages 883 and 884 as well as 15 (1973), 889–896 and J. Qual. Technol. 4 (1972), 190–195].
Nelson, W.: Applied Life Data Analysis. (Wiley-Interscience, pp. 634) New York 1982
Nelson, W., and Thompson, V. C.: Weibull probability papers. J. Qual. Technol. 3 (1971), 45–50
Oakes, D.: Survival analysis. European Journal of Operational Research 12 (1983), 3–14
Ostle, B.: Industry use of statistical test design. Industrial Quality Control 24 (July 1967), 24–34
Pearson, E. S.: Comments on the assumption of normality involved in the use of some simple statistical techniques. Rev. beige Statist. Rech. opérat. 9 (1969), Nr. 4, 2–18
Peng, K. C.: The Design and Analysis of Scientific Experiments. (Addison-Wesley, pp. 252) Reading, Mass. 1967, Chapter 8
Plait, A.: The Weibull distribution - with tables. Industrial Quality Control 19 (Nov. 1962), 17–26 [see also 15 (1973), 87–101]
Prairie, R. R.: Probit analysis as a technique for estimating the reliability of a simple system. Technometrics 9 (1967), 197–203
Proschan, F., and Serfling, R. J. (Eds.): Reliability and Biometry, Statistical Analysis of Lifelength. Society for Industrial and Applied Mathematics, Philadelphia, 1974, pp. 815
Qureishi, A. S., Nabavian, K. J., and Alanen, J. D.: Sampling inspection plans for discriminating between two Weibull processes. Technometrics 7 (1965), 589–601
Ravenis, J. V. J.: Estimating Weibull-distribution parameters. Electro-Technology, March 1964, 46–54 [see also Naval Res. Logist. Quart. 29 (1982), 419–428]
Rice, W. B.: Control Charts in Factory Management, 3rd ed. New York 1955
Roberts, N. H.: Mathematical Methods in Reliability Engineering. New York 1964
Sen, I., and Prabhashanker, V.: A nomogram for estimating the three parameters of the Weibull distribution. Journal of Quality Technology 12 (1980), 138–143
Sherif, Y. S.: Reliability analysis. Optimal inspection and maintenance schedules for failing systems. Microelectron. Reliab. 22 (1982), 59–115
Sherif, Y. S., and Smith, M. L.: Optimal maintenance models for systems subject to failure-a review. Naval Research Logistics Quarterly 28 (1981), 47–74 [for availability see 29 (1982), 411–418]
Shooman, M. L.: Probabilistic Reliability: An Engineering Approach. (McGraw-Hill, pp. 524) New York 1968 [see also J. Roy. Statist. Soc. A 136 (1973), 395–420]
Simonds, T. A.: MTBF confidence limits. Industrial Quality Control 20 (Dec. 1963), 21–27 [see also Technometrics 24 (1982), 67–72]
Sinha, S. K., and Kale, B. K.: Life Testing and Reliability Estimation. (Wiley; pp. 196) New York 1980
Stange, K.: Ermittlung der Abgangslinie für wirtschaftliche und technische Gesamtheiten. Mitteilungsbl. Mathem. Statistik 7 (1955), 113–151.
Stange, K.: Stichprobenpläne für messende Prüfung: Aufstellung und Handhabung mit Hilfe des doppelten Wahrscheinlichkeitsnetzes. Deutsche Arbeitsgemeinschaft für statistische Qualitätskontrolle beim Ausschuß für wirtschaftliche Fertigung. (ASQ/AWF). Beuth-Vertrieb, Berlin 1962.
Stange, K.: Optimalprobleme in der Statistik. Ablauf- und Planungs-forschung (Operational Research) 5 (1964), 171–190.
Stange, K.: Die Berechnung wirtschaftlicher Pläne für messende Prüfung. Metrika 8 (1964), 48–82.
Stange, K.: Statistische Verfahren im Betrieb zur Überwachung, Prüfung und Verbesserung der Qualität. Allgem. Statist. Arch. 49 (1965), 14–46.
Stange, K.: Die zeichnerische Ermittlung von Folgeplänen für messende Prüfung bei bekannter Varianz der Fertigung. Biometrische Zeitschr. 8 (1966), 55–74.
Stange, K.: Ein Näherungsverfahren zur Berechnung optimaler Pläne für messende Prüfung bei bekannten Kosten und bekannter Verteilung der Schlechtanteile in den vorgelegten Liefermengen. Metrika 10 (1966), 92–136.
Stange, K.: Die Wirksamkeit von Kontrollkarten. I. Die x- und x-Karte. Qualitätskontrolle 11 (1966), 129–137.
Stange, K.: Die Wirksamkeit von Kontrollkarten. II. Die s- und R-Karte zur Überwachung der Fertigungsstreuung. Qualitätskontrolle 12 (1967), 13–20 (see also 73–75).
Stange, K.: Die Bestimmung von Toleranzgrenzen mit Hilfe statistischer Überlegungen. Qualitätskontrolle 14 (1969), 57–63.
Stange, K.: Folgepläne für messende Prüfung bei bekannter Varianz der Fertigung und einem nach oben und unten abgegrenzten Toleranzbereich fùr die Merkmalwerte. Biometrische Zeitschr. 11 (1969), 1–24.
Stange, K.: Kontrollkarten für meßbare Merkmale. (Springer; 158 pages) 1975
Stange, K., and Henning, H.-J.: Formeln und Tabellen der mathematischen Statistik. 2nd revised edition, (Springer; pp. 362) Berlin 1966, pages 189–220
Störmer, H.: Mathematische Theorie der Zuverlässigkeit. Einführung und Anwendung. (Oldenbourg; 329 pages) München-Wien 1970 [see also Statist. Neerl. 28 (1974), 1–10]
Thoman, D. R., and Bain, L. J.: Two sample tests in the Weibull distribution. Technometrics 11 (1969), 805–815 [see Bain and Thoman]
Thoman, D. R., Bain, L. J., and Antle, C. E.: Inferences on the parameters of the Weibull distribution. Technometrics 11 (1969), 445–460 [see Bain and Thoman as well as Biometrika 61 (1974), 123–129 and H. Kübler, Statistische Hefte 20 (1979), 68–125]
Tillman, F. A., Hwang, C. L., and Kuo, W.: Optimization of Systems Reliability. (M. Dekker; pp. 311) New York 1980
Tillman, F. A., Kuo, W., Hwang, C. L., and Grosh, D. L.: Bayesian reliability and availability. A review. IEEE Trans. Reliab. R-31 (1982), 362–372
Tsokos, C. P. and Shimi, I. N. (Eds.): The Theory and Applications of Reliability with Emphasis on Bayesian and Nonparametric Methods, Academic Press, New York, 1977, Vols. I and II, pp. 549, 582
Uhlmann, W.: Kostenoptimale Prüfpläne. Tabellen, Praxis und Theorie eines Verfahrens der statistischen Qualitätskontrolle. (Physica-Vlg., 129 S.) Würzburg-Wien 1969
Watson, G. S., and Leadbetter, M. R.: Hazard analysis. I. Biometrika 51 (1964), 175–184
Weibull, W.: A statistical distribution function of wide applicability. J. Applied Mechanics 18 (1951), 293–297.
Weibull, W.: Fatigue Testing and Analysis of Results. Oxford 1961
Wilde, D. J.: Optimum Seeking Methods. (Prentice-Hall; pp. 202) Englewood Cliffs, N.J. 1964
Yang, C.-H., and Hillier, F. S.: Mean and variance control chart limits based on a small number of subgroups. J. Qual. Technol. 2 (1970), 9–16
Zaludova, Agnes H.: Problèmes de durée de vie. Applications à l’industrie automobile (1). Revue de Statistique Appliquée 13, (1965), No. 4, 75–98
H. Vogt, Metrika 14 (1969), 117–131
[8:2e] Linear programming and operations research
Anderson, M. Q.: Quantitative Management Decision Making. (Wadsworth; pp. 622) Belmont, Calif. 1982
Dantzig, G. B. (translated and revised by A. Jaeger): Lineare Programmierung und Erweiterungen. Berlin-Heidelberg 1966 [Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey]
Fabrycky, W. J., and Torgersen, P. E.: Operations Economy: Industrial Applications of Operations Research. Englewood Cliffs, N.J. 1966, Chapter 16
Flagle, C. D., Huggins, W. H., and Roy, R. H. (Eds.): Operations Research and Systems Engineering. Baltimore 1960
McCormick, G.: Nonlinear Programming: Theory, Algorithms and Applications. (Wiley; pp. 464) New York 1983
Gass, S. I.: Linear Programming. Methods and Applications. 3rd ed. (McGraw-Hill, pp. 325), New York 1969
Harnes, A., and Cooper, W. W.: Management Models and Industrial Applications of Linear Programming. New York 1961
Harper, W. M., and Lim, H. C.: Operational Research. 2nd ed. (Macdonald and Evans; pp. 310) Plymouth 1982
Hertz, D. B. (Ed.): Progress in Operations Research II. (Wiley; pp. 455) New York 1964
Hillier, F. S., and Lieberman, G. J.: Introduction to Operations Research. (Holden-Day, pp. 639) San Francisco 1967
Holzman, A. G. (Ed.): Operations Research Support Methodology. (M. Dekker; pp. 647) New York 1979
Kohlas, J.: Stochastic Methods of Operations Research. (Cambridge Univ. Press; pp. 224) Cambridge 1982
Moore, P. G.: A survey of operational research. J. Roy. Statist. Soc. A 129 (1966), 399–447
Müller-Merbach, H.: Operations Research. 3rd edition (Vahlen; 565 pages) München 1973
Philipson, C.: A review of the collective theory of risk. Skand. Aktuarietidskr. 51 (1968), 45–68 and 117–133 (see also H. Bühlmann: 174–177)
Saaty, T. L.: Operations research. Some contributions to mathematics. Science 178 (1972), 1061–1070
Sakarovitch, M.: Linear Programming. (Springer; pp. 210) New York, Berlin, Heidelberg, Tokyo 1983
Sasieni, M., Yaspan, A., and Friedman, L. Operations Research: Methods and Problems. (Wiley) New York 1959
Stoller, D. S.: Operations Research: Process and Strategy. Univ. of Calif. Press, Berkeley 1965
Theil, H., Boot, J. C. G., and Kloek, T.: Operations Research and Quantitative Economics, an Elementary Introduction. New York 1965
[8:2f] Game theory and war games
Bauknecht, K.: Panzersimulationsmodell „Kompaß“. Industrielle Organisation 36 (1967), 62–70
Berlekamp, E. R., Conway, J. H., and Guy, R. K.: Winning Ways. Vol. 1: Games in General, Vol. 2: Games in Particular (Academic Press; pp. 472 and 480) New York 1982
Bowen, K. C.: Research Games. An Approach to the Study of Decision Processes. (Halsted Press; pp. 126) New York 1978
Brams, S. J., Schotter, A., and Schwödiauer, G. (Eds): Applied Game Theory. (Physica-Vlg.; pp. 447) Würzburg 1979
Charnes, A., and Cooper, W. W.: Management Models and Industrial Applications of Linear Programming. Vol. I, II (Wiley; pp. 467, 393) New York 1961
Dresher, M.: Games of Strategy: Theory and Applications, Englewood Cliffs, N.J. 1961
Dresher, M., Shapley, L. S., and Tucker, A. W. (Eds.): Advances in Game Theory. Princeton (Univ. Press), N.J. 1964 [see also the bibliography on gaming in Simulation 23 (1974), 90–95, 115–116]
Eckler, A. R.: A survey of coverage problems associated with point and area targets. Technometrics 11 (1969), 561–589
Edwards, W.: The theory of decision making. Psychological Bulletin 51 (1954), 380–417 (see also Psychol. Rev. 69 [1962], 109)
Fain, W. W., Fain, J. B., and Karr, H. W.: A tactical warfare simulation program. Naval Res. Logist. Quart. 13 (1966), 413–436
Horvath, W. J.: A statistical model for the duration of wars and strikes. Behavioral Science 13 (1968), 18–28
Isaacs, R.: Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. (Wiley; pp. 384) New York 1965
Jones, A. J.: Game Theory. Mathematical Models of Conflict. (Halsted Press, Wiley; pp. 309) New York 1979
Kaplan, E. L.: Mathematical Programming and Games. Vol. 1 (Wiley; pp. 588) New York 1982
Kemeny, J. G., Schleifer, A., Jr., Snell, J. L., and Thompson, G. L.: Mathematik für die Wirtschaftspraxis. Translated by H.-J. Zimmermann. Berlin 1966, pp. 410–475
Luce, R. D., and Raiffa, H.: Games and Decisions. New York 1957
Neumann, J. von: Zur Theorie der Gesellschaftsspiele. Math. Annalen 100 (1928), 295–320
Neumann, J. von, and Morgenstern, O.: Theory of Games and Economic Behavior. Princeton 1944, 3rd ed. 1953
Owen, G.: Game Theory. 2nd ed. (Academic Press; pp. 368) New York 1982
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Sachs, L. (1984). Statistical Methods in Medicine and Technology. In: Applied Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5246-7_5
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