Quality pp 359-380 | Cite as

Statistics for Quality Management

  • Shyama Prasad MukherjeeEmail author
Part of the India Studies in Business and Economics book series (ISBE)


Planning before production, monitoring during production, evaluation at the end of production line and estimation of performance during use or deployment of any product or service delineate the ambit of Quality Management. Quality Planning—which has to be taken up along with product or service Planning—is an interdisciplinary activity wherein statistics (both as data and as a scientific method) has to play a crucial role in view of the uncertainties associated with most entities involved. Science, technology and innovation provide the hard inputs into this activity and statistics coupled with Information Technology is to enhance the contribution of each input, judged by its role in the overall ‘quality’ of the output taken in a broad sense. In the context of a concern for sustainability, this broad sense would remind us of the definition offered by Donkelaar a few decades back.


  1. Alwan, L. C. (2000). Statistical process analysis. New York: McGarw Hill.Google Scholar
  2. Antleman, G. R. (1985). Insensitivity to non-optimal design theory. Journal of the American Statistical Association, 60, 584–601.CrossRefGoogle Scholar
  3. Aroian, L. A., & Levene, H. (1950). The effectiveness of quality control charts. Journal of the American Statistical Association, 65(252), 520–529.CrossRefGoogle Scholar
  4. Baker, K. R. (1971). Two process models in the economic design of an X-Chart. AIIE Transactions, 3(4), 257–263.CrossRefGoogle Scholar
  5. Barnard, G. K. (1959). Control charts and stochastic process. Journal of the Royal Statistical Society: Series B, 21(24), 239–271.Google Scholar
  6. Basseville, M., & Nikiforov, I. V. (1993). Detection of abrupt changes, theory and applications. New Jersey: Prentice hall.Google Scholar
  7. Bather, J. A. (1963). Control charts and the minimization of costs. Journal of the Royal Statistical Society: Series B, 25(1), 49–80.Google Scholar
  8. Bissell, A. F. (1969). Cusum techniques for quality control. Journal of the Royal Statistical Society, Series C, 18(1), 1–30.Google Scholar
  9. Bowker, A. H., & Goode, H. P. (1952). Sampling inspection by variables. NY: McGraw Hill.Google Scholar
  10. Box, G. E. P., Hunter, W., & Hunter, J. S. (2005). Statistics for experiments: Design, innovation and discovery. Hoboken, New Jersey: Wiley.Google Scholar
  11. Burr, I. W. (1969). Control chart for measurements with varying sample sizes. Journal of Quality Technology, 1(3), 163–167.CrossRefGoogle Scholar
  12. Burr, I. W. (1967). The effect of non-normality on constants for \(\overline{X}\) and R Charts. Industrial Quality Control, 11, 563–569.Google Scholar
  13. Castillo, E. D., & Aticharkatan, S. (1997). Economic-statistical design of X-bar charts under initially unknown process variance. Economic Quality Control, 12, 159–171.Google Scholar
  14. Castillo, E. D., & Montgomery, D. C. (1993). Optimal design of control charts for monitoring short production runs. Economic Quality Control, 8, 225–240.Google Scholar
  15. Chiu, W. K., & Wetherill, G. B. (1974). A simplified scheme for the economic design for \(\overline{X}\) charts. Journal of Quality Technology, 6(2), 63–69.CrossRefGoogle Scholar
  16. Chung-How, Y., & Hillier, F. S. (1970). Mean and variance control chart limits based on a small number of subgroups. Journal of Quality Technology, 2(1), 9–16.CrossRefGoogle Scholar
  17. Collani, E. V. (1989). The economic design of control charts. Teubner Verlag.Google Scholar
  18. Craig, C. C. (1969). The \(\overline{X}\) and R chart and its competitors. Journal of Quality Technology, 1(2), 102–104.CrossRefGoogle Scholar
  19. Crowder, S. V. (1992). An SPC model for short production runs. Technometrics, 34, 64–73.CrossRefGoogle Scholar
  20. Das, N. G., & Mitra, S. K. (1964). The effect of non-normality on sampling inspection. Sankhya, A, 169–176.Google Scholar
  21. Dayananda, R. A., & Evans, I. G. (1973). Bayesian Acceptance-Sampling Schemes for Two-Sided Tests of the Mean of a Normal Distribution of Known Variance. Journal of the American Statistical Association, 68(341), 131–136.CrossRefGoogle Scholar
  22. Del Castillo, E., & Montgomery, D. C. (1993). Optimal design of control charts for monitoring short production runs. Economic Quality Control, 8, 225–240.Google Scholar
  23. Djauhari, M. A., et al. (2016). Monitoring multivariate process variability when sub-group size is small. Quality Engineering, 28(4), 429–440.CrossRefGoogle Scholar
  24. Does, R. J. M. M., Roes, K. C. B., & Trip, A. (1999). Statistical process control in industry. Netherlands: Kluwer PublishingGoogle Scholar
  25. Donkelaar, P. V. (1978). Quality—A valid alternative to growth. EOQC Quality, 4.Google Scholar
  26. Duncan, A. J. (1956a). The economic design of X-bar charts used to maintain current control of a process. Journal of the American Statistical Association, 51, 228–242.Google Scholar
  27. Duncan, A. J. (1956b). The economic design of—Charts when there in a multiplicity of assignable causes. Journal of the American Statistical Association, 66(333), 107–121.Google Scholar
  28. Duncan, A. J. (1956c). The economic design of X-charts used to maintain current control of a process. Journal of the American Statistical Association, 51(274), 228–242.Google Scholar
  29. Durbin, E. P. (1966). Pricing Policies Contingent on Observed Product Quality. Technometrics, 8(1), 123–134.CrossRefGoogle Scholar
  30. Enzer, H., & Dellinger, D. C. (1968). On some economic concepts of multiple incentive contracting. Naval Research Logistics Quarterly, 15(4), 477–489.CrossRefGoogle Scholar
  31. Ewan, W. D. (1968). When and how to use on-sum charts. Technometrics, 5(1), 1–22.CrossRefGoogle Scholar
  32. Ferrell, E. B. (1964). A median, midgrange chart using run-size subgroups. Industrial Quality Control, 20(10), 1–4.Google Scholar
  33. Ferrell, E. B. (1958). Control charts for log-normal universes. Industrial Quality Control, 15(2), 4–6.Google Scholar
  34. Foster, J. W. (1972). Price adjusted single sampling with indifference. Journal of Quality Technology, 4, 134–144.CrossRefGoogle Scholar
  35. Flehinger, B. J., & Miller, J. (1964). Incentive Contracts and Price Differential Acceptance Tests. Journal of the American Statistical Association, 59(305), 149–159.CrossRefGoogle Scholar
  36. Freund, R. A. (1960). A reconsideration of the variable control chart. Industrial Quality Control, 16(11), 35–41.Google Scholar
  37. Freund, R. A. (1957). Acceptance control charts. Industrial Quality Control, 14(4), 13–23.Google Scholar
  38. Freund, R. A. (1962). Graphical process control. Industrial Quality Control, 28(7), 15–22.Google Scholar
  39. Ghare, P. M., & Torgerson, P. E. (1968). The multi-characteristic control chart. The Journal of Industrial Engineering, 269–272.Google Scholar
  40. Ghosh, B. K., Reynolds, M. R., & Van Hiu, Y. (1981). Shewhart X-bar s with estimated variance. Communications in Statistics, Theory and Methods, 18, 1797–1822.CrossRefGoogle Scholar
  41. Gibra, I. N. (1971). Economically optimal determination of the parameters of X-control chart. Management Science, 17(9), 633–646.CrossRefGoogle Scholar
  42. Gibra, I. N. (1967). Optimal control of process subject to linear trends. The Journal of Industrial Engineering, 35–41.Google Scholar
  43. Girshick, M. A., & Robin, H. (1952). A bayes approach to a quality control model. Annals of Mathematical Statistics, 23, 114–125.CrossRefGoogle Scholar
  44. Goel, A. L., & Wu, S. M. (1973). Economically optimal design of cusum charts. Management Science, 19(11), 1271–1282.CrossRefGoogle Scholar
  45. Goel, A. L., Jain, S. C., & Wu, S. M. (1988). An algorithm for the determination of the economic design of X-charts based on Duncan’s Model. Journal of the American Statistical Association, 63(321), 304–320.Google Scholar
  46. Goldsmith, P. L., & Withfield, H. (1961). Average runs lengths in cumulative chart quality control schemes. Technometrics, 3, 11–20.CrossRefGoogle Scholar
  47. Grundy, P. N., Healy, M. J. R., & Ross, D. H. (1969). Economic choice of the amount of experimentation. Journal of the Royal Statistical Society B, 18, 32–55.Google Scholar
  48. Hald, A. (1981). Statistical theory of sampling inspection by attributes. Cambridge: Academic Press.Google Scholar
  49. Hawkins, D. M., & Olwell, D. H. (1998). Cumulative sum charts and charting for quality improvement. Berlin: Springer Verlag.CrossRefGoogle Scholar
  50. Hill, I. D. (1960). The Economic Incentive Provided by Sampling Inspection. Applied Statistics, 9(2), 69.CrossRefGoogle Scholar
  51. Hill, I. D. (1962). Sampling Inspection and Defence Specification DEF-131. Journal of the Royal Statistical Society. Series A (General), 125(1), 31.CrossRefGoogle Scholar
  52. Hillier, F. S. (1969). \(\overline{X}\)- and R-charts control limits based on a small number of subgroups. Journal of Quality Technology, 1(1), 17–26.CrossRefGoogle Scholar
  53. Iqbal, Z., Grigg, N. P., & Govindaraju, K. (2017). Performing competitive analysis in QFD studies using state multipole moments and bootstrap sampling. Quality Engineering, 29(2), 311–321.CrossRefGoogle Scholar
  54. Jackson, J. E. (1956). Quality control methods for two related variables. Industrial Quality Control, 12(7), 4–8.Google Scholar
  55. Johns, M. V., Jr., & Miller, R. G., Jr. (1963). Average renewal loss rates. Annals of Mathematical Statistics, 34, 396–401.CrossRefGoogle Scholar
  56. Johnson, N. L. (1966). Cumulative sum control charts and the Weibull Distribution. Technometrics, 8(3), 481–491.CrossRefGoogle Scholar
  57. Johnson, N. L., & Leone, F. C. (1962a). Cumulative sum control charts: Mathematical principles applied to construction and use, Part-12. Industrial Quality Control, 18(12), 15–21.Google Scholar
  58. Johnson, N. L., & Leone, F. C. (1962b). Cumulative sum control charts: Mathematical principles applied to construction and use, Part II. Industrial Quality Control, 19(1), 29–36.Google Scholar
  59. Johnson, N. L., & Leone, F. C. (1962c). Cumulative sum control charts: Mathematical principles applied to construction and use, Part III. Industrial Quality Control, 19(2), 22–28.Google Scholar
  60. Kemp, K. W. (1961). The average run length of a cumulative sum chart when a V-Maak is used. Journal of the Royal Statistical Society, 23, 149–153.Google Scholar
  61. King, S. P. (1959). The operating characteristics of the control chart for sample means. Annals of Mathematical Statistics, 23, 384–395.CrossRefGoogle Scholar
  62. Knappenberger, H. A., & Grandage, A. H. (1969). Minimum cost quality control tests. AIIE Transactions, 1(1), 24–32.CrossRefGoogle Scholar
  63. Kotz, S., & Lovelace, C. (1998). Process capability Indices in theory and Practice. London: Arnold Press.Google Scholar
  64. Ladany, S. P., & Bedi, D. N. (1976). Selection of the optimal set-up policy. Nabal Research Logistics Quarterly, 23, 219–233.CrossRefGoogle Scholar
  65. Ladany, S. P. (1973). Optimal use of control charts for controlling current production. Management Science, 19(7), 763–772.CrossRefGoogle Scholar
  66. Lave, R. E. (1969). A Markov Model for quality control plan selection. AIIE Transactions, 1(2), 139–145.CrossRefGoogle Scholar
  67. Lieberman, G. J. (1965). Statistical process control and the impact of automatic process control. Technometrics, 7(3), 283–292.CrossRefGoogle Scholar
  68. Lieberman, G. J., & Resnikoff, G. J. (1955) Sampling Plans for Inspection by Variables. Journal of the American Statistical Association, 50(270), 457.Google Scholar
  69. Mitra, S. K., & Subramanya, M. T. (1968). A robust property of the OC of binomial and Poisson sampling inspection plans. Sankhya B, 30, 335–342.Google Scholar
  70. Montgomery, D. C. (2004). Introduction to statistical quality control. New Jersey: Wiley.Google Scholar
  71. Montgomery, D. C., & Klatt, P. J. (1972). Economic design of T2 control charts to maintain current control of a process. Management Science, 19(1), 76–89.CrossRefGoogle Scholar
  72. Moore, P. G. (1958). Some properties of runs in quality control procedures. Biometrika, 45, 89–95.CrossRefGoogle Scholar
  73. Mukherjee, S. P. (1971). Control of multiple quality characteristics. I.S.Q.C. Bulletin, 13, 11–16.Google Scholar
  74. Mukherjee, S. P. (1976). Effects of process Adjustments based on control chart evidences. IAPQR Transactions, 2, 57–65.Google Scholar
  75. Mukherjee, S. P., & Das, B. (1977). A process control plan based on exceedances. IAPQR Transactions, 2, 45–54.Google Scholar
  76. Mukherjee, S. P., & Das, B. (1980). Control of process average by gauging I. IAPQR Transactions, 5, 9–25.Google Scholar
  77. Nagendra, Y., & Rai, G. (1971). Optimum sample size and sampling interval for controlling the mean of non-normal variables. Journal of the American Statistical Association, 637–640.CrossRefGoogle Scholar
  78. Owen, D. B. (1969). Summary of recent work on variable acceptance sapling with emphasis on non-normality. Technometrics, 11, 631–637.CrossRefGoogle Scholar
  79. Owen, D. B. (1967). Variables sampling plans based on the normal distribution. Technometrics, 9, 417–423.CrossRefGoogle Scholar
  80. Page, E. S. (1962). A modified control chart with warning limits. Biometrika, 49, 171–176.CrossRefGoogle Scholar
  81. Page, E. S. (1964). Comparison of process inspection schemes. Industrial Quality Control, 21(5), 245–249.Google Scholar
  82. Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41, 100–115.CrossRefGoogle Scholar
  83. Page, E. S. (1963). Controlling the standard deviation by Cusums and Warning Lines. Technometrics, 6, 307–316.CrossRefGoogle Scholar
  84. Page, E. S. (1961). Cumulative sum charts. Technometrics, 3(1), 1–9.CrossRefGoogle Scholar
  85. Parkhideh, S., & Parkhideh, B. (1996). The economic design of a flexible zone X¯-chart with AT&T rules. IIE Transactions, 28(3), 261–266.CrossRefGoogle Scholar
  86. Quesenberry, C. P. (1991). SPC Q-charts for start-up processes and short or long runs. Journal of Quality Technology, 23, 213–224.CrossRefGoogle Scholar
  87. Quesenberry, C. P. (2001). The multivariate short-run snapshot Q chart. Quality Engineering, 13(4), 679–683.CrossRefGoogle Scholar
  88. Reynolds, J. H. (1971). The run sum control chart procedure. Journal of Quality Technology, 3(1), 23–27.CrossRefGoogle Scholar
  89. Roberts, S. W. (1966). A comparison of some control chart procedures. Technometrics, 8(3), 411–430.CrossRefGoogle Scholar
  90. Roberts, S. W. (1959). Control charts based on geometric moving averages. Technometrics, 1(3), 239–250.CrossRefGoogle Scholar
  91. Roeloffs, R. (1967). Acceptance sampling Plans with price differentials. Journal of Industrial and Engineering, 18, 96–100.Google Scholar
  92. Rossow, B. (1972). Is it necessary to assume a Normal distribution in applying Sampling Schemes for variables? Qualitat Und Zuverlassigkeit, 17, 143.Google Scholar
  93. Ryan, T. (2000). Statistical methods for quality improvement. New Jersey: Wiley.Google Scholar
  94. Sarkar, P., & Meeker, W. Q. (1998). A Bayesian On-Line Change Detection algorithm with process monitoring applications. Quality Engineering, 10(3), 539–549.CrossRefGoogle Scholar
  95. Scheffe, H. (1949). Operating characteristics of average and range and range charts. Industrial Quality Control, 5(6), 13–18.Google Scholar
  96. Schilling, E. G. (1982). Acceptance sampling in quality control. New York: Marcel DekkerGoogle Scholar
  97. Shainin, D. (1950). The Hamilton Standard lot plot method of acceptance sampling by variables. Industrial Quality Control, 7, 15.Google Scholar
  98. Stange, K. (1966). Optimal sequential sampling plans for known costs (but unknown distribution of defectives in the lot), Minimax Solution. Unternehmensfurschung, 10, 129–151.Google Scholar
  99. Stange, K. (1964). Calculation of economic sampling plans for inspection by variables. Metrika, 8, 48–82.CrossRefGoogle Scholar
  100. Taguchi, G., & Jugulum, R. (2000). The Mahalanobis-Taguchi strategy: A pattern technology. New York: Wiley.Google Scholar
  101. Taguchi, G., & Jugulum, R. (2002). New trends in multivariate diagnosis. The Indian Journal of Statistics, Sankhya Series B, Part, 2, 233–248.Google Scholar
  102. Taylor, H. M. (1968). The economic design of cumulative sum control charts. Technometrics, 10(3), 479–488.CrossRefGoogle Scholar
  103. Tiago de Oliviera, J., & Littauer, S. B. (1965). Double limit and run control charts. Revue de Statique Appliques, 13(2).Google Scholar
  104. Tiago de Oliviera, J., & Littauer, S. B. (1966). Double limit and run control chart techniques for economic use of control charts. Revue do Statistique Appliques, 14(3).Google Scholar
  105. Truax, H. M. (1961). Cumulative sum charts and their application to the chemical industry. Industrial Quality Control, 18(6), 18–25.Google Scholar
  106. Wade, M. R., & Woodall , W. H. (1993). A review and analysis of cause-selecting control charts. Journal of Quality Technology, 25, 161–168.CrossRefGoogle Scholar
  107. Wadsworth, H. M, Stephens, K. S, & Godfrey, A. B. (2002). Modern methods for quality control and improvement. Berlin: Springer Verlag.Google Scholar
  108. Weigand, C. (1993). On the effect of SPC on production time. Economic Quality Control, 8, 23–61.Google Scholar
  109. Wetherill, G. B., & Campling, G. E. G. (1966). The decision theory approach to sampling inspection. Journal of the Royal Statistical Society. Series B (Methodological) 28, 381–416.Google Scholar
  110. Wetherill, G. B., & Chiu, W. K. (1974). A simplified attribute sampling scheme. Applied Statistics 22Google Scholar
  111. Wheeler, D. J. (1995). Advanced topics in statistical process control. Knoxville: SPC Press.Google Scholar
  112. Whittle, P. (1954). Optimum preventive sampling. Journal of the Operational Research Society, 2, 197.Google Scholar
  113. Wiklund, S. J. (1992). Estimating the process mean when using control charts. Economic Control Charts, 7, 105–120.Google Scholar
  114. Wiklund, S. J. (1993). Adjustment strategies when using Shewhart charts. Economic Quality Control, 8, 3–21.Google Scholar
  115. Xie, M., Goh, T. N. & Kuralmani, V. (2002). Statistical models and control charts for high quality processes. New York: Kluwer Academic Publishers.CrossRefGoogle Scholar
  116. Zhang, G. (1984). Cause-selecting control charts: Theory and practice. Beijing: The People’s Posts and Telecommunications Press.Google Scholar
  117. Zwetsloot, I. M., & Woodall, W. H. (2017). A head-to-head comparative study of the conditional performance of control charts based on estimated parameters. Quality Engineering, 29(2), 244–253.CrossRefGoogle Scholar
  118. Zhang, G. X. (1992). Cause–selecting control chart and diagnosis, theory and practice. Denmark.Google Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of CalcuttaHowrahIndia

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