Skip to main content

Statistics for Quality Management

  • Chapter
  • First Online:
Quality

Part of the book series: India Studies in Business and Economics ((ISBE))

  • 1346 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Alwan, L. C. (2000). Statistical process analysis. New York: McGarw Hill.

    Google Scholar 

  • Antleman, G. R. (1985). Insensitivity to non-optimal design theory. Journal of the American Statistical Association, 60, 584–601.

    Article  Google Scholar 

  • Aroian, L. A., & Levene, H. (1950). The effectiveness of quality control charts. Journal of the American Statistical Association, 65(252), 520–529.

    Article  Google Scholar 

  • Baker, K. R. (1971). Two process models in the economic design of an X-Chart. AIIE Transactions, 3(4), 257–263.

    Article  Google Scholar 

  • Barnard, G. K. (1959). Control charts and stochastic process. Journal of the Royal Statistical Society: Series B, 21(24), 239–271.

    Google Scholar 

  • Basseville, M., & Nikiforov, I. V. (1993). Detection of abrupt changes, theory and applications. New Jersey: Prentice hall.

    Google Scholar 

  • 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 

  • Bissell, A. F. (1969). Cusum techniques for quality control. Journal of the Royal Statistical Society, Series C, 18(1), 1–30.

    Google Scholar 

  • Bowker, A. H., & Goode, H. P. (1952). Sampling inspection by variables. NY: McGraw Hill.

    Google Scholar 

  • Box, G. E. P., Hunter, W., & Hunter, J. S. (2005). Statistics for experiments: Design, innovation and discovery. Hoboken, New Jersey: Wiley.

    Google Scholar 

  • Burr, I. W. (1969). Control chart for measurements with varying sample sizes. Journal of Quality Technology, 1(3), 163–167.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Collani, E. V. (1989). The economic design of control charts. Teubner Verlag.

    Google Scholar 

  • Craig, C. C. (1969). The \(\overline{X}\) and R chart and its competitors. Journal of Quality Technology, 1(2), 102–104.

    Article  Google Scholar 

  • Crowder, S. V. (1992). An SPC model for short production runs. Technometrics, 34, 64–73.

    Article  Google Scholar 

  • Das, N. G., & Mitra, S. K. (1964). The effect of non-normality on sampling inspection. Sankhya, A, 169–176.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Djauhari, M. A., et al. (2016). Monitoring multivariate process variability when sub-group size is small. Quality Engineering, 28(4), 429–440.

    Article  Google Scholar 

  • Does, R. J. M. M., Roes, K. C. B., & Trip, A. (1999). Statistical process control in industry. Netherlands: Kluwer Publishing

    Google Scholar 

  • Donkelaar, P. V. (1978). Quality—A valid alternative to growth. EOQC Quality, 4.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Durbin, E. P. (1966). Pricing Policies Contingent on Observed Product Quality. Technometrics, 8(1), 123–134.

    Article  Google Scholar 

  • Enzer, H., & Dellinger, D. C. (1968). On some economic concepts of multiple incentive contracting. Naval Research Logistics Quarterly, 15(4), 477–489.

    Article  Google Scholar 

  • Ewan, W. D. (1968). When and how to use on-sum charts. Technometrics, 5(1), 1–22.

    Article  Google Scholar 

  • Ferrell, E. B. (1964). A median, midgrange chart using run-size subgroups. Industrial Quality Control, 20(10), 1–4.

    Google Scholar 

  • Ferrell, E. B. (1958). Control charts for log-normal universes. Industrial Quality Control, 15(2), 4–6.

    Google Scholar 

  • Foster, J. W. (1972). Price adjusted single sampling with indifference. Journal of Quality Technology, 4, 134–144.

    Article  Google Scholar 

  • Flehinger, B. J., & Miller, J. (1964). Incentive Contracts and Price Differential Acceptance Tests. Journal of the American Statistical Association, 59(305), 149–159.

    Article  Google Scholar 

  • Freund, R. A. (1960). A reconsideration of the variable control chart. Industrial Quality Control, 16(11), 35–41.

    Google Scholar 

  • Freund, R. A. (1957). Acceptance control charts. Industrial Quality Control, 14(4), 13–23.

    Google Scholar 

  • Freund, R. A. (1962). Graphical process control. Industrial Quality Control, 28(7), 15–22.

    Google Scholar 

  • Ghare, P. M., & Torgerson, P. E. (1968). The multi-characteristic control chart. The Journal of Industrial Engineering, 269–272.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gibra, I. N. (1971). Economically optimal determination of the parameters of X-control chart. Management Science, 17(9), 633–646.

    Article  Google Scholar 

  • Gibra, I. N. (1967). Optimal control of process subject to linear trends. The Journal of Industrial Engineering, 35–41.

    Google Scholar 

  • Girshick, M. A., & Robin, H. (1952). A bayes approach to a quality control model. Annals of Mathematical Statistics, 23, 114–125.

    Article  Google Scholar 

  • Goel, A. L., & Wu, S. M. (1973). Economically optimal design of cusum charts. Management Science, 19(11), 1271–1282.

    Article  Google Scholar 

  • 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 

  • Goldsmith, P. L., & Withfield, H. (1961). Average runs lengths in cumulative chart quality control schemes. Technometrics, 3, 11–20.

    Article  Google Scholar 

  • 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 

  • Hald, A. (1981). Statistical theory of sampling inspection by attributes. Cambridge: Academic Press.

    Google Scholar 

  • Hawkins, D. M., & Olwell, D. H. (1998). Cumulative sum charts and charting for quality improvement. Berlin: Springer Verlag.

    Book  Google Scholar 

  • Hill, I. D. (1960). The Economic Incentive Provided by Sampling Inspection. Applied Statistics, 9(2), 69.

    Article  Google Scholar 

  • Hill, I. D. (1962). Sampling Inspection and Defence Specification DEF-131. Journal of the Royal Statistical Society. Series A (General), 125(1), 31.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Jackson, J. E. (1956). Quality control methods for two related variables. Industrial Quality Control, 12(7), 4–8.

    Google Scholar 

  • Johns, M. V., Jr., & Miller, R. G., Jr. (1963). Average renewal loss rates. Annals of Mathematical Statistics, 34, 396–401.

    Article  Google Scholar 

  • Johnson, N. L. (1966). Cumulative sum control charts and the Weibull Distribution. Technometrics, 8(3), 481–491.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • King, S. P. (1959). The operating characteristics of the control chart for sample means. Annals of Mathematical Statistics, 23, 384–395.

    Article  Google Scholar 

  • Knappenberger, H. A., & Grandage, A. H. (1969). Minimum cost quality control tests. AIIE Transactions, 1(1), 24–32.

    Article  Google Scholar 

  • Kotz, S., & Lovelace, C. (1998). Process capability Indices in theory and Practice. London: Arnold Press.

    Google Scholar 

  • Ladany, S. P., & Bedi, D. N. (1976). Selection of the optimal set-up policy. Nabal Research Logistics Quarterly, 23, 219–233.

    Article  Google Scholar 

  • Ladany, S. P. (1973). Optimal use of control charts for controlling current production. Management Science, 19(7), 763–772.

    Article  Google Scholar 

  • Lave, R. E. (1969). A Markov Model for quality control plan selection. AIIE Transactions, 1(2), 139–145.

    Article  Google Scholar 

  • Lieberman, G. J. (1965). Statistical process control and the impact of automatic process control. Technometrics, 7(3), 283–292.

    Article  Google Scholar 

  • Lieberman, G. J., & Resnikoff, G. J. (1955) Sampling Plans for Inspection by Variables. Journal of the American Statistical Association, 50(270), 457.

    Google Scholar 

  • 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 

  • Montgomery, D. C. (2004). Introduction to statistical quality control. New Jersey: Wiley.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Moore, P. G. (1958). Some properties of runs in quality control procedures. Biometrika, 45, 89–95.

    Article  Google Scholar 

  • Mukherjee, S. P. (1971). Control of multiple quality characteristics. I.S.Q.C. Bulletin, 13, 11–16.

    Google Scholar 

  • Mukherjee, S. P. (1976). Effects of process Adjustments based on control chart evidences. IAPQR Transactions, 2, 57–65.

    Google Scholar 

  • Mukherjee, S. P., & Das, B. (1977). A process control plan based on exceedances. IAPQR Transactions, 2, 45–54.

    Google Scholar 

  • Mukherjee, S. P., & Das, B. (1980). Control of process average by gauging I. IAPQR Transactions, 5, 9–25.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Owen, D. B. (1969). Summary of recent work on variable acceptance sapling with emphasis on non-normality. Technometrics, 11, 631–637.

    Article  Google Scholar 

  • Owen, D. B. (1967). Variables sampling plans based on the normal distribution. Technometrics, 9, 417–423.

    Article  Google Scholar 

  • Page, E. S. (1962). A modified control chart with warning limits. Biometrika, 49, 171–176.

    Article  Google Scholar 

  • Page, E. S. (1964). Comparison of process inspection schemes. Industrial Quality Control, 21(5), 245–249.

    Google Scholar 

  • Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41, 100–115.

    Article  Google Scholar 

  • Page, E. S. (1963). Controlling the standard deviation by Cusums and Warning Lines. Technometrics, 6, 307–316.

    Article  Google Scholar 

  • Page, E. S. (1961). Cumulative sum charts. Technometrics, 3(1), 1–9.

    Article  Google Scholar 

  • Parkhideh, S., & Parkhideh, B. (1996). The economic design of a flexible zone X¯-chart with AT&T rules. IIE Transactions, 28(3), 261–266.

    Article  Google Scholar 

  • Quesenberry, C. P. (1991). SPC Q-charts for start-up processes and short or long runs. Journal of Quality Technology, 23, 213–224.

    Article  Google Scholar 

  • Quesenberry, C. P. (2001). The multivariate short-run snapshot Q chart. Quality Engineering, 13(4), 679–683.

    Article  Google Scholar 

  • Reynolds, J. H. (1971). The run sum control chart procedure. Journal of Quality Technology, 3(1), 23–27.

    Article  Google Scholar 

  • Roberts, S. W. (1966). A comparison of some control chart procedures. Technometrics, 8(3), 411–430.

    Article  Google Scholar 

  • Roberts, S. W. (1959). Control charts based on geometric moving averages. Technometrics, 1(3), 239–250.

    Article  Google Scholar 

  • Roeloffs, R. (1967). Acceptance sampling Plans with price differentials. Journal of Industrial and Engineering, 18, 96–100.

    Google Scholar 

  • Rossow, B. (1972). Is it necessary to assume a Normal distribution in applying Sampling Schemes for variables? Qualitat Und Zuverlassigkeit, 17, 143.

    Google Scholar 

  • Ryan, T. (2000). Statistical methods for quality improvement. New Jersey: Wiley.

    Google Scholar 

  • Sarkar, P., & Meeker, W. Q. (1998). A Bayesian On-Line Change Detection algorithm with process monitoring applications. Quality Engineering, 10(3), 539–549.

    Article  Google Scholar 

  • Scheffe, H. (1949). Operating characteristics of average and range and range charts. Industrial Quality Control, 5(6), 13–18.

    Google Scholar 

  • Schilling, E. G. (1982). Acceptance sampling in quality control. New York: Marcel Dekker

    Google Scholar 

  • Shainin, D. (1950). The Hamilton Standard lot plot method of acceptance sampling by variables. Industrial Quality Control, 7, 15.

    Google Scholar 

  • 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 

  • Stange, K. (1964). Calculation of economic sampling plans for inspection by variables. Metrika, 8, 48–82.

    Article  Google Scholar 

  • Taguchi, G., & Jugulum, R. (2000). The Mahalanobis-Taguchi strategy: A pattern technology. New York: Wiley.

    Google Scholar 

  • Taguchi, G., & Jugulum, R. (2002). New trends in multivariate diagnosis. The Indian Journal of Statistics, Sankhya Series B, Part, 2, 233–248.

    Google Scholar 

  • Taylor, H. M. (1968). The economic design of cumulative sum control charts. Technometrics, 10(3), 479–488.

    Article  Google Scholar 

  • Tiago de Oliviera, J., & Littauer, S. B. (1965). Double limit and run control charts. Revue de Statique Appliques, 13(2).

    Google Scholar 

  • 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 

  • Truax, H. M. (1961). Cumulative sum charts and their application to the chemical industry. Industrial Quality Control, 18(6), 18–25.

    Google Scholar 

  • Wade, M. R., & Woodall , W. H. (1993). A review and analysis of cause-selecting control charts. Journal of Quality Technology, 25, 161–168.

    Article  Google Scholar 

  • Wadsworth, H. M, Stephens, K. S, & Godfrey, A. B. (2002). Modern methods for quality control and improvement. Berlin: Springer Verlag.

    Google Scholar 

  • Weigand, C. (1993). On the effect of SPC on production time. Economic Quality Control, 8, 23–61.

    Google Scholar 

  • 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 

  • Wetherill, G. B., & Chiu, W. K. (1974). A simplified attribute sampling scheme. Applied Statistics 22

    Google Scholar 

  • Wheeler, D. J. (1995). Advanced topics in statistical process control. Knoxville: SPC Press.

    Google Scholar 

  • Whittle, P. (1954). Optimum preventive sampling. Journal of the Operational Research Society, 2, 197.

    Google Scholar 

  • Wiklund, S. J. (1992). Estimating the process mean when using control charts. Economic Control Charts, 7, 105–120.

    Google Scholar 

  • Wiklund, S. J. (1993). Adjustment strategies when using Shewhart charts. Economic Quality Control, 8, 3–21.

    Google Scholar 

  • Xie, M., Goh, T. N. & Kuralmani, V. (2002). Statistical models and control charts for high quality processes. New York: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Zhang, G. (1984). Cause-selecting control charts: Theory and practice. Beijing: The People’s Posts and Telecommunications Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Zhang, G. X. (1992). Cause–selecting control chart and diagnosis, theory and practice. Denmark.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shyama Prasad Mukherjee .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mukherjee, S. (2019). Statistics for Quality Management. In: Quality. India Studies in Business and Economics. Springer, Singapore. https://doi.org/10.1007/978-981-13-1271-7_17

Download citation

Publish with us

Policies and ethics