Statistical Quality Control and Reliability Tests

Statistical quality control and reliability tests are performed to estimate or demonstrate quality and reliability characteristics on the basis of data collected from sampling tests. Estimation leads to a point or interval estimate of an unknown characteristic. Demonstration is a test of a given hypothesis on the unknown characteristic, often at an acceptance test. Estimation and demonstration of an unknown probability is investigated in Section 7.1 for the case of a defective probability p (fraction of defective items) and applied in Section 7.2.1 to reliability, maintainability, and availability figures. Estimation and demonstration of a constant failure rate λ (or MTBF=1/λ) and of an MTTR are discussed in depth in Sections 7.2.2 and 7.3. Basic models for accelerated tests and for goodness-of-fit tests are considered in Sections 7.4 and 7.5, respectively. Empirical & graphical methods are given in Section 7.5. Some refinement on reliability data analysis are discussed in Section 7.6. To simplify the notation, sample will be used instead of random sample. Theoretical foundations for this chapter are in Appendix A8. A large number of examples illustrate practical aspects.

[1]  E. J. Gumbel,et al.  Statistics of Extremes. , 1960 .

[2]  J. Kalbfleisch.  Statistical Inference Under Order Restrictions , 1975 .

[3]  R. Fisher,et al.  On the Mathematical Foundations of Theoretical Statistics , 1922 .

[4]  M. Sobel,et al.  SEQUENTIAL LIFE TESTS IN THE EXPONENTIAL CASE , 1955 .

[5]  Robert J. Beaver,et al.  An Introduction to Probability Theory and Mathematical Statistics , 1977 .

[6]  R. Fisher.  034: The Conditions Under Which x2 Measures the Discrepancy Between Observation and Hypothesis. , 1924 .

[7]  J. J. Higgins,et al.  A new model for step-stress testing , 1998 .

[8]  Gisela Hartler,et al.  Parameter Estimation for the Arrhenius Model , 1986, IEEE Transactions on Reliability.

[9]  D. S. Peck,et al.  Accelerated testing handbook , 1981 .

[10]  Floyd W. Spencer,et al.  Statistical methods in accelerated life testing , 1988 .

[11]  Albert H. Moore,et al.  An Evaluation of Exponential and Weibull Test Plans , 1976, IEEE Transactions on Reliability.

[12]  William Q. Meeker,et al.  Pitfalls of accelerated testing , 1998 .

[13]  W. Nelson,et al.  Optimum Simple Step-Stress Plans for Accelerated Life Testing , 1983, IEEE Transactions on Reliability.

[14]  Moshe Shaked,et al.  Nonparametric Estimation and Goodness-of-Fit Testing of Hypotheses for Distributions in Accelerated Life Testing , 1982, IEEE Transactions on Reliability.

[15]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  R. S. Chadwick,et al.  Complex system Reliability Demonstration Technology , 1975 .

[17]  L. H. Miller.  Table of Percentage Points of Kolmogorov Statistics , 1956 .

[18]  N. Singpurwalla,et al.  Methods for Statistical Analysis of Reliability and Life Data. , 1975 .

[19]  Z. Birnbaum.  Numerical Tabulation of the Distribution of Kolmogorov's Statistic for Finite Sample Size , 1952 .

[20]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[21]  Benjamin Epstein,et al.  THE EXACT ANALYSIS OF SEQUENTIAL LIFE TESTS WITH PARTICULAR APPLICATION TO AGREE PLANS , 1963 .

[22]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[23]  Genichi Taguchi.  System Of Experimental Design: Engineering Methods To Optimize Quality And Minimize Costs , 1987 .

[24]  K. Sarkadi,et al.  Mathematical methods of statistical quality control , 1974 .

[25]  C. K. Hansen,et al.  Spurious exponentiality observed when incorrectly fitting a distribution to nonstationary data , 1998 .

[26]  H. Martz.  Bayesian reliability analysis , 1982 .

[27]  Michael Pecht,et al.  Assessing time-to-failure due to conductive filament formation in multi-layer organic laminates , 1994 .

[28]  Ralph B. D'Agostino,et al.  Goodness-of-Fit-Techniques , 2020 .

[29]  D. J. Klinger.  On the notion of activation energy in reliability: Arrhenius, Eyring, and thermodynamics , 1991, Annual Reliability and Maintainability Symposium. 1991 Proceedings.

[30]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data. , 1983 .

[31]  H. Chernoff,et al.  The Use of Maximum Likelihood Estimates in {\chi^2} Tests for Goodness of Fit , 1954 .

[32]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[33]  D. Darling.  The Kolmogorov-Smirnov, Cramer-von Mises Tests , 1957 .

[34]  W. G. Cochran.  The $\chi^2$ Test of Goodness of Fit , 1952 .

[35]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[36]  W. Feller.  On the Kolmogorov–Smirnov Limit Theorems for Empirical Distributions , 1948 .

[37]  Z. A. Lomnicki.  Methods for Statistical Analysis of Reliability and Life Data , 1976 .

[38]  R. E. Barlow,et al.  Total time on test processes and applications to failure data , 1975 .

[39]  E. S. Pearson,et al.  THE USE OF CONFIDENCE OR FIDUCIAL LIMITS ILLUSTRATED IN THE CASE OF THE BINOMIAL , 1934 .

[40]  Abraham Wald,et al.  Statistical Decision Functions , 1951 .