In traditional quality control charts, fixed sampling interval (FSI) schemes are used where the time between samples has fixed intervals. More efficient methods called variable sampling interval (VSI) schemes have been developed where one takes the next observation sooner than usual if there is an indication that the process is operating off the target value. Another traditional assumption behind most statistical process control charts is that the sequential observations are independent. However, there are many situations where the sequential observations should not to be treated as independent. Rather, a time series model, in particular the first order autoregressive (AR (1)) model, is appropriate. A Markov chain representation is used to study the properties of the FSI and VSI Shewhart X control charts. First, the results show that if the process variance is properly estimated and if traditional control limits are used in the FSI control charts, then the detection time is shorter when the consecutive observations are negatively correlated than when they are positively correlated. If they are positively correlated, then the false alarm rate decreases as the correlation between consecutive observations increases. On the other hand, the detection time increases as the correlation increases. In VSI control charts with traditional control limits, if the process mean is on or near the target, then the average time to signal (A TS) and average number of samples to signal (ANSS) tend to decrease as the correlation increases until the correlation becomes rather moderate. Then, for more highly correlated data, the A TS and ANSS tend to increase as the correlation increases. Next, the results show that, even under the AR (1) process, the VSI chart is more efficient than the FSI chart in terms of ATS. In contrast, the VSI chart is less efficient than the FSI chart in terms of ANSS. The efficiency (inefficiency) of ATS (ANSS) tends to decrease (increase) as the correlation between the consecutive observations becomes stronger. Steady state ATS (A TS·) and steady state ANSS (ANSSO) under the AR (1) process show the same trend as the 'regular' ATS and 'regular' ANSS except when the deviation is very large. If the deviation is very large, then the VSI control chart does not seem to be more efficient than the FSI control chart in terms of steady state ATS. If we have an AR (2) process, then for any given value of tP2 a PSI control chart has a shorter detection time when tPl is negative than when tPl is positive. In a FSI control chart, the effect of positive </>2 in addition to positive tPl is that the false alarm rate decreases even further and the detection time is even longer. / Ph. D.

No description available.

This thesis is an extension of the work on variable sampling charts (<i>VSI</i>) for monitoring a single parameter. An attempt is made to develop a chart which can simultaneously monitor both the process mean and process variance. The chart is based on a statistic which combines both mean and variance. After developing such a chart variable sampling intervals are introduced and it is evaluated against alternative methods of monitoring mean and variance with variable sampling intervals. The statistic chosen is an approximate statistic and simulation studies are performed for the evaluation. The results are at times counter-intuitive thus an analysis of the properties of the chart is made and explanations are provided. / Master of Science

The purpose of this work is to discover an optimum sample size to be used for deciding between two methods (populations) to choose for future production. The procedure involves the formulation of a loss function, expressing the expected loss due to choosing the population with the small mean, as a function of the difference between the population means, the amount to be produced and the cost of sampling. A minimax procedure is applied to obtain the optimum sample size. Since the function does not lend itself conveniently to mathematical considerations, special cases involving the difference between the means are considered and an optimum sample size is found for these cases. In all cases, the optimum sample size is an explicit function of the amount to be produced, the cost of sampling and the standard deviation. / Master of Science

Since its issuance in June 1981, Statement on Auditing Standards (SAS) No. 39, "Audit Sampling," has been the center of much controversy. Practitioners are voicing their concerns as they anticipate difficulties in designing, selecting, and evaluating a nonstatistical sampling procedure in accordance with SAS 39. This proposed exploratory study seeks to identify those factors that underlie the auditor's judgment with respect to nonstatistical sample size decisions in substantive tests. The research will utilize Egon Brunswik's Lens Model to provide mathematical representations of the auditor's judgment process. Correlational statistics will be used to assess judgment accuracy, agreement (consensus) , and auditor "self-insight" into his decision process. The study will provide empirical insight, into whether the auditor's determination of the appropriate extent of testing is consistent with his judgment as to the assurance level needed from his sampling application, or conversely, the degree of risk he is willing to accept. The ability of auditors to formulate their sample size decisions properly is crucial because of their impact on audit effectiveness and efficiency. In addition, this project should provide additional evidence bearing upon the arguments of both proponents and opponents of SAS 39. / Ph. D.

No description available.

published_or_final_version / Applied Statistics / Master / Master of Social Sciences

by Carl Ka-fai Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter §1.1 --- Directional Data and Computer Simulation --- p.1 / Chapter §1.2 --- Computer Simulation Techniques --- p.2 / Chapter §1.3 --- Implementation and Preliminaries --- p.4 / Chapter Chapter 2 --- Generating Random Points on the N-sphere --- p.6 / Chapter §2.1 --- Methods --- p.6 / Chapter §2.2 --- Comparison of Methods --- p.10 / Chapter Chapter 3 --- Generating Variates from Non-uniform Distributions on the Circle --- p.14 / Chapter §3.1 --- Introduction --- p.14 / Chapter §3.2 --- Methods for Circular Distributions --- p.15 / Chapter Chapter 4 --- Generating Variates from Non-uniform Distributions on the Sphere --- p.28 / Chapter §4.1 --- Introduction --- p.28 / Chapter §4.2 --- Methods for Spherical Distributions --- p.29 / Chapter Chapter 5 --- Generating Variates from Non-uniform Distributions on the N-sphere --- p.56 / Chapter §5.1 --- Introduction --- p.56 / Chapter §5.2 --- Methods for Higher Dimensional Spherical Distributions --- p.56 / Chapter Chapter 6 --- Summary and Discussion --- p.69 / References --- p.72 / Appendix 1 --- p.77 / Appendix 2 --- p.98

by Chi-van Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 71-72). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- The Model and the Bayes risk --- p.7 / Chapter § 2.1 --- The Model / Chapter § 2.2 --- The Bayes risk / Chapter Chapter 3 --- The Algorithm --- p.16 / Chapter § 3.1 --- A finite algorithm / Chapter § 3.2 --- The Number Theoretical Method for Optimization / Chapter § 3.2.1 --- NTMO / Chapter § 3.2.2 --- SNTMO / Chapter Chapter 4 --- Quadratic Loss Function --- p.26 / Chapter §4.1 --- The Bayes risk / Chapter § 4.2 --- An optimal plan / Chapter § 4.3 --- Numerical Examples / Chapter Chapter 5 --- Conclusions and Comments --- p.42 / Chapter § 5.1 --- Comparison between various plans / Chapter § 5.2 --- Sensitivity Analysis / Chapter § 5.3 --- Further Developments / Tables --- p.46 / Appendix A --- p.60 / Appendix B --- p.65 / References --- p.71

Au Siu Chun Brian. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 54-57). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Related sampling methods --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Gibbs sampler --- p.4 / Chapter 2.3 --- Importance sampling --- p.5 / Chapter 2.4 --- Sampling-importance resampling (SIR) --- p.7 / Chapter 2.5 --- Inverse Bayes formulae sampling (IBF sampling) --- p.10 / Chapter 3 --- Resampling weights in the SIR algorithm --- p.13 / Chapter 3.1 --- Resampling weights --- p.13 / Chapter 3.2 --- Problem in IBF sampling --- p.18 / Chapter 3.3 --- Adaptive finite mixture of distributions --- p.18 / Chapter 3.4 --- Allowing general distribution of 9 --- p.21 / Chapter 3.5 --- Examples and graphical comparison --- p.24 / Chapter 4 --- Resampling weight in Gibbs sampling --- p.32 / Chapter 4.1 --- Introduction --- p.32 / Chapter 4.2 --- Use Gibbs sampler to obtain ISF --- p.33 / Chapter 4.3 --- How many iterations? --- p.36 / Chapter 4.4 --- Applications --- p.41 / Chapter 4.4.1 --- The genetic linkage model --- p.41 / Chapter 4.4.2 --- Example --- p.43 / Chapter 4.4.3 --- The probit binary regression model --- p.44 / Chapter 5 --- Conclusion and discussion --- p.49 / Appendix A: Exact bias of the SIR --- p.52 / References --- p.54