In recent years, variable sampling interval (VSI) control charts have been intensively investigated. In contrast to traditional fixed sampling interval (FSI) control charts, VSI charts vary the sampling interval as a function of the data. VSI charts detect many process changes faster than their FSI counterparts. A disadvantage, however, of VSI charts as recently formulated is that the advance prediction of sampling times is impossible for more than the next sample. A control chart is proposed which applies a sequential probability ratio test (SPRT) at fixed sampling intervals, the SPRT chart, to monitor the mean of a process with a normal distribution. A natural modification of the SPRT chart, the SPRT chart with sampling at fired times (SFT), is also proposed in which samples are always taken at pre-specified, equally spaced fixed times, with additional samples taken between these times as indicated by the data. A third control chart is introduced as a generalization of the VSI cumulative sum (CUSUM) chart that uses two sampling intervals, called the universal CUSUM (UC) chart, in order to address the need for a general framework for the study of control charts that are equivalent to a sequence of SPRT’s. The UC chart can also be viewed as a generalization of the SPRT chart. The integral equation approach is adapted for the evaluation of properties of both the unmodified and modified with SFT versions of the SPRT chart, such as average time to signal (ATS), steady state ATS (SSATS), and average number of observations to signal (ANOS). After comparisons are performed within the general framework of the UC chart, the unmodified SPRT chart is found to be more efficient than both the FSI and VSI X charts and the FSI CUSUM chart, though very similar in efficiency to the VSI CUSUM chart. The modified SPRT chart with SFT is found to be more efficient than all five of the other control charts, including its unmodified version and the VSI CUSUM chart. General guidelines are provided for the design of both versions of the SPRT chart. / Ph. D.

The standard Shewhart control chart for monitoring process stability is generalized by selecting a point in time at which the distance between the control limits is reduced. Three cost models are developed to describe the total cost per unit time of monitoring the mean of a process using both the standard and the generalized Shewhart control chart. The cost models are developed under the assumption that the quality characteristic of interest is normally distributed with known and constant variance. In the development of the first model, the negative exponential distribution is employed to model the time to process shift. Then, the uniform distribution and the Weibull distribution are used for the same purpose in the second and the third model, respectively. The motivation for this effort is to increase chart sensitivity to small but anticipated shifts in the process average. Cost models are constructed to allow the optimal choice of change over time and the best values for the initial and adjusted control limit values. The cost models are analyzed to determine the optimal control chart parameters including those associated with both the standard and the generalized control chart. The models are also used to provide a comparison with conventional implementation of the control chart. It is shown that the proposed cost models are efficient and economical. Figures and tables are provided to aid in the design of models for both the standard and the generalized Shewhart control chart. / Ph. D.

Control charts based on cumulative gauging scores rely on gauge scoring systems used for transforming actual observations into integer gauging scores. In some cases, the gauging scores are easy to obtain by using a mechanical device such as in the go-no-go inspection process. Thus, accurate measurements of selected quality characteristics are not necessary. Also, different control purposes can be achieved p by using different scoring systems. Cumulative gauging score charts based on two pairs of gauges are proposed to control the process mean or the standard deviation by either gauging one or several observations. Both random walk and cusum type cumulative gauging score charts are used. For controlling the process mean and standard deviation at the same time, a cusum type and a two-dimensional random walk type procedure are proposed. A gauging scheme can be applied to multivariate quality control by gauging either x² or T² statistics. A simple multivariate control chart which is based on the multivariate sign score vector is also proposed. The exact run length distribution of these cumulative gauging score charts can be obtained by formulating the procedures as Markov chain processes. For some procedures, the average run length (ARL) can be obtained in a closed form expression by solving a system of difference equations with appropriate boundary conditions. Comparisons based on the ARL show that the cumulative gauging score charts can detect small shifts in the quality characteristic more quickly than the Shewhart type X-chart. The efficiency of the cusum type gauging score chart is close to the regular CUSUM chart. The random walk type gauging score chart is more robust than the Shewhart and CUSUM charts to observations which have heavy a tailed distribution or which are serially correlated. For multivariate quality control. A procedure based on gauging the x² statistic has better performance than the x² chart. Also, a new multivariate control chart procedure which is more robust to the misspecification of the correlation than the x² chart is proposed. / Ph. D.

Most control charts monitor only one quality characteristic. There are, however, many manufactured products for which good quality requires meeting specifications in more than one physical characteristic. Typical practice when dealing with multiple quality characteristics is to take a separate sample for each characteristic and then create individual univariate control charts which are independently monitored. This method can result in errors due to not accounting for the effects of correlation. In order to avoid these errors, an alternate approach to multivariate quality control problems is proposed and studied here. The original problem is converted into a univariate problem by using the following transformation: y=Σ a_ix_i i where αi = weighting coefficient for the i^th quality characteristic X_i = represents the i^th quality characteristic This transformation retains sensitivity to changes in the original quality variables. The resulting univariate quality control model takes into account the sampling error probabilities for each of several candidate hypotheses. The probabilities of correctly diagnosing process shifts when an out-of-control state occurs are calculated and tabulated as are the probabilities that the model will signal when an out-of-control state occurs. / Master of Science

A common problem encountered in practice is determining when it is appropriate to change the sampling interval for control charts. This thesis examines this problem for Shewhart X̅ charts. Duncan's economic model (1956) is used to develop a relationship between the most appropriate sampling interval and the present rate of"disturbances,” where a disturbance is a shift to an out of control state. A procedure is proposed which switches the interval to convenient values whenever a shift in the rate of disturbances is detected. An example using simulation demonstrates the procedure. / M.S.

Assignment (MSc)--Stellenbosch University, 2004. / ENGLISH ABSTRACT: The design of control charts refers to the selection of the parameters implied, including the sample size n, control limit width parameter k, and the sampling interval h. The design of the X -control chart that is based on economic as well as statistical considerations is presently one of the more popular subjects of research. Two assumptions are considered in the development and use of the economic or economic statistical models. These assumptions are potentially critical. It is assumed that the time between process shifts can be modelled by means of the exponential distribution. It is further assumed that there is only one assignable cause. Based on these assumptions, economic or economic statistical models are derived using a total cost function per unit time as proposed by a unified approach of the Lorenzen and Vance model (1986). In this approach the relationship between the three control chart parameters as well as the three types of costs are expressed in the total cost function. The optimal parameters are usually obtained by the minimization of the expected total cost per unit time. Nevertheless, few practitioners have tried to optimize the design of their X -control charts. One reason for this is that the cost models and their associated optimization techniques are often too complex and difficult for practitioners to understand and apply. However, a user-friendly Excel program has been developed in this paper and the numerical examples illustrated are executed on this program. The optimization procedure is easy-to-use, easy-to-understand, and easy-to-access. Moreover, the proposed procedure also obtains exact optimal design values in contrast to the approximate designs developed by Duncan (1956) and other subsequent researchers. Numerical examples are presented of both the economic and the economic statistical designs of the X -control chart in order to illustrate the working of the proposed Excel optimal procedure. Based on the Excel optimization procedure, the results of the economic statistical design are compared to those of a pure economic model. It is shown that the economic statistical designs lead to wider control limits and smaller sampling intervals than the economic designs. Furthermore, even if they are more costly than the economic design they do guarantee output of better quality, while keeping the number of false alarm searches at a minimum. It also leads to low process variability. These properties are the direct result of the requirement that the economic statistical design must assure a satisfactory statistical performance. Additionally, extensive sensitivity studies are performed on the economic and economic statistical designs to investigate the effect of the input parameters and the effects of varying the bounds on, a, 1-f3 , the average time-to-signal, ATS as well as the expected shift size t5 on the minimum expected cost loss as well as the three control chart decision variables. The analyses show that cost is relatively insensitive to improvement in the type I and type II error rates, but highly sensitive to changes in smaller bounds on ATS as well as extremely sensitive for smaller shift levels, t5 . Note: expressions like economic design, economic statistical design, loss cost and assignable cause may seen linguistically and syntactically strange, but are borrowed from and used according the known literature on the subject. / AFRIKAANSE OPSOMMING: Die ontwerp van kontrolekaarte verwys na die seleksie van die parameters geïmpliseer, insluitende die steekproefgrootte n , kontrole limiete interval parameter k , en die steekproefmterval h. Die ontwerp van die X -kontrolekaart, gebaseer op ekonomiese sowel as statistiese oorwegings, is tans een van die meer populêre onderwerpe van navorsing. Twee aannames word in ag geneem in die ontwikkeling en gebruik van die ekonomiese en ekonomies statistiese modelle. Hierdie aannames is potensieel krities. Dit word aanvaar dat die tyd tussen prosesverskuiwings deur die eksponensiaalverdeling gemodelleer kan word. Daar word ook verder aangeneem dat daar slegs een oorsaak kan wees vir 'n verskuiwing, of te wel 'n aanwysbare oorsaak (assignable cause). Gebaseer op hierdie aannames word ekonomies en ekonomies statistiese modelle afgelei deur gebruik te maak van 'n totale kostefunksie per tydseenheid soos voorgestel deur deur 'n verenigende (unified) benadering van die Lorenzen en Vance-model (1986). In hierdie benadering word die verband tussen die drie kontrole parameters sowel as die drie tipes koste in die totale kostefunksie uiteengesit. Die optimale parameters word gewoonlik gevind deur die minirnering van die verwagte totale koste per tydseenheid. Desnieteenstaande het slegs 'n minderheid van praktisyns tot nou toe probeer om die ontwerp van hulle X -kontrolekaarte te optimeer. Een rede hiervoor is dat die kosternodelle en hulle geassosieerde optimeringstegnieke té kompleks en moeilik is vir die praktisyns om te verstaan en toe te pas. 'n Gebruikersvriendelike Excelprogram is egter hier ontwikkel en die numeriese voorbeelde wat vir illustrasie doeleindes getoon word, is op hierdie program uitgevoer. Die optimeringsprosedure is maklik om te gebruik, maklik om te verstaan en die sagteware is geredelik beskikbaar. Wat meer is, is dat die voorgestelde prosedure eksakte optimale ontwerp waardes bereken in teenstelling tot die benaderde ontwerpe van Duncan (1956) en navorsers na hom. Numeriese voorbeelde word verskaf van beide die ekonomiese en ekonomies statistiese ontwerpe vir die X -kontrolekaart om die werking van die voorgestelde Excel optimale prosedure te illustreer. Die resultate van die ekonomies statistiese ontwerp word vergelyk met dié van die suiwer ekomomiese model met behulp van die Excel optimerings-prosedure. Daar word aangetoon dat die ekonomiese statistiese ontwerpe tot wyer kontrole limiete en kleiner steekproefmtervalle lei as die ekonomiese ontwerpe. Al lei die ekonomies statistiese ontwerp tot ietwat hoër koste as die ekonomiese ontwerpe se oplossings, waarborg dit beter kwaliteit terwyl dit die aantal vals seine tot 'n minimum beperk. Hierbenewens lei dit ook tot kleiner prosesvartasie. Hierdie eienskappe is die direkte resultaat van die vereiste dat die ekonomies statistiese ontwerp aan sekere statistiese vereistes moet voldoen. Verder is uitgebreide sensitiwiteitsondersoeke op die ekonomies en ekonomies statistiese ontwerpe gedoen om die effek van die inset parameters sowel as van variërende grense op a, 1- f3 , die gemiddelde tyd-tot-sein, ATS sowel as die verskuiwingsgrootte 8 op die minimum verwagte kosteverlies sowel as die drie kontrolekaart besluitnemingsveranderlikes te bepaal. Die analises toon dat die totale koste relatief onsensitief is tot verbeterings in die tipe I en die tipe II fout koerse, maar dat dit hoogs sensitief is vir wysigings in die onderste grens op ATS sowel as besonder sensitief vir klein verskuiwingsvlakke, 8. Let op: Die uitdrukkings ekonomiese ontwerp (economic design), ekonomies statistiese ontwerp (economic statistical design), verlies kostefunksie (loss cost function) en aanwysbare oorsaak (assignable cause) mag taalkundig en sintakties vreemd voordoen, maar is geleen uit, en word so gebruik in die bekende literatuur oor hierdie onderwerp.

When the nonconformities are independent, a multivariate control chart for nonconformities called a demerit control chart using a distribution approximation technique called an Edgeworth Expansion, is proposed. For a demerit control chart, an exact control limit can be obtained in special cases, but not in general. A proposed demerit control chart uses an Edgeworth Expansion to approximate the distribution of the demerit statistic and to compute the demerit control limits. A simulation study shows that the proposed method yields reasonably accurate results in determining the distribution of the demerit statistic and hence the control limits, even for small sample sizes. The simulation also shows that the performances of the demerit control chart constructed using the proposed method is very close to the advertised for all sample sizes. Since the demerit control chart statistic is a weighted sum of the nonconformities, naturally the performance of the demerit control chart will depend on the weights assigned to the nonconformities. The method of how to select weights that give the best performance for the demerit control chart has not yet been addressed in the literature. A methodology is proposed to select the weights for a one-sided demerit control chart with and upper control limit using an asymptotic technique. The asymptotic technique does not restrict the nature of the types and classification scheme for the nonconformities and provides an optimal and explicit solution for the weights. In the case presented so far, we assumed that the nonconformities are independent. When the nonconformities are correlated, a multivariate Poisson lognormal probability distribution is used to model the nonconformities. This distribution is able to model both positive and negative correlations among the nonconformities. A different type of multivariate control chart for correlated nonconformities is proposed. The proposed control chart can be applied to nonconformities that have any multivariate distributions whether they be discrete or continuous or something that has characteristics of both, e.g., non-Poisson correlated random variables. The proposed method evaluates the deviation of the observed sample means from pre-defined targets in terms of the density function value of the sample means. The distribution of the control chart test statistic is derived using an approximation technique called a multivariate Edgeworth expansion. For small sample sizes, results show that the proposed control chart is robust to inaccuracies in assumptions about the distribution of the correlated nonconformities. / Graduation date: 2004

Tabular data is pervasive in the form of spreadsheets and relational databases. Although tables often describe multivariate data without explicit network semantics, it may be advantageous to explore the data modeled as a graph or network for analysis. Even when a given table design conveys some static network semantics, analysts may want to look at multiple networks from different perspectives, at different levels of abstraction, and with different edge semantics. This dissertation is motivated by the observation that a general approach for performing multi-dimensional and multi-level network-based visual analysis on multivariate tabular data is necessary. We present a formal framework based on the relational data model that systematically specifies the construction and transformation of graphs from relational data tables. In the framework, a set of relational operators provide the basis for rich expressive power for network modeling. Powered by this relational algebraic framework, we design and implement a visual analytics system called Ploceus. Ploceus supports flexible construction and transformation of networks through a direct manipulation interface, and integrates dynamic network manipulation with visual exploration for a seamless analytic experience.

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The objective of this research is to explore high-speed analog-to-digital converters (ADCs) using silicon-germanium (SiGe) heterojunction bipolar transistors (HBTs) for wireless digital receiver applications. The stringent requirements of ADCs for the high-performance next-generation wireless digital receiver include (1) low power, (2) low cost, (3) wide input signal bandwidth, (4) high sampling rate, and (5) medium to high resolution. The proposed research achieves the objective by implementing high-performance ADC's key building blocks and integrating these building blocks into a complete sigma-delta analog-to-digital modulator that satisfies the demanding specifications of next-generation wireless digital receiver applications. The scope of this research is divided into two main parts: (1) high-performance key building blocks of the ADC, and (2) high-speed sigma-delta analog-to-digital modulator. The research on ADC's building blocks includes the design of two high-speed track-and-hold amplifiers (THA) and two wide-bandwidth comparators operating at the sampling rate > 10 GS/sec with satisfying resolution. The research on high-speed sigma-delta analog-to-digital modulator includes the design and experimental characterization of a high-speed second-order low-pass sigma-delta modulator, which can operate with a sampling rate up to 20 GS/sec and with a medium resolution. The research is envisioned to demonstrate that the SiGe HBT technology is an ideal platform for the design of high-speed ADCs.