This dissertation studies three classes of estimators for the asymptotic variance parameter of a stationary stochastic process. All estimators are based on the concept of data "re-use" and all transform the output process into functions of an approximate Brownian motion process. The first class of estimators consists folded standardized time series area and Cramér-von Mises (CvM) estimators. Detailed expressions are obtained for their expectation at folding levels 0 and 1; those expressions explain the puzzling increase in small-sample bias as the folding level increases. In addition, we use batching and linear combinations of estimators from different levels to produce estimators with significantly smaller variance. Finally, we obtain very accurate approximations of the limiting distributions of batched folded estimators. These approximations are used to compute confidence intervals for the mean and variance parameter of the underlying stochastic process. The second class --- folded overlapping area estimators --- are computed by averaging folded versions of the standardized time series corresponding to overlapping batches. We establish the limiting distributions of the proposed estimators as the sample size tends to infinity. We obtain statistical properties of these estimators such as bias and variance. Further, we find approximate confidence intervals for the mean and variance parameter of the process by approximating the theoretical distributions of the proposed estimators. In addition, we develop algorithms to compute these estimators with only order-of-sample-size work. The third class --- reflected area and CvM estimators --- are computed from reflections of the original sample path. We obtain the expected values and variance of individual estimators. We show that it is possible to obtain linear combinations of reflected estimators with smaller variance than the variance of each constituent estimator, often at no cost in bias. A quadratic optimization problem is solved to find an optimal linear combination of estimators that minimizes the variance of the linearly combined estimator. For all classes of estimators, we provide Monte Carlo examples to show that the estimators perform as well in practice as advertised by the theory.

Thesis (MScEng)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Reconfigurable Manufacturing Systems (RMSs) have the ability to reconfigure hardware and control resources at all of the functional and organizational levels. This allows for quick adjustment of production capacity and functionality in response to sudden changes in market or in regulatory requirements. This study evaluates the characteristics and operation of automated reconfigurable assembly lines using discrete event simulation. The assembly line uses a conveyor system which transports pallets to various machines to perform the assembly process. Different conveyor configurations are developed for the same assembly process using Simio simulation software. A part family consisting of five variants are assembled on the same assembly line with a large variation in the production quantities for each product. This requires the assembly system to be able to quickly adjust its functionality and capacity. Multi-objective optimization is performed on the models through the use of a Pareto exhaustive search experiment. The two contradicting objectives used are the throughput rate of the system and the average work in progress, with the aim of maximizing the former and minimizing the latter. From the Pareto exhaustive search experiment, a Pareto front is constructed showing which configuration is preferred under certain operation conditions. However it is concluded that the Pareto front can be tailored to fit the specific needs of the decision maker, depending on what the decision maker is willing to pay. An experiment that evaluates the effect of changing the conveyor speed is performed. It is established that under certain operating conditions, increasing the conveyor speed higher than the ceiling value will not improve the performance of the system. A production scenario was also developed which include different order sizes for each of the five parts of the part family. The configurations have to alter their capacities based on the order sizes to test which system performs the best under these operating conditions. For this experiment, the ramp-up time was of interest but the best system was chosen based on the combination of throughput rate and the average work in progress. From the results of the different experiments, it is recommended to first determine the maximum capacity and the operating logic before choosing one of the configurations. Once this is decided, the information gathered from the experiments can then be tailored for the decision maker to establish the best operating conditions for the chosen con guration. The developed simulation models are used as a Decision Support System for future research on the topic. It is recommended for future research to focus on using Automated Guided Vehicles (AGVs) instead of a conveyor system as transportation method. / AFRIKAANSE OPSOMMING: Herkonfigureerbare Vervaardigingstelsels (HVSs) het die vermoee om alle hardeware en beheer hulpbronne, op alle funksionele en organisatoriese vlakke te herkonfigureer. Dit maak dit moontlik vir vinnige verstellings aan produksie kapasiteit en funksionaliteit, indien daar 'n skielike verandering in die mark of wetgewing is. Hierdie studie evalueer die karakteristieke en werking van outomatiese herkon gureerbare monteerlyne met behulp van diskrete gebeurtenis simulasie. Die monteerlyne gebruik vervoerbande om pallette na verskeie masjiene te vervoer, sodat die parte aanmekaar gesit kan word. Simio simulasie sagteware is gebruik om verskillende vervoerband kon gurasies vir dieselfde monteringsproses te ontwikkel. 'n Part familie van vyf variante word op dieselfde monteerlyn aanmekaargesit. Daar is 'n groot variasie in die produksie hoeveelhede van elk van die vyf variante, dus moet die monteerlyne vinnig die kapasiteit en funksionaliteit kan aanpas. Multi-doelwitoptimering is toegepas op die modelle deur 'n Pareto alomvattende soek eksperiment uit te voer. Die twee teenstrydige doelwitte wat gebruik is, is die deurset tempo van die stelsel asook die gemiddelde werk-in-proses. Die doel is om die deurset tempo te maksimeer en terselfde tyd die gemiddelde werk-in-proses te minimeer. Die Pareto alomvattende soek eksperiment word verder gebruik om 'n Pareto front te skep wat uitwys watter vervoerband kon gurasies verkies word onder sekere bedryfstoestande. Die Pareto front kan egter aangepas word om die spesi eke behoeftes van die besluitnemer te pas. 'n Eksperiment is uitgevoer om die uitwerking van die vervoerbandspoed op die stelsel te toets. Resultate het getoon dat onder sekere bedryfstoestande die werkverrigting van die stelsel nie verbeter indien die spoed 'n maksimum grenswaarde oorskry nie. 'n Eksperiment wat 'n produksie scenario voorstel is ontwikkel waarin die vraag na die vyf part variante gevarieer word. Die vervoerband konfigurasies moet dan die kapasiteit aanpas gebaseer op die vraag na die parte. Die doel van die eksperiment is om te toets watter kon gurasie die beste vaar onder hierdie bedryfstoestande. Die tyd wat dit neem vir die stelsel om weer op dreef te kom na 'n verandering in kapasiteit is ondersoek in hierdie eksperiment, maar die beste stelsel is nog steeds gekies gebaseer op die kombinasie van deurset tempo en die gemiddelde werk-in-proses. Gegewe die resultate van die verskillende eksperimente, word dit voorgestel dat die besluitnemer eers die maksimum kapasiteit en die bedryfstoestande vasstel, voordat 'n vervoerband kon gurasie gekies word. Sodra dit besluit is, kan die inligting wat tydens die eksperimente ingesamel is, aangepas word om die beste bedryfstoestande vir die kon gurasie wat gekies is, vas te stel. Die simulasie modelle wat ontwikkel is word gebruik as 'n besluitnemingsondersteuningstelsel vir toekomstige navorsing oor die onderwerp. Dit word voorgestel dat toekomstige navorsing die moontlikheid van geoutomatiseerde begeleide voertuie (GBV), in plaas van vervoerbande as vervoermiddel, ondersoek.