Doctor of Philosophy (Ph.D.)
Permanent URI for this collectionhttp://192.248.9.226/handle/123/13838
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- item: Thesis-Full-textModeling weekly rainfall in Colombo city(2020) Silva HPTN; Peiris TSGModeling weekly rainfall has become a demanding assignment due to the complexity of rainfall pattern. Accurate inferences on weekly rainfall prediction facilitate to fill the noticeable gap with respect to the climate monitoring to reduce the climate stress in the country. However, relatively, few measures have been taken to perform the modeling of rainfall in the context of long memory. This study therefore, provides an assessment of such a phenomenon by fitting a novel time series models to weekly rainfall. As the weekly rainfall exhibits the blend features of long memory and time dependence variance, various class of long memory models were fitted by accounting the heteroskedasticity. The best fitted model developed is ARFIMA-GARCH for deseasonalized data. The model was trained using weekly rainfall data from 1990 to 2014 and validated using data from 2015 to 2017 in Colombo city, obtained from the Department of Meteorology, Sri Lanka. The exact maximum likelihood estimation method was utilized to estimate model parameters. For the evaluation of the suitability of the method for parameter estimation, Monte Carlo simulations were carried out with various non seasonally and seasonally fractionally differenced parameter values along with the variance model parameters. The forecasting performance of the five types of long memory models developed was evaluated based on the novel index developed using absolute error for an independent data set in addition to the classical indicators. The rainfall percentiles with the 95% confidence intervals were also developed by exploring temporal variability of weekly rainfall based on parametric approach and bootstrapping approach. It was found that the high likelihood to form extreme rainfall events during beginning of South West Monson (SWM) (30th April to 10th June) and during withdrawal of SWM rainfall (17th-30th September) as well as with the time span from 8th October to 11th November during Second Inter Monsoon (SIM) rainfall. Based on the real coverage probabilities which derived using bootstrap calibration, it was found that there is a discrepancy of the nominal and calculated coverage probabilities of the 95% confidence intervals of rainfall percentiles. The deviation of the normality of the fitted distribution with the small size of sample could be a reason for the such a disparity. The novel long range dependency model is recommended to be used in forecasting weekly rainfall in Colombo city in Sri Lanka since the forecasting performance of the new model is not much diluted with the increase of the forecasting length. The study highlights various challenges for applied statisticians in modeling weekly rainfall.
- item: Thesis-AbstractSemi-elliptical exponentially weighted moving average scheme for jointly monitoring mean and variance of Gaussian processesRazmy, AM; Peiris, TSGShewhart, cumulative sum and exponentially weighted moving average control charts were introduced for monitoring process mean. These charts were subsequently used for monitoring process variance. Later, it was realized that process monitoring is a bivariate problem and several joint monitoring scheme for process mean and variance were introduced by many authors. The challenge in the advanced joint monitoring scheme is that it should be sensitive for both small and larger changes either in process mean, variance or both. In this thesis, a new advanced joint monitoring scheme for process mean and variance called semi-elliptical exponentially weighted moving average scheme is proposed for Gaussian processes with its design procedure for the industry. The performance of this new scheme is compared with the joint monitoring schemes suggested by other authors using a new comparison index proposed in this thesis. Application of this new scheme is tested with real and simulated data sets. Most frequently, this new scheme detected various magnitudes ofshifts in mean and variance quicker than any other schemes. In overall, the new scheme developed in this study performs better than the existing schemes with some limitations when the shift in mean, variance or both is large. A big advantage ofthis new scheme is, the design parameters are independent ofsample size. As this scheme use the standardized mean and variance, this scheme can be used to monitor several parameters at a time in a single display. Unlike most ofthe joint monitoring scheme, this new scheme takes the drop in variance as the desirable state when the mean is on target. Therefore this scheme can be recommended for advanced joint monitoring of process mean and variance. The new methodology is very useful for many industrial applications. Furthermore improvements are suggested on this scheme to monitor multi quality parameters simultaneously.
- item: Thesis-AbstractShort term forecasting of dry spells in dry zone of Sri Lanka(2014-08-07) Mathugama, SC; Peiris, TSGDroughts and dry spells are a recurrent feature of the natural climate in the dry zone of Sri Lanka. The unpredictable pattern of dry spells cause significant damages to the agricultural system, livelihood of people and the economy of the country. This research was initiated to investigate the temporal and spatial variability of the starting time and the lengths of dry spells in the dry zone (DZ) of Sri Lanka using daily rainfall data (1950-2005) in 11 rain gauge locations and to explore the possibility of forecasting properties of critical dry spells. A review on statistical anlysis on dry spells noted that no studies were reported to predict the starting date or length of dry spells. The mean number of dry spells (≥ 7 dry days) per year, irrespective of locations, was 12 while the duration varied from 15 to 23 days with a mean of 19 days. The four longest dry spells within a year according to the time of occurrence were considered as critical dry spells. The mean lengths of such critical dry spells in the dry zone were 31, 33, 38 and 33 days respectively. The mean length of the critical dry spell increased from the first to the fourth in some locations while it decreased in some locations. In a few locations the longest spell occurred during the middle of the year, i.e. the third spell. Based on the results obtained on the temporal and spatial variability of critical dry spells, climate charts were developed to be used by the decision makers in the respective locations. Linear and non linear regression with or without autoregressive error models (p<0.05) were developed to forecast the starting dates of second, third and fourth critical dry spells separately for all locations. Validity of models were confirmed using various statistical indicators and they were also validated using an independant data set ( 2000-2005). It was not possible to develop standard models for the four critical dry spell length series separately. Thus one critical length series was formed by pooling all four series for a given location. New types of models known as non linear bilinear type with one, two or three customer-specific input variables were developed for each location separately. A new approach was developed to identify customer-specific input variables using the same series. The prediction performance of the proposed models was demonstrated using a real data set of 12 individual points. The results obtained in this study will be helpful in minimizing unexpected damage due to droughts and will help effective and efficient planning for farmers, irrigation engineers, coconut growers, policy makers and researchers.
- item: Thesis-AbstractApplication of random field linear model for quality improvement in product design(6/11/2011) Kanthasay, S; Gunathilake, PD; Dayananda, RAThe quality revolution of the late 80' s and 90' s led to researches in quality improvement in product and process designs. Taguchi's methodology for quality improvement called robust parameter design gained the interest of practitioners working in industry in quality improvement. Several approaches proposed as alternative to Taguchi's method embraced the important aspects of parameter design and this resulted in a collection of alternatives to Taguchi approach. Some of these alternatives highlighted the use of response surface methodology for quality improvement in engineering designs. Computer simulation modeling is an important part of engineering design. Running simulators to obtain observations for analysis are very often expensive. Some designs may require several simulator runs to find the appropriate settings of the design parameters. So statistical models are used as surrogates of the computer simulation models for analysis and design optimization. In robust engineering design, the parameter settings of the engineering designs are sought, so that the designed product will be insensitive to the effects of noise factors such as statistical fluctuations in the design parameters or external noise factors humidity that may affect a product's performance. The modeling approach used in this thesis, models the response from the computer simulation model using the Random Field Linear Model. This model is a multi-dimensional spatial linear model with structure in the covariance function. The predictor is used for further statistical analysis. The fitting of this model involves the estimation of covariance parameters. The methods of estimation of model parameters and model building are also described. It IS also show that for particular values of the correlation parameters, the model approximates to a multinomial model in the predictor variables. Latin hypercube sampling design is used for sampling design points for model building and for exploratory data analysis. This design is easy to generate and is found to be useful in multi-level, multi-factor experiments. The LHS designs have better statistical properties for estimation of main effects, interaction effects than simple random sampling designs. The use of Random Field Linear Model and Latin Hypercube Sampling for modeling and analysis in robust parameter design is illustrated with observations from circuit simulation models. The effect of using prior information on the mean with RFLM is also investigated.