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

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.

Visualisering av statistik är ett tydligt sätt att presentera data som annars kan ses som svår att tyda och analysera. Med hjälp av visualiseringar på webben kan man nå ut till många och det är ett smidigt sätt att ta med sig och dela med sig av information. Denna rapport bygger på ett experiment där olika JavaScriptbibliotek jämförs baserat på tiden det tar att rita ut diagram av olika storlekar och typer. Linjediagram, punktdiagram och stapeldiagram skapas med de olika biblioteken. Vilka bibliotek som jämförs väljs ut utifrån ett antal kriterier och Chart.js, Google Charts och Plotly.js är de som uppfyller alla krav. Undersökningar där utritningstiden mäts genomförs och resultaten visar att Chart.js är snabbast på att rita ut diagram i de flesta mätningarna. Det finns signifikanta skillnader mellan alla diagrammätningar förutom mellan Linjediagram 2 skapat med Chart.js och Linjediagram 2 skapat med Plotly.js samt Plotly.js Stapeldiagram 1 och Plotly.js Stapeldiagram 5. Mätningarna visar också att diagram som baseras på större datamängd, i de flesta fall, också har längre utritningstid än diagram baserade på mindre datamängd.

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.

This study uses simulation to examine differences between fixed sampling interval (FSI) and variable sampling interval (VSI) Shewhart X-bar control charts for processes that produce positively autocorrelated data. The influence of sample size (1 and 5), autocorrelation parameter, shift in process mean, and length of time between samples is investigated by comparing average time (ATS) and average number of samples (ANSS) to produce an out of control signal for FSI and VSI Shewhart X-bar charts. These comparisons are conducted in two ways: control chart limits pre-set at ±3σ_x / √n and limits computed from the sampling process. Proper interpretation of the Shewhart X-bar chart requires the assumption that observations are statistically independent; however, process data are often autocorrelated over time. Results of this study indicate that increasing the time between samples decreases the effect of positive autocorrelation between samples. Thus, with sufficient time between samples the assumption of independence is essentially not violated. Samples of size 5 produce a faster signal than samples of size 1 with both the FSI and VSI Shewhart X-bar chart when positive autocorrelation is present. However, samples of size 5 require the same time when the data are independent, indicating that this effect is a result of autocorrelation. This research determined that the VSI Shewhart X-bar chart signals increasingly faster than the corresponding FSI chart as the shift in the process mean increases. If the process is likely to exhibit a large shift in the mean, then the VSI technique is recommended. But the faster signaling time of the VSI chart is undesirable when the process is operating on target. However, if the control limits are estimated from process samples, results show that when the process is in control the ARL for the FSI and the ANSS for the VSI are approximately the same, and exceed the expected value when the limits are fixed.

Disertaciniame darbe pasitelkiant kompleksinė vertinimo metodika analizuojami karinių aeronavigacinių žemėlapių ženklai, ženklų sistemos ir užrašai. Šios analizės pagrindu tobulinami sutartiniai ženklai, optimizuojamas žemėlapio turinys ir pateikiama vieningos Lietuvos karo aeronavigacinių duomenų bazės struktūrą. Kompleksiškai parengta tyrimo metodika rėmėsi Lietuvoje nusistovėjusia teminių žemėlapių ir ženklų kartosemiotine vertinimo praktika. Įvairūs ženklų ir užrašų vertinimo aspektai leido tiksliai ir nuodugniai atlikti aeronavigacinių ženklų ir užrašų vertinimą. Analizės metu nustatyta kad ne visi karinių aeronavigacinių žemėlapių ženklai atitinka kartosemiotikos reikalavimų, todėl galėtu būti keičiami. Karinių aeronavigacinių ženklų analizė ir tobulinimas rėmėsi ankščiau vykdytais psichofiziologinio suvokimo tyrimais bei išvadomis. Siūlomi nauji aeronavigacinių žemėlapių ženklai pilnai atitinka psichofiziologinių tyrimų rekomendacijas. Išnagrinėjus karinius NATO šalių aeronavigacinius žemėlapius ir atsižvelgiant į vieningą žemėlapių sistemą, klasifikacijos požymius ir atitinkamus klasifikacijų reikalavimus, darbe pateikta apibendrinta NATO šalių karinių aeronavigacinių žemėlapių klasifikacija, kurioje yra numatyta galimybė sugebėti integruoti naujai atsirandančių žemėlapių grupes. / This dissertation provides an overall in-depth use evaluation methodology that assists in analysing of military aeronautical maps, sign system and records. On the basis of this research of signs and their conventions an optimised map and content of a unified Lithuanian military aeronautical database structures is suggested for improvement. Methodically prepared research was collected and based on already established and consistent thematic maps, signs and carto-semiotic assessment practices already used in Lithuania. A variety of illustrations and aspect assessments established an accurate and in-depth aeronautical value of signs and their practices. The analysis highlighted that not all carto-semiotic characters and signs of military aeronautical charts meet the criteria, and therefore could be changed. Previous military aeronautical sign analysis and their improvements were based on exercises of psycho-physiological studies of perception with their conclusions. Therefore a set of new aeronautical map characters that fully comply with psycho-physiological research recommendations are proposed. Through the examination of NATO's military aeronautical maps, charts and a look at a unified system of classifications, and its requirements, the dissertation summarises the overall work of the NATO’s military aeronautical maps and their classifications, which provides the possibility of integration for the newly emerging sign and map groups.

Disertaciniame darbe pasitelkiant kompleksinė vertinimo metodika analizuojami karinių aeronavigacinių žemėlapių ženklai, ženklų sistemos ir užrašai. Šios analizės pagrindu tobulinami sutartiniai ženklai, optimizuojamas žemėlapio turinys ir pateikiama vieningos Lietuvos karo aeronavigacinių duomenų bazės struktūrą. Kompleksiškai parengta tyrimo metodika rėmėsi Lietuvoje nusistovėjusia teminių žemėlapių ir ženklų kartosemiotine vertinimo praktika. Įvairūs ženklų ir užrašų vertinimo aspektai leido tiksliai ir nuodugniai atlikti aeronavigacinių ženklų ir užrašų vertinimą. Analizės metu nustatyta kad ne visi karinių aeronavigacinių žemėlapių ženklai atitinka kartosemiotikos reikalavimų, todėl galėtu būti keičiami. Karinių aeronavigacinių ženklų analizė ir tobulinimas rėmėsi ankščiau vykdytais psichofiziologinio suvokimo tyrimais bei išvadomis. Siūlomi nauji aeronavigacinių žemėlapių ženklai pilnai atitinka psichofiziologinių tyrimų rekomendacijas. Išnagrinėjus karinius NATO šalių aeronavigacinius žemėlapius ir atsižvelgiant į vieningą žemėlapių sistemą, klasifikacijos požymius ir atitinkamus klasifikacijų reikalavimus, darbe pateikta apibendrinta NATO šalių karinių aeronavigacinių žemėlapių klasifikacija, kurioje yra numatyta galimybė sugebėti integruoti naujai atsirandančių žemėlapių grupes. / This dissertation provides an overall in-depth use evaluation methodology that assists in analysing of military aeronautical maps, sign system and records. On the basis of this research of signs and their conventions an optimised map and content of a unified Lithuanian military aeronautical database structures is suggested for improvement. Methodically prepared research was collected and based on already established and consistent thematic maps, signs and carto-semiotic assessment practices already used in Lithuania. A variety of illustrations and aspect assessments established an accurate and in-depth aeronautical value of signs and their practices. The analysis highlighted that not all carto-semiotic characters and signs of military aeronautical charts meet the criteria, and therefore could be changed. Previous military aeronautical sign analysis and their improvements were based on exercises of psycho-physiological studies of perception with their conclusions. Therefore a set of new aeronautical map characters that fully comply with psycho-physiological research recommendations are proposed. Through the examination of NATO's military aeronautical maps, charts and a look at a unified system of classifications, and its requirements, the dissertation summarises the overall work of the NATO’s military aeronautical maps and their classifications, which provides the possibility of integration for the newly emerging sign and map groups.

Notre thèse analyse la production artistique de Michael Jackson, en termes commerciaux, stylistiques, visuels, en ciblant les dynamiques et tensions raciales qui innervent ses strates narratives. La première partie porte sur les classements coloristes et la posture ubiquitaire des opus jacksoniens, recontextualisés au sein de la société américaine et de l’industrie du disque racialisée. La deuxième partie analyse les composantes éclectiques et stylistiques de la pop jacksonienne et la manière dont les conventions employées se situent et opèrent face aux constructions catégoristes existantes. Enfin, la troisième partie traite des dynamiques et tensions raciales portées par les productions visuelles (vidéos, image artistique) et les textes, comme autant de fondements identitaires de son potentiel crossover et fédérateur auprès d’un public international et transracial. / Our thesis analyses Michael Jackson’s artistic production, through marketing, stylistic and visual aspects, targeting racial dynamics and tensions which invigorate its narrative layers. The first part is about the colorist charts and the ubiquitous posture of jacksonian opuses, recontextualized against american society and racialized record industry. The second part analyzes the stylistic eclectism of Jackson’s pop music and the way he uses the conventions from the musical and racial categorization. Finally, the third part is about racial dynamics and tensions carried by visual productions (video clip, artistic image) and lyrics, as elements of identity fundations of Jackson’s crossover and his federative appeal to an international and transracial audience.