Academic literature on the topic 'Quality control – Statistical methods'

Much attention has been directed at off-line quality control techniques in recent literature. This study is a refinement of and an enhancement to one technique, the Taguchi Method, for determining the optimum setting of design parameters in a product or process. In place of the signal-to-noise ratio, the mean square error (MSE) for each quality characteristic of interest is used. Polynomial models describing mean response and variance are fit to the observed data using statistical methods. The settings for the design parameters are determined by minimizing a statistical model. The model uses a multicriterion objective consisting of the MSE for each quality characteristic of interest. Minimum bias central composite designs are used during the data collection step to determine the settings of the parameters where observations are to be taken. Included is the development of minimum bias designs for various cases. A detailed example is given.

Assignment (MSc)--Stellenbosch University, 2004.<br>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.<br>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.

Quality oriented management systems and methods have become the dominant business and governance paradigm. From this perspective, satisfying customers’ expectations by supplying reliable, good quality products and services is the key factor for an organization and even government. During recent decades, Statistical Quality Control (SQC) methods have been developed as the technical core of quality management and continuous improvement philosophy and now are being applied widely to improve the quality of products and services in industrial and business sectors. Recently SQC tools, in particular quality control charts, have been used in healthcare surveillance. In some cases, these tools have been modified and developed to better suit the health sector characteristics and needs. It seems that some of the work in the healthcare area has evolved independently of the development of industrial statistical process control methods. Therefore analysing and comparing paradigms and the characteristics of quality control charts and techniques across the different sectors presents some opportunities for transferring knowledge and future development in each sectors. Meanwhile considering capabilities of Bayesian approach particularly Bayesian hierarchical models and computational techniques in which all uncertainty are expressed as a structure of probability, facilitates decision making and cost-effectiveness analyses. Therefore, this research investigates the use of quality improvement cycle in a health vii setting using clinical data from a hospital. The need of clinical data for monitoring purposes is investigated in two aspects. A framework and appropriate tools from the industrial context are proposed and applied to evaluate and improve data quality in available datasets and data flow; then a data capturing algorithm using Bayesian decision making methods is developed to determine economical sample size for statistical analyses within the quality improvement cycle. Following ensuring clinical data quality, some characteristics of control charts in the health context including the necessity of monitoring attribute data and correlated quality characteristics are considered. To this end, multivariate control charts from an industrial context are adapted to monitor radiation delivered to patients undergoing diagnostic coronary angiogram and various risk-adjusted control charts are constructed and investigated in monitoring binary outcomes of clinical interventions as well as postintervention survival time. Meanwhile, adoption of a Bayesian approach is proposed as a new framework in estimation of change point following control chart’s signal. This estimate aims to facilitate root causes efforts in quality improvement cycle since it cuts the search for the potential causes of detected changes to a tighter time-frame prior to the signal. This approach enables us to obtain highly informative estimates for change point parameters since probability distribution based results are obtained. Using Bayesian hierarchical models and Markov chain Monte Carlo computational methods, Bayesian estimators of the time and the magnitude of various change scenarios including step change, linear trend and multiple change in a Poisson process are developed and investigated. The benefits of change point investigation is revisited and promoted in monitoring hospital outcomes where the developed Bayesian estimator reports the true time of the shifts, compared to priori known causes, detected by control charts in monitoring rate of excess usage of blood products and major adverse events during and after cardiac surgery in a local hospital. The development of the Bayesian change point estimators are then followed in a healthcare surveillances for processes in which pre-intervention characteristics of patients are viii affecting the outcomes. In this setting, at first, the Bayesian estimator is extended to capture the patient mix, covariates, through risk models underlying risk-adjusted control charts. Variations of the estimator are developed to estimate the true time of step changes and linear trends in odds ratio of intensive care unit outcomes in a local hospital. Secondly, the Bayesian estimator is extended to identify the time of a shift in mean survival time after a clinical intervention which is being monitored by riskadjusted survival time control charts. In this context, the survival time after a clinical intervention is also affected by patient mix and the survival function is constructed using survival prediction model. The simulation study undertaken in each research component and obtained results highly recommend the developed Bayesian estimators as a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances as well as industrial and business contexts. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered. The empirical results and simulations indicate that the Bayesian estimators are a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered. The advantages of the Bayesian approach seen in general context of quality control may also be extended in the industrial and business domains where quality monitoring was initially developed.

Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2005.<br>Victoria Chen, Committee Co-Chair ; Kwok Tsui, Committee Chair ; Janet Allen, Committee Member ; David Goldsman, Committee Member ; Roshan Vengazhiyil, Committee Member. Vita. Includes bibliographical references.

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.

Statistical quality control (SQC) is one technique companies are using in the development of a Total Quality Management (TQM) culture. Shewhart control charts, a widely used SQC tool, rely on an underlying normal distribution of the data. Often data are skewed. The inverse Gaussian distribution is a probability distribution that is wellsuited to handling skewed data. This analysis develops models and a set of tools usable by practitioners for the constrained economic statistical design of control charts for inverse Gaussian distribution process centrality and process dispersion. The use of this methodology is illustrated by the design of an x-bar chart and a V chart for an inverse Gaussian distributed process.

We design, implement and evaluate statistical methods for managing uncertainty when consuming and provisioning resources in a federated computational market. To enable efficient allocation of resources in this environment, providers need to know consumers' risk preferences, and the expected future demand. The guarantee levels to offer thus depend on techniques to forecast future usage and to accurately capture and model uncertainties. Our main contribution in this thesis is threefold; first, we evaluate a set of techniques to forecast demand in computational markets; second, we design a scalable method which captures a succinct summary of usage statistics and allows consumers to express risk preferences; and finally we propose a method for providers to set resource prices and determine guarantee levels to offer. The methods employed are based on fundamental concepts in probability theory, and are thus easy to implement, as well as to analyze and evaluate. The key component of our solution is a predictor that dynamically constructs approximations of the price probability density and quantile functions for arbitrary resources in a computational market. Because highly fluctuating and skewed demand is common in these markets, it is difficult to accurately and automatically construct representations of arbitrary demand distributions. We discovered that a technique based on the Chebyshev inequality and empirical prediction bounds, which estimates worst case bounds on deviations from the mean given a variance, provided the most reliable forecasts for a set of representative high performance and shared cluster workload traces. We further show how these forecasts can help the consumers determine how much to spend given a risk preference and how providers can offer admission control services with different guarantee levels given a recent history of resource prices.<br>QC 20100909