Statistically controlling processes

Imagine a chemical industry of some complexity, such as pol3rmer manufacturing. The engineers hired to plan and build the plant have to make sure that it will be capable of producing pol5uners with the characteristics required by its customers. To accomplish this they need to consider carefuUy all of the relevant variables — usually more than just a few — and project the plant so that these variables are kept under control. 

One of the most important variables used to control polymer production is viscosity. From time to time, a polymer sample is collected from the production line and sent to the laboratory, where its viscosity is measured. The values obtained in this way — or, more commonly, their averages — are systematically plotted as a function of time. If the process is completely under control, in the absence of crass or systematic errors, what kind of distribution should the points have  

You are right a normal distribution, for the individual observations, or Student s -distribution, for the averages. When the process is under control, its variability is only due to random errors, and for this reason its responses should follow a normal distribution or a distribution closely related to it. This is the basic principle of quality control — again, another consequence of the central limit theorem. 

In Fig. 2.13, which shows a histogram of these values, we see that their distribution is quite accurately represented by a normal distribution. This ideal situation is the dream of every production engineer. 

In practice, graphs such as Fig. 2.12 — called control charts — are traced point by point, in real time, by the production line personnel, and serve as an important tool to detect problems that could be perturbing the process. As each point is added, the graph is analyzed. Any anomalous 

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Setting reasonable specifications depends on the development of reliable test procedures and well-characterized reference materials for method development. Statistical control processes can be used to eliminate variations to reduce off-specification catalysts and contractual disputes. 

Westgard, J. O., and T. Groth. 1981. Design and evaluation of statistical control processes Application of a computer quality control simulator program. Clinical Chemistry 27 1536-1547. 

Variability analysis by Statistical Control Process and Functional Data Analysis. Case of study applied to power system harmonics... 

Abstract. Functional data appear in a multitude of industrial applications and processes. However, in many cases at present, such data continue to be studied from the conventional standpoint based on Statistical Process Control (SPC), losing the capacity of analyzing different aspects over the time. In this study is presented a Statistical Control Process based on functional data analysis to identify outliers or special causes of variability of harmonics appearing in power systems which can negatively impact on quality of electricity supply. The results obtained from the functional approach are compared with those obtained with conventional Statistical Process Control that has been done firstly. 

Control graphs and the concept of rational subgroups can be used successfully in the search and elimination of outliers in harmonics present in electrical systems, provided that the data set follows a normal distribution. When data do not follow a normal distribution. Functional Data Analysis can be utilized effectively in the detection of outliers, also contributing major advantages in the detection of specific variability compared to traditional techniques such as Statistical Control Process. The functional approach greatly enhances the capacity for analysis facilitating massive and systematic analysis of the data. 

Determine whether there is any evidence that the measurement process is not under statistical control at a = 0.05. 

The variance for the sample of ten tablets is 4.3. A two-tailed significance test is used since the measurement process is considered out of statistical control if the sample s variance is either too good or too poor. The null hypothesis and alternative hypotheses are... 

Control charts were originally developed in the 1920s as a quality assurance tool for the control of manufactured products.Two types of control charts are commonly used in quality assurance a property control chart in which results for single measurements, or the means for several replicate measurements, are plotted sequentially and a precision control chart in which ranges or standard deviations are plotted sequentially. In either case, the control chart consists of a line representing the mean value for the measured property or the precision, and two or more boundary lines whose positions are determined by the precision of the measurement process. The position of the data points about the boundary lines determines whether the system is in statistical control. 

Statistical Process Control. A properly miming production process is characterized by the random variation of the process parameters for a series of lots or measurements. The SPG approach is a statistical technique used to monitor variation in a process. If the variation is not random, action is taken to locate and eliminate the cause of the lack of randomness, returning the process or measurement to a state of statistical control, ie, of exhibiting only random variation. 

Statistical Control. Statistical quahty control (SQC) is the apphcation of statistical techniques to analytical data. Statistical process control (SPC) is the real-time apphcation of statistics to process or equipment performance. Apphed to QC lab instmmentation or methods, SPC can demonstrate the stabihty and precision of the measurement technique. The SQC of lot data can be used to show the stabihty of the production process. Without such evidence of statistical control, the quahty of the lab data is unknown and can result in production challenging adverse test results. Also, without control, measurement bias cannot be determined and the results derived from different labs cannot be compared (27). 

If process is not m statistical control, is there a plan to achieve control ... 

Have all production processes (final hatch and in-process parameters) heen shown to he m statistical control ... 

Statistical Process Control (SPC) The use of statistical techniques (such as control charts) to analyze a process and take appropriate action to maintain statistical control and improve process capability. 

A process is in control when the average spread of variation coincides with the nominal specification for a parameter. The range of variation may extend outside the upper and lower limits but the proportion of parts within the limits can be predicted. This situation will remain as long as the process remains in statistical control. A process is in statistical... 

Process capability studies are studies conducted to obtain information about the inherent variation present in processes that are under statistical control, in order to reduce the spread of variation to less than the tolerances specified in the product specification. 

Preliminary process capability studies are those based on measurements collected from one operating run to establish that the process is in statistical control and hence no special causes are present. Studies of unpredictable processes and the determination of associated capability indices have little value. Preliminary studies should show acceptable results for special characteristics before production approval can be given. These studies and associated indices only apply to the measurement of variables and not to attributes (see below). 

It is only possible to supply parts with identical characteristics if the measurement system as well as the production processes are under statistical control. In an environment in which daily production quantities are in the range of 1,000 to 10,000 units, inaccuracies in the measurement system that go undetected can have a disastrous impact on customer satisfaction and hence profits. 

There are three phases in the evolution of most QC systems (1) defect detection where an army of inspectors tries to identify defects (2) defect prevention where the process is monitored, and statistical methods are used to control process variation, enabling adjust-... 

Definition and Uses of Standards. In the context of this paper, the term "standard" denotes a well-characterized material for which a physical parameter or concentration of chemical constituent has been determined with a known precision and accuracy. These standards can be used to check or determine (a) instrumental parameters such as wavelength accuracy, detection-system spectral responsivity, and stability (b) the instrument response to specific fluorescent species and (c) the accuracy of measurements made by specific Instruments or measurement procedures (assess whether the analytical measurement process is in statistical control and whether it exhibits bias). Once the luminescence instrumentation has been calibrated, it can be used to measure the luminescence characteristics of chemical systems, including corrected excitation and emission spectra, quantum yields, decay times, emission anisotropies, energy transfer, and, with appropriate standards, the concentrations of chemical constituents in complex S2unples. 

For an example of a control chart see Fig. 1.31 and Sections 4.1 and 4.8. Control charts have a grave weakness the number of available data points must be relatively high in order to be able to claim statistical control . As is often the case in this age of increasingly shorter product life cyeles, decisions will have to be made on the basis of a few batch release measurements the link between them and the more numerous in-process controls is not necessarily straight-forward, especially if IPC uses simple tests (e.g. absorption, conductivity) and release tests are complex (e.g. HPLC, crystal size). 

Metrics for this might include number of excursions from statistical process control, but one very useful metric for controllability is process capability, or more accurately, process capability indices. Process capability compares the output of an in-control process to the specification limits by using capability indices. The comparison is made by forming the ratio of the spread between the process specifications (the specification width ) to the spread of the process values. In a six-sigma environment, this is measured by six standard deviation units for the process (the process width ). A process under control is one where almost all the measurements fall inside the specification limits. The general formula for process capability index is ... 

There are a number of prerequisites for properly using CRMs in these tasks, including established quality control of the laboratory s analytical measurement operations and proven statistical control of the analytical measurement process. Publications describing the use of RMs and CRMs are not as plentiful as those on how CRMs are made but, in addition to the ISO/REMCO Guides 30-35, the ISO/REMCO publication The role of reference materials in achieving quality in analytical chemis-try"(ISO 9000 1987), the NIST Handbook for SRM users (Taylor 1995), and the various LGC-VAM publications listed under Further Reading should all be consulted. 

A given device, procedure, process, or method is usually said to be in statistical control if numerical values derived from it on a regular basis (such as daily) are consistently within 2 standard deviations from the established mean, or the most desirable value. As we learned in Section 1.7.3, such numerical values occur statistically 95.5% of the time. Thus if, say, two or more consecutive values differ from the established value by more than 2 standard deviations, a problem is indicated because this should happen only 4.5% of the time, or once in roughly every 20 events, and is not expected two or more times consecutively. The device, procedure, process, or method would be considered out of statistical control, indicating that an evaluation is in order. 

Analytical laboratories, especially quality assurance laboratories, will often maintain graphical records of statistical control so that scientists and technicians can note the history of the device, procedure, process, or method at a glance. The graphical record is called a control chart and is maintained on a regular basis, such as daily. It is a graph of the numerical value on the y-axis vs. the date on the x-axis. The chart is characterized by five horizontal lines designating the five numerical values that are important for statistical control. One is the value that is 3 standard deviations from the most desirable value on the positive side. Another is the value that is 3 standard deviations from the most desirable value on the negative side. These represent those values that are expected to occur only less than 0.3% of the time. These two numerical values are called the action limits because one point outside these limits is cause for action to be taken. 

FIGURE 1.5 An example of a control chart showing a device, procedure, process, or method that is in statistical control because the numerical values are consistently between the warning limits. 

In agreement with Flory s predictions, hyperbranched polymers based on A,jB monomers reported in the literature exhibit a broad molecular weight distribution (typically 2-5 or more). The polydispersity of a hyperbranched polymer is due to the statistical growth process. A strategy to overcome this disadvantage is to add a By-functional core molecule, or a chain terminator, which Hmits the polydispersity and also provides a tool to control the molecular weight of the final polymer. The concept of copolymerizing an A2B monomer with a B3 functional core molecule was first introduced by Hult et al. [62] and more recently also utilized by Feast and Stainton [63] and Moore and Bharathi [64]. 

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