Statistical control, state

The written directives of a quality control program are a necessary, but not a sufficient, condition for obtaining and maintaining an analysis in a state of statistical control. Although quality control directives explain how an analysis should be properly conducted, they do not indicate whether the system is under statistical control. This is the role of quality assessment, which is the second component of a quality assurance program. 

The goals of quality assessment are to determine when a system has reached a state of statistical control to detect when the system has moved out of statistical control and, if possible, to suggest why a loss of statistical control has occurred so that corrective actions can be taken. For convenience, the methods of quality assessment are divided into two categories internal methods that are coordinated within the laboratory and external methods for which an outside agency or individual is responsible. The incorporation of these methods into a quaKty assurance program is covered in Section 15C. 

The most useful methods for quality assessment are those that are coordinated by the laboratory and that provide the analyst with immediate feedback about the system s state of statistical control. Internal methods of quality assessment included in this section are the analysis of duplicate samples, the analysis of blanks, the analysis of standard samples, and spike recoveries. 

Analysis of Standards The analysis of a standard containing a known concentration of analyte also can be used to monitor a system s state of statistical control. Ideally, a standard reference material (SRM) should be used, provided that the matrix of the SRM is similar to that of the samples being analyzed. A variety of appropriate SRMs are available from the National Institute of Standards and Technology (NIST). If a suitable SRM is not available, then an independently prepared synthetic sample can be used if it is prepared from reagents of known purity. At a minimum, a standardization of the method is verified by periodically analyzing one of the calibration standards. In all cases, the analyte s experimentally determined concentration in the standard must fall within predetermined limits if the system is to be considered under statistical control. 

A graph showing the time-dependent change in the results of an analysis that is used to monitor whether an analysis is in a state of statistical control. 

In a performance-based approach to quality assurance, a laboratory is free to use its experience to determine the best way to gather and monitor quality assessment data. The quality assessment methods remain the same (duplicate samples, blanks, standards, and spike recoveries) since they provide the necessary information about precision and bias. What the laboratory can control, however, is the frequency with which quality assessment samples are analyzed, and the conditions indicating when an analytical system is no longer in a state of statistical control. Furthermore, a performance-based approach to quality assessment allows a laboratory to determine if an analytical system is in danger of drifting out of statistical control. Corrective measures are then taken before further problems develop. 

The principal tool for performance-based quality assessment is the control chart. In a control chart the results from the analysis of quality assessment samples are plotted in the order in which they are collected, providing a continuous record of the statistical state of the analytical system. Quality assessment data collected over time can be summarized by a mean value and a standard deviation. The fundamental assumption behind the use of a control chart is that quality assessment data will show only random variations around the mean value when the analytical system is in statistical control. When an analytical system moves out of statistical control, the quality assessment data is influenced by additional sources of error, increasing the standard deviation or changing the mean value. 

Construct a property control chart for these data, and evaluate the state of 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. 

Unlike non-radiometric methods of analysis, uncertainty modelling in NAA is facilitated by the existence of counting statistics, although in principle an additional source of uncertainty, because this parameter is instantly available from each measurement. If the method is in a state of statistical control, and the counting statistics are small, the major source of variability additional to analytical uncertainty can be attributed to sample inhomogeneity (Becker 1993). In other words, in Equation (2.1) ... 

Suitable quality control and quality assurance procedures should be in place and the analytical system must be in a state of statistical control. 

If this range overlaps the stated confidence interval of the certified value, then the analytical procedure may be assumed to be under satisfactory statistical control. Discussion about the accepted degree of overlap may inevitably occur so when reporting results it is good practice that the certified value of the CRM should be within the experimentally determined confidence interval. 

In general, inferences about the future of processes that have been brought to a state of statistical control are more reliable than inferences about poorly behaved systems [W. Deming (1982), Wheeler (1983), Wheeler and Chambers (1986), Wheeler (1987)]. 

The student used the fitted model to predict future clearings with the results shown in Figure 10.16. If the check clearings remain in a state of statistical control, then the uncertainty of prediction in the future should be well represented by the residuals shown in the bottom panel of this figure (see Section 3.5). 

If there is just one point outside the action limits, there should be an immediate evaluation. If there are two points or more in a brief period of time, the system should be shut down and analyzed for the cause. An example is Figure 5.13. As stated there, one possibility is a temporary contamination in the distilled water supply, which is certainly a concern even for a short period of time. A system out of statistical control, even for a short period of time, diminishes the reliability of any results. 

Being in statistical control in an analytical laboratory is a state in which the results are without uncorrected bias and vary randomly with a known... 

Energy-resolved rate constant measurements near the threshold for diplet methylene formation from ketene have been used to provide confirmation of the fundamental hypothesis of statistical transition state theory (that rates are controlled by the number of energetically accessible vibrational states at the transition state).6 The electronic structure and aromaticity of planar singlet n2-carbenes has been studied by re-election coupling perturbation theory.7 The heats of formation of three ground-state triplet carbenes have been determined by collision-induced dissociation threshold analysis.8 The heats of formation of methylene, vinylcarbene (H2C=CHCH), and phenylcarbene were found to be 92.2 3.7, 93.3 3.4, and 102.8 33.5 kcal mol-1, respectively. 

This approach is made possible if the process (step) is demonstrated to be under a state of statistical control. A number of tests were listed by Ekvall and Juran to learn whether or not this condition exists. One approach to validating the technique involves the comparison of the process capability curve with the tolerance limits for the product. The intent of the validation is to determine whether or not the data from the process conform to the state of statistical control. It may also be used to determine whether or not quality costs can be reduced without changing the process s status. 

Sets of instructions that detail the procedures designed to reduce errors occurring during analytical procedures and ensure accurate quantitations are found in the quality assurance (QA) and quality control (QC) manuals. Quality assurance procedures are used by the laboratory to detect and correct problems in analytical processes. As newer methods and instrumentation are added to the laboratory, older procedures must be modified or changed completely. Quality control procedures are used to maintain a measurement system (i.e., a gas chromatograph) in a statistically satisfactory state to ensure the production of accurate and reliable data. 

Quality control (QC) concerns procedures that maintain a measurement system in a state of statistical control. This does not mean that statistics control the analytical... 

Two elements of quality assurance are quality control and quality assessment. Quality control is a set of measures implemented within an analytical procedure to assure that the process is in control. A combination of these measures constitutes the laboratory QC program. A properly designed and executed QC program will result in a measurement system operating in a state of statistical control, which means that errors have been reduced to acceptable levels. An effective QC program includes the following elements ... 

Certainly any organization that requires traceability to national standards ought to focus on whether the measurements made by the organization subject to the trace-ability requirement are sufficiently accurate for their intended purpose and not simply on whether NBS calibration certificate(s) is on file. Without a valid uncertainty statement and evidence that the measurement process remains in a state of statistical control, no one can deter-... 

The major objective in SPC is to use process data and statistical techniques to determine whether the process operation is normal or abnormal. The SPC methodology is based on the fundamental assumption that normal process operation can be characterized by random variations around a mean value. The random variability is caused by the cumulative effects of a number of largely unavoidable phenomena such as electrical measurement noise, turbulence, and random fluctuations in feedstock or catalyst preparation. If this situation exists, the process is said to be in a state of statistical control (or in control), and the control chart measurements tend to be normally distributed about the mean value. By contrast, frequent control chart violations would indicate abnormal process behavior or an out-of-control situation. Then a search would be initiated to attempt to identify the assignable cause or the. special cause of the abnormal behavior... 

When more than one state correlates with the electronic states of the separated species, collisions populate the various molecular states at statistically controlled relative rates. If more than one such state is bound, then it may be stabilized in a third-order process. For complex species, the rate of predissociation of the energy-rich complex, that is, k i[Rt], depends on its dissociation energy, so the ground-state complex will survive longest and have the highest chance of being collisionally stabilized. For diatomic molecules, for example, N2, 02, and NO, dipole transitions from these excited states to the ground state are not fully allowed and the excited species are almost certainly quenched in collisions. 

Statistical process control (SPC) provides a statistical approach for evaluating processes and for improving the quality of these processes through elimination of special causes. When SPC is effectively implemented within a company, benefits can be derived through a reduced cost of manufacture, improved quality, fewer troubleshooting crises, and improved relationships with customers. Process capability is a companion tool—one that can be used once a state of statistical control is achieved—to assess the performance of a process relative to its product specifications. Process capability can be used to determine whether processes are capable of continually operating within their stated specification limits. 

Superimposed on this time plot are the upper and lower control limits, traditionally set at a distance of 3 times the standard error (SE) of the statistic from the center line or process mean. This controls the risk of a false alarm at a low level (a chance of 3 of 1000 if the distribution is normal). The process is said to be in a state of statistical control if the plotted points appear to occur in a random pattern and are contained within the control limits. The centerline and control limits are calculated from retrospective data from the process. 

Around the CL are the control limits, set at 3 SE of the statistic being plotted. If the statistic value falls outside the control limits, this is a signal that the process is not in a state of statistical control. Because the standard errors are functions of the process standard deviation a, an estimate of this quantity is necessary. This can be supplied by the average range. The lower control limit (LCL) and upper control limit (UCL) are calculated as follows ... 

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