Control chart design

Economic design Economic control chart design requires the availability of cost coefficients that are not easy to estimate in practice. 

Coherently with the steps proposed by CCSM, for the creation of the model five steps are necessary, which consists in (1) Dendritic construction, (2) Random Sampling, (3) Control chart design (4) Test for out of control conditions, and (5) Action. 

This tutorial shows how MATLAB can be used to construct all the classical frequency domain plots, i.e. Bode gain and phase diagrams, Nyquist diagrams and Nichols charts. Control system design problems from Chapter 6 are used as examples. 

Appropriately designed, Cusum control charts give sensitive and instructive impressions on process changes. Cumulative stuns S = YT,= ( — 0) also contain information on actual as well as on previously obtained values. Therefore their display enables one to perceive earlier changes leading to OCS than by means of the chart of original values (see Woodward and Goldsmith [1964] Marshall [1977] Doerffel [1990]). 

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. 

It is often helpful to record the results of control samples in a visible manner not only because of the greater impact of a visual display but also for the relative ease with which it is possible to forecast trends. A variety of styles of quality control charts have been suggested but the most commonly used are those known as Levey-Jennings or Shewart charts, which indicate the scatter of the individual control results about the designated mean value (Procedure 1.7). 

There are broadly two uses of chemometrics that interest the process chemist. The first of these is simply data display. It is a truism that the human eye is the best analytical tool, and by displaying multivariate data in a way that can be easily assimilated by eye a number of diagnostic assessments can be made of the state of health of a process, or of reasons for its failure [ 153], a process known as MSPC [154—156]. The key concept in MSPC is the acknowledgement that variability in process quality can arise not just by variation in single process parameters such as temperature, but by subtle combinations of process parameters. This source of product variability would be missed by simple control charts for the individual process parameters. This is also the concept behind the use of experimental design during process development in order to identify such variability in the minimum number of experiments. 

The licensee shall establish and maintain a statistical control system including control charts and formal statistical procedures, designed to monitor the quality of each type of program measurement. Control chart limits shall be established to be equivalent to levels of (statistical) significance of 0.05 and 0.001. Whenever control data exceed the 0.05 control limits, the licensee shall investigate the condition and take corrective action in a timely manner. 

The relative performance of the Shewhart and CUSUM control charts is compared in Fig. 8-48 for a set of simulated data for the tensile strength of a resin. It is assumed that the tensile strength x is normally distributed with a mean of p = 70 M Pa and a standard deviation of a = 3 MPa. A single measurement is available at each sampling instant. A constant (a = 0.5a = 1.5) was added to x(k) for k >10 in order to evaluate each charts ability to detect a small process shift. The CUSUM chart was designed using K = 0.5a and H = 5a. 

Malvern (Insitec) ECPS2 is designed to monitor and control particle size distributions from 0.5 to 1,500 pm, at concentrations up to 10,000 ppm, directly in pneumatic powder flow streams. Up to one thousand size distribution measurements per second are carried out at flow velocities from static to ultrasonic. Discrete data point, extracted from the log file, can be viewed. The data can also be viewed in tabular form and as a size distribution curve. Data can also be integrated over any selected range. A Statistical Process Control (SPC) option enables the file data to be viewed in standard control chart format either as an X or R chart. Various interface arrangements have been described, [203] ... 

By monitoring the validation status of the applied analytical procedure, for example, with control charts, reliable information on the long-term behavior of the procedure can be obtained and trends can be detected very early. Transferring in this way data to information to knowledge, the analytical system (or the production process) can be adjusted before problems such as OOS results occur (action instead of reaction). In analogy to equipment qualification, a continuous system is proposed design, operational, and performance validation (three Vs). 

Since the proposed EPC/SPC was designed to be applied in sequential stages, the construction of the different scenarios starts with an open-loop process, followed by the incorporation of the control charts and then the manual controller. The scenarios are ... 

The original methods have been extended in many ways. The design of control charts is always prospective, and their shape depends upon the a priori expectations of the development team. For example, when it is important to test only the tolerability of a compound, the chart can have an open top this is when it is important for the... 

The individual observations in sequential order are compared with control limits established from a past measurement to generate the control chart in the initial case. If the mean value x and standard deviation a of a constant quantity have been established from 15 to 30 measurements, these quantities may be regarded as valid estimates of x and action limits and these limits are usually set, and are based on the sensitivity and importance of the measurements. Special attention should be paid to one-sided deviations from control limits, because systematic errors cause deviation in one direction and may indicate an abnormally wide scatter. Therefore laboratories, production, test methods, or operator can be checked for consistency of measured results. 

Control charts are designed to incorporate the entire process of the analytical measurement from sampling variability, instrument stability, calibration standards and sample preparation. The chart presents data in a framework that clearly shows whether corrective actions are necessary to ensure that results reported are correct, and allows extrapolation from sample results to conclusion about the whole population with known risks of error or misinterpretation. 

The quality control (QC) tests discussed in Sections 10.5 and 11.2.9 are integral parts of QA designed to check results. Some QC measures are prompt indicators that warn of problem occurrence at the time of analysis others are delayed indicators that require backtracking to And when a problem first arose. Control charts for radiation detector operation are an example of a prompt indicator of reliability. Records of deviations from the norm in an analysis or a measurement may also be prompt indicators if immediately considered. Periodic blank, blind, and replicate analyses, especially interlaboratory comparisons, are delayed indicators for which results may not be available for days or weeks after a problem has arisen. Review and assessment of compiled data are delayed indicators of information quality. 

Figure 11.2 Illustration of the Armitage sequential analysis study design. Patients are paired, and one of each pair receives each alternative treatment. If the patient receiving treatment A does better than the one receiving treatment B (A > B), then the line moves upwards vice versa, if the patient receiving B does better than the one receiving A (B > A), then the line moves downward. If the treatments cannot be distinguished within a pair of patients, then the line moves horizontally. The critical boundaries (broken lines) are computed from prospective measures of a and fj (e.g. p = 0.05 and 80% power, respectively). The technique derives from an engineering control chart and, once again, can be adapted to more sophisticated forms, including limits on the study size for indeterminate results...

Once preliminary estimates have been made, the aneilyst can determine the desired accuracy of the results expressed as a tolerance, or limit error, within a stated confidence level. Next, the anMyst must estimate the number of observations to be made turd determine the frequency of observations. Finally, the work sampling form on which to tabulate the data is designed, as well as the control charts used in conjunction with the study. 

Figure 12 Sample Control Chart. (From B. Niebel and A. Freivalds, Methods, Standards, and Work Design, 10th Ed. 1999 McGraw-Hill Companies, Inc. Reprinted by permission.)...

Individual differences in job design/redesign, 886-888 and team design, 886-888 Individualism (in national cultures), 957 Individual learning, 1250, 1400 Individual measurement, control charts for, 1841-1844... 

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