Monitoring charts standard deviation

Construction of Property Control Charts The simplest form for a property control chart is a sequence of points, each of which represents a single determination of the property being monitored. To construct the control chart, it is first necessary to determine the mean value of the property and the standard deviation for its measurement. These statistical values are determined using a minimum of 7 to 15 samples (although 30 or more samples are desirable), obtained while the system is known to be under statistical control. The center line (CL) of the control chart is determined by the average of these n points... 

STL s quality-control programme includes the recovery of known additions of analyte, analysis of externally supplied standards, calibration, analysis of duplicates and control charting. Each analyte is monitored by analysing at least one AQC standard for every 20 samples. AQC results are plotted on control charts and action is taken if a point Hes outside +3 standard deviations (SD) or if two consecutive points He outside +2 SDs. 

The MR chart is used to monitor process variability. Considering MR as a random variable with a mean of Fmr and a standard deviation of °mr, the theoretical parameters of the MR chart can then be stated as... 

Shewhart control charts enable average process performance to be monitored, as reflected by the sample mean. It is also advantageous to monitor process variability. Process variability within a sample of k measurements can be characterized by its range, standard deviation, or sample variance. Consequently, control charts are often used for one of these three statistics. 

The control chart is the basic analytical tool of SPC and is used for first assessing a process, then for monitoring a process output with respect to on-target control and process variability. A control chart is basically a time plot of a statistic calculated from a variable associated with a process. This variable may either be a process variable, such as temperature or flow rate, or a product variable, such as fill weight or potency. Examples of statistics are an individual measurement, an average of two or more measurements, a percentage of defective output items, a count of defect occurrences in time or space, or a measure of variation such as a range or standard deviation of two or more measurements. 

Samples can be divided into two aliquots and analyzed, and the duplicates used for control purposes. This is a simple quality control procedure that does not require stable control materials and therefore can be used when stable materials are not available or as a supplemental procedure when stable control materials are available. The differences between duplicates are plotted on a range type of control chart that has limits calculated from the standard deviation of the differences. When the duplicates are obtained from the same method, this range chart monitors only random error and thus is not adequate for ensuring the accuracy of the analytical method. When the duplicates are obtained from two different laboratory methods, then the range chart actually monitors both random and systematic errors but cannot separate the two types of errors. The interpretation becomes more difficult, particularly when there are stable systematic differences or biases between the two analytical methods. Multiplicative factors may be necessary to deal with proportional differences, and additive factors may be necessary to allow for constant differences. Interpretation of observed differences becomes more qualitative nevertheless, this procedure still provides a useful way of monitoring the consistency of the data being generated by the laboratory. 

The following table gives the sample means and standard deviations for six measurements each day of the purity of a polymer in a process. The purity is monitored for 24 days. Determine the overall mean and standard deviation of the measurements and construct a control chart with upper and lower control limits. Do any of the means indicate a loss of statistical control ... 

The Range chart R chart), or the standard deviation chart, is used S chart) to monitor within sample process variation or spread (process variability at a given time). The process spread must be in-control for proper interpretation of the x chart. The x chart must be used together with a spread chart. 

The S chart is preferable for monitoring variation when the sample size is large or var3ung from sample to sample. Although 8 is an unbiased estimate of the sample standard deviation S is not an unbiased estimator of a. For a variable with a Normal distribution, S estimates c a, where C4 is a parameter that depends on the sample size m. The standard deviation of S is — c. When a is to be estimated from past data of n samples,... 

The AR model and the variance of e k) can be estimated from an incontrol data set using software such as Matlab System Identification Toolbox [191]. A standard x-chart is designed using control limits at 3 standard deviations (3(t limits) to monitor the residuals j k) and consequently Jhistit). 

In precision charts (the range chart or R-chart), the data from duplicates are plotted with the vertical scale (ordinate) in units such as percent, and the horizontal scale (abscissa) in units of batch number or time. Usually the mean of the duplicates is reported and the difference between the duplicates, or range, is examined for acceptability. The mean and standard deviation are calculated from the data. It is common practice in analytical laboratories to run duplicate analyses at frequent intervals as a means of monitoring the precision of analyses and detecting out-of-control situations. This is often done for analyses for which there are no suitable control samples or reference materials available. 

On receipt of kits, operators should have everything to be able to perform the assay. The control sera enable operators to monitor the assay routinely, and the use of these data in control charts is the basis of this chapter. The necessary data for plotting on various charts is obtained through the calculation of the mean and standard deviation iSD), from the mean of control samples as raw OD... 

The philosophy of SPC is to monitor the output of a process and determine when control action is necessary to correct deviations of the output from its setpoint. The most common tool for accomplishing this is the Shewhart (x-bar) chart shown in Figure 5.19. In the discrete parts manufacturing industries, multiple samples are taken at fixed intervals. Quality tests are run on these samples, and the mean is plotted on one Shewhart chart, and the range on another. In the absence of a disturbance, the means should be normally distributed around the setpoint. If the upper and lower control limits (UCL and LCL, respectively) are placed at three standard deviations above and below the target, a range is defined into which all of the means should fall. The... 

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