Control charts - meaning

Synonyms are X-control chart, mean control chart or average control chart. 

Some measure of dispersion of the subgroup data should also be plotted as a parallel control chart. The most reliable measure of scatter is the standard deviation. For small groups, the range becomes increasingly significant as a measure of scatter, and it is usually a simple matter to plot the range as a vertical line and the mean as a point on this line for each group of observations. 

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. 

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. 

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... 

Property control charts can also be constructed using points that are the mean value, Xj, for a set of r replicate determinations on a single sample. The mean for the ith sample is given by... 

To construct the control chart, ranges for a minimum of 15-20 samples (preferably 30 or more samples) are obtained while the system is known to be in statistical control. The line for the average range, R, is determined by the mean of these n samples... 

Interpreting Control Charts The purpose of a control chart is to determine if a system is in statistical control. This determination is made by examining the location of individual points in relation to the warning limits and the control limits, and the distribution of the points around the central line. If we assume that the data are normally distributed, then the probability of finding a point at any distance from the mean value can be determined from the normal distribution curve. The upper and lower control limits for a property control chart, for example, are set to +3S, which, if S is a good approximation for O, includes 99.74% of the data. The probability that a point will fall outside the UCL or LCL, therefore, is only 0.26%. The... 

The statistical techniques applicable to control charts are thus restricted to those of Section 1.5, that is detecting deviations from the long-term mean respectively crossing of the specified limits. 

The conventional control chart is a graph having a time axis (abscissa) consisting of a simple raster, such as that provided by graph or ruled stationary paper, and a measurement axis (ordinate) scaled to provide six to eight standard deviations centered on the process mean. Overall standard deviations are used that include the variability of the process and the analytical uncertainty. (See Fig. 1.8.) Two limits are incorporated the outer set of limits corresponds to the process specifications and the inner one to warning or action levels for in-house use. Control charts are plotted for two types of data ... 

Figure 4.10. At the top the raw data for dry residue for 63 successive batches is shown in a standard control chart format. The fact that as of batch 34 (arrow ) a different composition was manufactured can barely be discerned, see the horizontals that indicate the means DRi 33 resp. DR34 g3- A hypothesis that a change occurred as of batch 37 would find support, though. Cusum charts for base period 1. .. 63 resp. base period 1. .. 37 make the change fairly obvious, but the causative event cannot be pinpointed without further information. Starting with batch 55 (second arrow ), production switched back to the old composition.

No averaging has taken place (option 5 in the menu) the individual average is equal to the over-all mean y ,ean which is displayed as a horizontal line this corresponds to the classical use of the Cusum technique. By this means, slight shifts in the average (e.g., when plotting process parameters on control charts) can be detected even when the shift is much smaller than the process dispersion, because the Cusum trace changes slope. 

One can apply a similar approach to samples drawn from a process over time to determine whether a process is in control (stable) or out of control (unstable). For both kinds of control chart, it may be desirable to obtain estimates of the mean and standard deviation over a range of concentrations. The precision of an HPLC method is frequently lower at concentrations much higher or lower than the midrange of measurement. The act of drawing the control chart often helps to identify variability in the method and, given that variability in the method is less than that of the process, the control chart can help to identify variability in the process. Trends can be observed as sequences of points above or below the mean, as a non-zero slope of the least squares fit of the mean vs. batch number, or by means of autocorrelation.106... 

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]). 

Here the concentration range of the analyte in the ran is relatively small, so a common value of standard deviation can be assumed. Insert a control material at least once per ran. Plot either the individual values obtained, or the mean value, on an appropriate control chart. Analyse in duplicate at least half of the test materials, selected at random. Insert at least one blank determination. 

Longer (e g. n > 20) frequent runs of similar materials Again a common level of standard deviation is assumed. Insert the control material at an approximate frequency of one per ten test materials. If the run size is likely to vary from run to run it is easier to standardise on a fixed number of insertions per run and plot the mean value on a control chart of means. Otherwise plot individual values. Analyse in duplicate a minimum of five test materials selected at random. Insert one blank determination per ten test materials. 

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). 

Figure 10.2 Statistical process control charts for clearings. Top panel runs chart showing clearings as a function of measurement number. Middle panel x-bar chart with dashed upper control limit (UCL) and lower control limit (LCL) solid horizontal line is the grand mean, X. Bottom panel range chart with dashed upper control limit (UCL) solid horizontal line is the average range, r.

In preparing a control chart, the mean upper control limit (UCL) and lower control limit (LCL) of an approved process and its data are calculated. A control chart with mean UCL and LCL with no data points is created data points are added as they are statistically calculated from the raw data. (See also the chapter on control charts)... 

If control charts are transferred to analytical chemistry the first thing to do is to assign the target value. If a reference material / certified reference material (RM/CRM) is used, the certified value can be used as the target value. This is advisable only, if the mean of the measnrements is close to the reference valne. Otherwise out-of-control sitnations would occur very frequently. So in most cases the arithmetic mean of the measurements is used as target value... 

The Cusum Control Chart is a very special chart from which a lot of information can be drawn. Cusum is the abbreviation for cumulative sum and means the sum of all differences from the target value. Every day the difference of the control analysis from the target value is added to the sum of all the previous ddferences. 

Both the EC50 values and the 3-pM point of the 2,3,7,8TCDD ealibration curve serve as quality criteria. For each participant, the results for both data points from all 96-well plates analyzed during the presented study were collected and reeorded in Shewhart control charts. The Shewhart control chart is used to identify variations on performanee of the DR CALUX bioassay brought about by unexpected or unassigned causes. The Shewhart eontrol chart shows the mean of the EC50 and 3-pM control point and the upper and lower eontrol limits. In Figure 2, a typical Shewhart control chart is shown. Over the analysis period, none of the participants exceeded the aetion levels (AVG 3 S). 

CUSUM Control Chart A CUSUM chart provides an efficient way of detecting small shifts in the mean of a process (l/2 a), the chart is usually used.The CUSUM chart incorporates information contained in a sequence of sample points. It keeps track of the cumulative sum of the deviations between each sample point (a sample mean) and a target value. Unlike the x chart, which often bases its out-of-control decision on just the most recently collected sample, the CUSUM calculated for a sample point carries the history prior to that sample. For example, a sequence of sample points above the centerline can trigger an out-of-control signal although all of them stayed well below the UCLs of the x chart. 

EWMA Control Chart An EWMA control chart plots weighted moving average values for variables data. A weighting factor is chosen by the user to determine how older data points affect the mean value compared to more recent ones. Because the EWMA chart uses information from all samples, it is a good alternative to the CUSUM chart in detecting smaller process shifts. 

The terms validation and QA are widely used. However, a lot of analysts and laboratories do not know the exact meaning—neither the difference nor the relationship between the two terms. Validating a method is investigating whether the analytical purpose of the method is achieved, which is obtaining analytical results with an acceptable uncertainty level [4]. Analytical method validation forms the first level of QA in the laboratory (Figure 6). AQA is the complete set of measures a laboratory must undertake to ensure that it is able to achieve high-quality data continuously. Besides the use of validation and/or standardized methods, these measures are effective IQC procedures (use of reference materials, control charts, etc.), participation in proficiency-testing schemes, and accreditation to an international standard, normally ISO/IEC 17025 [2,4, 6]. 

Precision data can be documented in bar charts or control charts such as Shewhart control charts (see the discussion of internal quality control in Section 8.2.3.5). Bar charts plot %RSD values with their corresponding confidence interval. Control charts plot the individual measurement results and the means of sets of measurements with their confidence level (or with horizontal lines representing limits, see below) as a function of the measurement number and the run number, respectively [15,55,56, 58,72, 85]. 

Trueness or exactness of an analytical method can be documented in a control chart. Either the difference between the mean and true value of an analyzed (C)RM together with confidence limits or the percentage recovery of the known, added amount can be plotted [56,62]. Here, again, special caution should be taken concerning the used reference. Control charts may be useful to achieve trueness only if a CRM, which is in principle traceable to SI units, is used. All other types of references only allow traceability to a consensus value, which however is assumed not to be necessarely equal to the true value [89]. The expected trueness or recovery percent values depend on the analyte concentration. Therefore, trueness should be estimated for at least three different concentrations. If recovery is measured, values should be compared to acceptable recovery rates as outlined by the AOAC Peer Verified Methods Program (Table 7) [56, 62]. Besides bias and percent recovery, another measure for the trueness is the z score (Table 5). It is important to note that a considerable component of the overall MU will be attributed to MU on the bias of a system, including uncertainties on reference materials (Figures 5 and 8) [2]. 

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