Variables control chart

Plotted points on a control chart are usually based on data collected from samples in a process. After a sufficient number of samples are collected and the data are plotted on a control chart, the stability of the process can be evaluated. A stable process is in control while an out-of-control process is unstable. Depending on the type of quality characteristic, control charts can be divided into two groups variable control charts and attribute control charts. Variable control charts are used to monitor quality characteristic that are continuously varying in nature attribute control charts are used to monitor those quality characteristics that are not numerically measurable.The determination of the centerline and control limits are described in Sections 3.4.2.2 and 3.4.2.3 with respect to different types of control charts. 

Attribute control charts are less used compared to variable control charts. When it is not possible or practical to measure the quality characteristic of a product, attribute control charts are often applied. Examples of their application include monitoring the fraction of nonconforming of a certain sensor production, the number of defective diodes in an electronic assembly, the number of imperfections in textile... 

In most applications, the choice between a variable control chart and an attribute control chart is clear-cut. In some cases, the choice will not be obvious. For instance, if the quality characteristic is the softness of an item, such as the case of pillow production, then either an actual measurement or a classification of softness can be used. Quality managers and engineers will have to consider several factors in the choice of a control chart, including cost, effort, sensitivity, and sample size. Variable control charts usually provide more information to analysts but cost more to implement and use. Attribute control charts are less sensitive and expensive but usually requires large samples to reach certain statistical significance. 

TABLE 4 Values of Constants in Variable Control Chart Parameters... 

The different kinds of control charts are based on two groupings of types of data attribute data and variable data. Attribute data includes classification, count, and rank data Variable data refers primarily to continuous data, but rank data are often analyzed using a variable-control chart (realizing that the arithmetic functions are not theoretically valid). Otherwise the ranks can be converted to classification data and analyzed using attribute charts. Figure 8 contains examples of each of these categories of data. 

Because of these advantages, the control cheat for individuals is sometimes used when another type of control chart is more appropriate. The X chart is somewhat less sensitive than other variable control charts with larger subgroup sizes in its abflity to detect the presence of a special cause. Sometimes data analyzed with an X chart will indicate a stable process, but the same data analyzed with a more appropriate chart (P chart, C chart, or X-bar and R chart, discussed in later sections) will clearly indicate the presence of special causes. 

The outcomes of test and inspection can thus be classified by the level of measurement upon which they are based and the type of decision required. These outcomes in turn define the typical statistical methods used, such as prototype testing for decision 1 above. For in-process quaUty control (decision 3 above), nominal scale decisions lead to attributes control charts, while interval or ratio scales lead to variables control charts (Vardeman and Jobe 1998). The second type of decision above would lead to either attributes of variables sampling plans, although the whole concept of sampling a batch to determine its quality has largely been abandoned in favor of in-process quality control. 

There are two types of variable control charts. They are the X and R chart and the X and s chart. 

This is the most common variable control chart. The principles that were developed by Shewhart are applied to the data and the statistical calculations for mean and control limits are completed. To be in statistical control a process must fall within three standard deviations from the mean of the data. At least 25 data points are necessary to calculate the control limits for a process. Once the control limits have been calculated, they stay the same unless a change has been made to the process. If a data point falls outside the calculated control limits a special cause is sought out for the variation. This control chart uses the constants that were developed by Shewhart to estimate the standard deviation of the data. The formulas that are used and the development of a control chart can be found in any good SPC textbook, therefore I will not be covering that material here. 

A variable control chart can provide a lot of statistical information. First, if all of the data points lie within the control limits, the process may be in statistical control. There are some other rules that have to be followed that could indicate an out-of-control situation These rules are covered in SPC texts where chart interpretation is discussed. Once you have a stable process, several types of analyses can be done. The one that 1 have found to be most useful is to use a z-statistic and analyze the data. This way the amount of out-of-specification material that is produced can be calculated. Once... 

What is the difference between an attribute control chart and a variable control chart ... 

In order to calculate control limits and the mean for variable charts, samples of size 4 or 5 observations are usually used whereas for attribute charts, samples of 50 to 100 observations are most often used (Juran and Godfrey 1999,45-47). For example, when constructing a variable control chart such as an X chart, samples of 4 to 5 observations are collected over a period of time with each sample collected over equal intervals. After 30 samples have been collected, the sample averages of 4 to 5 observations can be calculated, and then an overall average for the 30 sample averages. The overall average of the 30 samples is then used to construct the upper and lower control limits. 

Control charts based on measurements of quality characteristics are often found to be a more economical means of controlling performance than control charts based on attributes (Duncan 1974, 431). The two most common types of variables control charts are x -charts and R-charts. 

These control charts are referred to as variable control charts. They are based upon measurements of quality characteristics. 

There are two main facets of statistical quality control. One of them is the use of process control charts for in-process manufacturing operations. These charts, also referred to as variables control charts or attributes control charts, are aimed at evaluating present as well as future performance. The other facet of statistical quality control is acceptance inspection or acceptance sampling. This technique forms the basis for scientihcally evaluating past performance and accepting or rejecting the product. 

Figure 16-2a illustrates a typical variables control chart (x and R chart). The center line of the x chart represents the average of a series of x values. 

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