Attributes control charts

Attribute charts are used when the data being measured meet certain conditions or attributes. Attributes are involved when the safety measures are categorical (Griffin 2000,434). Examples of categorical data include the departments in which accidents are occurring, the job classification of the injured employee, and the type of injury sustained. The type of attribute control chart used depends on the data format of the specific attribute measured. The attribute charts covered in this chapter are 

The control limits for the p-chart are normally expressed in terms of the standard deviation. The formula for calculating the standard deviation is Quran and Godfrey 1999, 45.12)  

So the upper and lower control limits for a p-chart will be at  

Another problem that safety managers are faced with is that the number of observations in the samples may not be equal. If the subgroup size (n) varies, there are three possibilities that can be used to construct the p-chart Quran and Godfrey 1999,45.13)  

We can calculate the average size of the subgroups. This is appropriate when the sizes are similar or all data lie near the centerline. 

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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. 

Other tools The cause-and-effect diagram may give useful information regarding which categories to measure. A Pareto chart is often used to analyze further a characteristic evaluated using an attribute control chart. 

To develop an attribute control chart, a subgrouping strategy must first be determined. The subgroup size (n) is the number of units tested for classification data, or the area of opportunity for the incidence to occur for count data. There are four commonly used control charts for attribute data, depending on the type of attribute data and the constancy of the subgroup size. Table 1 summarizes these charts. 

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. 

Asynchronous transfer mode (ATM), 250 ATC, see Apparent tardiness cost ATM (Asynchronous transfer mode), 250 ATO, see Assemble to order ATP (available to promise), 2046 Attention, limited-resource model of, 1016 AT T Laboratories, 268, 913 Attribute control charts, 1844-1851 Attribute data, 1856-1857 Attribute modeling, 2279—2280 AT T runs rules, 1863—1868 Attributes ... 

There are four different attribute control charts that are used. They are the p chart, the np chart, the c chart, and the u chart. Let s look at each one. 

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

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. 

C Charts. The C chart is also known as the C-bar chart and is a special type of attributes control chart. Unlike the P chart, which portrays percent defective, the C chart uses the number of defects per unit. For example, a black speck and a deep sink mark on a molded part are two defects per part for C chart calculation but one part defective for P chart purposes. 

There are four basic types of attribute control charts. The P Chart and its variation, the nP-chart , deal with the Percentage Defective and the number of defective items respectively. 

There are numerous approaches to the problem of capturing all the information in a set of multi endpoint data. When the data are continuous in nature, approaches such as the analog plot can be used (Chemoff, 1973 Chambers et al., 1983 Schmid, 1983). A form of control chart also can be derived for such uses when detecting effect rather than exploring relationships between variables is the goal. When the data are discontinuous, other forms of analysis must be used. Just as the control chart can be adapted to analyzing attribute data, an analog plot can be adapted. Other methods are also available. 

Control charts based on attribute data include the p chart, np chart, c chart, and chart. The former two are applied when fraction nonconforming or number of non-conforming is a concern, and the latter two are used to deal with the nonconformities. Most pharmaceutical manufacturing industries employ one or more of these charts. 

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]. 

Examination of product control charts is most useful in trying to distinguish between process-related or non-process-related causes.Trend analysis of key production parameters and attributes could assist in localizing a possible cause of the OOS. For example, if the potency of the product has been trending higher than usual for the last few batches produced (and the OOS resulted from an upper limit failure), this could be indicative of such causations as inaccurate moisture analysis or operator compensation error, error in the batch record, weighing error due to balance or scale bias, change in excipient purity which could impact functional characteristics or failure to maintain and/or calibrate apiece of equipment. 

QC tools will be used, such as check sheets, histograms, Pareto diagrams, and cause-and-effect diagrams. Scatter diagrams and control charts will be provided, where appropriate, for in-process attributes and finished-product data as an attachment. 

The relevance of Fig. 5.11 to the problem of setting control chart limits on means is that if one is furnished with a description of the typical pattern of variation in y, sensible expectations for variation in y follow from simple normal distribution calculations. So Shewhart reasoned that since about 99.7 percent (most) of a Gaussian distribution is within three standard deviations of the center of the distribution, means found to be farther than three theoretical standard deviations (of y) from the theoretical mean (of y) could be safely attributed to other than chance causes. Hence, furnished with standard values for /x and a (describing individual observations), sensible control limits for y become... 

Statistical data can be employed to construct control charts (Shewart charts) which provide action limits and warning limits for values of mean and standard deviation. Charts can be used for measurement of variability (size, volume, hardness, etc.) or attributes (good/bad or acceptable/rejectable). Values calculated from routine samples are plotted onto the relevant chart, and provided the results fall within the acceptance area, manufacture can continue until the next sample is called for. 

As with in-process production checking, finished product control can employ statistical techniques and control charts or can be derived from national sampling procedures such as MIL-STD 414 (sampling, procedures and tables for inspection by variables for per cent defectives). These sampling procedures are very similar to and complement the sampling, procedures and tables for inspection by attributes (e.g. MIL-STD 105E) and can be used in a similar manner. 

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. 

CHARTS 3.1. Data Patterns on Control 1861 5.1. Attribute Data 5.2. Control Chart for Percent 1871... 

In Section 4, two control charts for variable data are presented. Both the X control chart for monitoring the process mean and the R control chart for monitoring the process variation are presented. In Section 5, two control charts for attribute data are discussed the p control chart for monitoring percent nonconforming and the c chart for monitoring the number of defects in a sample. Furthermore, brief discussions of data patterns on control charts and recommended supplemental rules for judging nonrandom trends on a control chart are presented. 

CONTROL CHARTS FOR ATTRIBUTE DATA 5.1. Attribute Data... 

At this point, we have reviewed X and R control charts. Both of these charts are used for variable data. Many more control charts exist for varying conditions for variable data, as described above. In this section, two control charts are presented that are most useful in monitoring attribute data. In particular, a control chart known as the p chart is presented to provide a tool for monitoring the... 

Many statistical tools have been developed to control critical process parameters. The most commonly used is the control chart, which is an effective way to monitor and control processes and can be defined for both vtuiables and attributes data. The selection of variables data will typically make basic statistical tools more efficient (i.e., lower sample size requirements to achieve necessary confidence levels). 

There are two types of control charts variable and attribute. 

Attribnte control charts are the second type of control chart. These are prepared from a set of go/no-go type data. One of the issues with attribute charts is that a large data set is required. 

The p chart is used to present percent defective. A sample of 100 to 1000 items would be examined for each data point and the percent defective would be calculated and plotted on the chart. This calculation involves taking the number of defectives divided by the number in the sample and then multiplying by 100 to get the percent. The graph can be in fractions or percent. The p chart is one of the control charts for attributes that can have a variable sample size due to the ratio calculation from the data. The thing to remember is that when making a p chart the sample size should not vary much more than 25 percent from the largest sample size to the smallest sample size. 

Just as the control chart can be adapted to analyzing attribute data, an analog plot can be adapted. Other methods are also available. 

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