U chart

When actual counts of incidence (often nonconformities) rather than classification of units are made, either a C chart or a U chart is usually the appropriate control chtut. Figure 14 illustrated the difference between counts and classifications. Since the subgrouping method for counts is not always based on the selection of a certain number of units, a subgroup is defined as an area of opportunity, when working with count data. 

The decision whether to use a C chart or a U chart is made by determining whether the area of opportunity will be constant or will vary for each group of counts. For example, an area of opportunity could be the number of bills received in an office each week. If the number of errors on these bills is counted, the count wiU be distorted if the number of bills received from week to week is different. How to deal with this situation will be included in the discussion of when and how to use the C chart or U chart in the remaining part of this section. Table 3 lists examples of applications of C and U charts. 

Figure 18 C and U Chart Calculation Form. (Copyright 1980-1998 Associates in Process Improvement)...

Area of Opportunity Use a C Chart if c Statistic Use a U Chart if u Statistic... 

U-CHART CONTROL LIMITS (area of opportunity may vary)... 

Uarco, Inc., 1713 U charts, 1844, 1847-1849, 1851 UILS, see Universeil indirect labor standards Ultrasonic detection, 1614-1615 Ultrasonic machining, 1323 Ultrasound sensors, 385, 386 UML, see Unified Modeling Language UMTRCA (Uranium Mill Tailings Radiation Control Act), 1153 Uncertainty interval of, 2548 optimization under, 2625-2628 Uncertainty avoidance (in national cultures), 957, 958, 960... 

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. 

The u chart is a ratio of the number of defects found per another variable like square foot, and so on. This is plotted on the same form as the c chart. Since this chart is based on a ratio the sample size can vary for this chart. 

The u-chart can be used when counting accidents per sample when the sample size varies for each observation (Training Resources and Data Exchange [TRADE] 1995). U-charts are used when it is not possible to have an inspection unit of a fixed size. This chart is also referred to as a standardized chart Quran and Godfrey 1999). A good example of data suited to this chart is the number of lost or restricted workday cases... 

The upper and lower control limits for a u chart are set by Quran and Godfrey 1999) ... 

Figure 4.6 represents a U chart for the entire population of 6,000. What is plotted is the recordable rate, month by month. The control limits represent the mean rate plus or minus three times the standard deviation U. At the beginning, there is a run of 29 months, during which the monthly... 

It is important to note that the statistical basis of the U chart is the Poisson distribution. One of the underlying assumptions is that it describes incidents, not the number of persons injured. An incident that injured nine persons would logically be plotted as a single incident on the control chart, whereas the OSHA log would reflect nine recordable injuries. That is what is actually plotted in Figure 4.7. 

The U chart is a critical tool for avoiding the overmanagement of a system that is in statistical control. It has been our experience that the U chart is frequently successful in helping traditional managers understand that accidents are produced by the process not by incompetent or unmotivated employees. These managers can then begin to look at safety improvement with a longer-term view and a systems perspective. 

The U chart helps us recognize accidents for what they are. They are the result of the design and operation of the process producing them. The further back in the process we can move to intervene and interrupt the sequence of complex events that result in the accident, the better our chances of preventing not only the accident types we are aware of and have experienced in the past, but also those new accidents we might never have predicted and, therefore, never have taken action to prevent. 

This small plant size presented a problem for safety measurement in the company. In 1993 the company was well along with the implementation of a total quality management implementation. Based on the recent training in variation and the use of control charts, the safety managers had begun to use U charts when looking at incident-rate measures. The wide limits of variation encountered with small plant sizes convinced them that incident rates would not be particularly useful as a measure of performance in the company, at least for small sites and for short time periods. 

The two other attribute charts are of imperfections rather than rejections. Not every imperfection in an item makes it unacceptable. The number of imperfections can be counted and some interpretation made of the process level via these charts. The C-Chart is a count of the number of nonconformances or imperfections typically for an entire part or structure. The U-Chart looks at the number of nonconformances for a given unit of measure. An example of a C-Chart could be the number of imperfections on a roof of an automobile. For the U-Chart , the number of imperfections per square meter of a sheet of plastic or steel would be measured. Grant and Leavenworth provide an excellent review of these chart types. Computational details can be found in Bissell and the other references suggested in Section 2.3.1.1. 

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