When problems are indicated by dispersion base your

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Unformatted text preview: cs Technical standards Problem concerning dispersion Problem solution through dispersion reduction Technical standards Technical standards Problem concerning outliers Problem solution though the prevention ofoutliers Discussion This text briefly introduces some of the key concepts related to the dispersion of data. You will find much more detail in Unit 11 – Statistical Methods. In the meantime, discuss how these concepts could be used to recognize abnormalities in your work processes. This text does not have an action plan. A Roadmap to Quality 21 Unit 9 - Problem solving 05-87581_unit 9.qxd 09/09/2005 11:54 Page 22 9.8 Control charts Introduction 1. Control charts are a key tool in interpreting data. They can distinguish between dispersions caused by accidental factors and dispersions caused by abnormal factors, and can show whether the process is in a stable condition or not. A control chart consists of a central line (CL) and upper and lower control limits (UCL and LCL). UCLs and LCLs are based on calculated values. 2. When characteristic values that indicate process conditions are plotted as data points on the control chart, and all the points fall within the upper and lower control limits, or there is no bias in the way the points are distributed (i.e. they are not distributed in any particular way), the process is said to be “under control”. When the plotted points fall outside the control limits or there is a bias in the way the points are distributed, the process is “out of control”. In other words, an abnormality has emerged in the process. You should then investigate the causes of the abnormality and take countermeasures. (Texts 11.4.1 to 11.4.5 in Unit 11, Statistical Methods, provide more detailed guidelines on using control charts.) 3. The following criteria indicate when the process is out of control: a. When one or more plotted points fall outside the control lines. b. When the points indicate a bias. This can be: i. When seven or more points form a chain above or below the central line. ii. When a large number of points are on one side of the central line, e.g. 10 out of 11 consecutive points. iii. When five or more consecutive points form an upward or downward line. iv. Other cases which show periodicity. 4. Data may include variables or discrete values or both. Variables include measured values such as length (meter) and weight (kilogram). These are continuous values (i.e. they are uncountables – you cannot count them). Discrete values are non-continuous values such as the number of defective units and flaws within a sheet (i.e. they are countable). Types of control chart 5. There are several kinds of control chart: a. –-R control charts (average and range). x These are used in the management of variable data. – and R represent a sub-group x – control charts are used for average and sub-group range respectively. The x monitoring changes in the sub-group average (variation among sub-groups), while the R control charts are used for managing dispersions within a sub-group (variation within a sub group). These two charts are paired for use. Unit 9 - Problem solving 22 A Roadmap to Quality 05-87581_unit 9.qxd 09/09/2005 11:54 Page 23 b. “p” control charts and “pn” control charts: These manage processes in which the characteristic values of discrete values are considered. “pn” control charts are used when the number of samples (n) is constant and the number of defective units (pn) is considered. When the number of samples (n) is not constant, in other words when the ratio of defects (p) is considered, “p” control charts are used. c. “c” control charts (defects per unit) or “u” control charts (standard defects per unit) may be used depending on the characteristics of measured values. Figure 9.8a Flow chart for selection of control chart types Selection of control charts Does the data indicate the number of defective units? –-x-R Control x– charts –-Rs Control x charts pn Control charts Is the group size constant? Not constant –-R Control charts x –-R Control charts x Is the group size constant? Not constant Can the data be compiled and grouped? Constant Does the central line (CL) take –? x Discrete values n=2 Grouping impossible Does the group (n) contain two or more members? Grouping possible n≥2 Is the data variable? Constant Variables c Control charts p Control charts u Control charts How to draw control charts 6. These directions are for –-R control charts, the type that is most frequently used. x Step 1. Gather data In principle, more than 100 pieces of data should be collected. This data must be relatively new, nearly identical to what future processes are expected to produce in terms of technology, and accompanied by a clear history. Step 2. Classify the data Classify the data into sub-groups and arrange it by measuring times or lots. The number of data items that one sub-group contains is known as the sub-group size. It is represented by the letter “n”. Usually, “n...
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