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Develop your understanding of Control Charts, Process Capability, Process Improvement, etc. … Attribute Control Charts:Attribute control charts are utilized when monitoring count data. There are two categories of count data, namely data which arises from “pass/fail” type measurements, and data which arises where a count in the form of 1,2,3,4,…. arises. Depending on which form of data is being recorded, differing forms of control charts should be applied.“u” and “c” control charts.The “u” and “c” control charts are applied when monitoring and controlling count data in the form of 1,2,3, …. i.e. specific numbers. An example of such data is the number of defects in a batch of raw material, or the number of defects identified within a finished product. The c chart is used where there can be a number of defects per sample unit and the number of samples per sampling period remains constant. In the u chart, again similar to the c chart, the number of defects per sample unit can be recorded, however, with the u chart, the number of samples per sampling period may vary.“p” and “np” control charts.P charts are utilized where there is a pass / fail determination on a unit inspected. The p chart will show if the proportion defective within a process changes over the sampling period (the p indicates the portion of successes). In the p chart the sample size can vary over time. A similar chart to the p chart is the np chart. However, with the np chart the sample size needs to stay constant over the sampling period. An advantage of the np chart is that the number non-conforming is recorded onto the control rather than the fraction non conforming. Some process operators are more comfortable plotting the number rather than the fraction of non-conformances.Pre-control Charts.Where a process is confirmed as being within statistical control, a pre-control chart can be utilized to check individual measurements against allowable specifications. Pre-control charts are simpler to use than standard control charts, are more visual and provide immediate “call to actions” for process operators. If however a process is not statistically “capable” i.e. having a Cpk of at least 1, pre-control can result in excessive process stoppages.Develop your understanding of Control Charts, Process Capability, Process Improvement, etc. … MDME: MANUFACTURING, DESIGN, MECHANICAL ENGINEERING
Control charts are used for monitoring a process. This helps to provide warnings and corrective data for adjusting a manufacturing process, or scheduling overhauls and re-builds. A Guide to Control Chartshttp://www.isixsigma.com/tools-templates/control-charts/a-guide-to-control-charts/ Identifying Variation When a process is stable and in control, it displays common cause variation, variation that is inherent to the process. A process is in control when based on past experience it can be predicted how the process will vary (within limits) in the future. If the process is unstable, the process displays special cause variation, non-random variation from external factors. Control charts are simple, robust tools for understanding process variability. The Four Process States Processes fall into one of four states: 1) the ideal, 2) the threshold, 3) the brink of chaos and 4) the state of chaos (Figure 1).3 When a process operates in the ideal state, that process is in statistical control and produces 100 percent conformance. This process has proven stability and target performance over time. This process is predictable and its output meets customer expectations. A process that is in the threshold state is characterized by being in statistical control but still producing the occasional nonconformance. This type of process will produce a constant level of nonconformances and exhibits low capability. Although predictable, this process does not consistently meet customer needs. The brink of chaos state reflects a process that is not in statistical control, but also is not producing defects. In other words, the process is unpredictable, but the outputs of the process still meet customer requirements. The lack of defects leads to a false sense of security, however, as such a process can produce nonconformances at any moment. It is only a matter of time. The fourth process state is the state of chaos. Here, the process is not in statistical control and produces unpredictable levels of nonconformance. Figure 1: Four Process States Four Process States Every process falls into one of these states at any given time, but will not remain in that state. All processes will migrate toward the state of chaos. Companies typically begin some type of improvement effort when a process reaches the state of chaos (although arguably they would be better served to initiate improvement plans at the brink of chaos or threshold state). Control charts are robust and effective tools to use as part of the strategy used to detect this natural process degradation (Figure 2).3 Figure 2: Natural Process Degradation Natural Process Degradation Elements of a Control Chart There are three main elements of a control chart as shown in Figure 3. 1.A control chart begins with a time series graph. 2.A central line (X) is added as a visual reference for detecting shifts or trends – this is also referred to as the process location. 3.Upper and lower control limits (UCL and LCL) are computed from available data and placed equidistant from the central line. This is also referred to as process dispersion. Figure 3: Elements of a Control Chart 3.Adding (3 x ? to the average) for the UCL and subtracting (3 x ? from the average) for the LCL Mathematically, the calculation of control limits looks like: Calculation of Control Limits (Note: The hat over the sigma symbol indicates that this is an estimate of standard deviation, not the true population standard deviation.) Because control limits are calculated from process data, they are independent of customer expectations or specification limits. Control rules take advantage of the normal curve in which 68.26 percent of all data is within plus or minus one standard deviation from the average, 95.44 percent of all data is within plus or minus two standard deviations from the average, and 99.73 percent of data will be within plus or minus three standard deviations from the average. As such, data should be normally distributed (or transformed) when using control charts, or the chart may signal an unexpectedly high rate of false alarms. Controlled Variation Controlled variation is characterized by a stable and consistent pattern of variation over time, and is associated with common causes. A process operating with controlled variation has an outcome that is predictable within the bounds of the control limits. Figure 4: Example of Controlled Variation Uncontrolled Variation Uncontrolled variation is characterized by variation that changes over time and is associated with special causes. The outcomes of this process are unpredictable; a customer may be satisfied or unsatisfied given this unpredictability. Figure 5: Example of Uncontrolled Variation Example of Uncontrolled Variation Please note: process control and process capability are two different things. A process should be stable and in control before process capability is assessed. Figure 6: Relationship of Control Chart to Normal Curve Relationship of Control Chart to Normal Curve Control Charts for Continuous DataIndividuals and Moving Range ChartThe individuals and moving range (I-MR) chart is one of the most commonly used control charts for continuous data; it is applicable when one data point is collected at each point in time. The I-MR control chart is actually two charts used in tandem (Figure 7). Together they monitor the process average as well as process variation. With x-axes that are time based, the chart shows a history of the process. The I chart is used to detect trends and shifts in the data, and thus in the process. The individuals chart must have the data time-ordered; that is, the data must be entered in the sequence in which it was generated. If data is not correctly tracked, trends or shifts in the process may not be detected and may be incorrectly attributed to random (common cause) variation. There are advanced control chart analysis techniques that forego the detection of shifts and trends, but before applying these advanced methods, the data should be plotted and analyzed in time sequence. The MR chart shows short-term variability in a process – an assessment of the stability of process variation. The moving range is the difference between consecutive observations. It is expected that the difference between consecutive points is predictable. Points outside the control limits indicate instability. If there are any out of control points, the special causes must be eliminated. Once the effect of any out-of-control points is removed from the MR chart, look at the I chart. Be sure to remove the point by correcting the process – not by simply erasing the data point. Figure 7: Example of Individuals and Moving Range (I-MR) Chart Example of Individuals and Moving Range (I-MR) Chart The I-MR chart is best used when: 1.The natural subgroup size is unknown. 2.The integrity of the data prevents a clear picture of a logical subgroup. 3.The data is scarce (therefore subgrouping is not yet practical). 4.The natural subgroup needing to be assessed is not yet defined. Xbar-Range ChartsAnother commonly used control chart for continuous data is the Xbar and range (Xbar-R) chart (Figure 8). Like the I-MR chart, it is comprised of two charts used in tandem. The Xbar-R chart is used when you can rationally collect measurements in subgroups of between two and 10 observations. Each subgroup is a snapshot of the process at a given point in time. The chart’s x-axes are time based, so that the chart shows a history of the process. For this reason, it is important that the data is in time-order. The Xbar chart is used to evaluate consistency of process averages by plotting the average of each subgroup. It is efficient at detecting relatively large shifts (typically plus or minus 1.5 ? or larger) in the process average. The R chart, on the other hand, plot the ranges of each subgroup. The R chart is used to evaluate the consistency of process variation. Look at the R chart first; if the R chart is out of control, then the control limits on the Xbar chart are meaningless. Figure 8: Example of Xbar and Range (Xbar-R) Chart Example of Xbar and Range (Xbar-R) Chart Table 1 shows the formulas for calculating control limits. Many software packages do these calculations without much user effort. (Note: For an I-MR chart, use a sample size, n, of 2.) Notice that the control limits are a function of the average range (Rbar). This is the technical reason why the R chart needs to be in control before further analysis. If the range is unstable, the control limits will be inflated, which could cause an errant analysis and subsequent work in the wrong area of the process. Table 1: Control Limit Calculations Control Limit Calculations Can these constants be calculated? Yes, based on d2, where d2 is a control chart constant that depends on subgroup size. The I-MR and Xbar-R charts use the relationship of Rbar/d2 as the estimate for standard deviation. For sample sizes less than 10, that estimate is more accurate than the sum of squares estimate. The constant, d2, is dependent on sample size. For this reason most software packages automatically change from Xbar-R to Xbar-S charts around sample sizes of 10. The difference between these two charts is simply the estimate of standard deviation. Control Charts for Discrete Datac-ChartUsed when identifying the total count of defects per unit (c) that occurred during the sampling period, the c-chart allows the practitioner to assign each sample more than one defect. This chart is used when the number of samples of each sampling period is essentially the same. Figure 9: Example of c-Chart Example of c-Chart u-ChartSimilar to a c-chart, the u-chart is used to track the total count of defects per unit (u) that occur during the sampling period and can track a sample having more than one defect. However, unlike a c-chart, a u-chart is used when the number of samples of each sampling period may vary significantly. Figure 10: Example of u-Chart Example of u-Chart np-ChartUse an np-chart when identifying the total count of defective units (the unit may have one or more defects) with a constant sampling size. Figure 11: Example of np-Chart Example of np-Chart |