![]() The scale divisions correspond to the frequency of sampling and should be labeled by the hour or date when the data was collected, starting at the left. The horizontal scale should be the same on both charts. The R chart should be scaled similarly, with the expected range at the midpoint, and the scale extending at least 40% beyond any element. As a rule of thumb, the scale should extend at least 20% beyond any element that would be put on the graph, such as control limits. The scale should extend far enough from the midpoint to take in any expected variation. The scale increments should be sufficiently wide to graph significant changes in the average. Extending above and below the midpoint should be evenly-spaced scale divisions. This could also be thought of as the expected operating level of the process. The vertical scale of an x chart should have the grand average of the data at the midpoint (Figure 3.2.3). Figure 3.2.3 is a computer illustration of a chart, but it can also be done manually. To explain the elements of an x & R chart, it helps to create one from scratch as if we were to do it manually. The advantages of a computer lie in minimizing errors, improving the readability of the graph, and freeing the auditor to perform the more human tasks of analysis: judgment and action. Since the main calculations are finding the average and range of a set of 5 or so numbers, the charts could also be done manually. Some of the graphs shown on the following pages were produced by an IBM PC computer. Instead of calculating and graphing small histograms of data subgroups, we graph the averages and ranges on separate charts.Īn x & R chart can be made manually or by computer. The difference between the chart shown in Figure 3.2.1 and an x & R chart is that an x & R chart is easier to make. An x and R chart may possibly have alerted the operator to an out-of-control process after the first hour, and steps could have been taken to correct it. Imagine an operator taking a measurement that happens to fall within specification and, therefore, not making any adjustments. In this case, the operating level, or mean, is always within specification, but the distribution of data shows evidence of a lack of stability. Type II errorĪ Type II error is also easy to illustrate, as shown in Figure 3.2.2. Just as importantly, it could have told him when to leave it alone. An x & R chart could have told him when to adjust the operating level and by how much. Even though the process is stable and capable of making a high proportion of good parts, a large proportion of bad parts are being produced because the operator is taking only one sample and basing his decisions on it. In fact, for the whole day, about half of what he produces is out of specification and unusable. and 11:00 a.m., every part he makes is out of specification. So he moves the stops inward enough to compensate for the shifts. ![]() After his next batch, he takes a second sample and finds he is way above the upper limit. This shifts the operating level of his process. It happens to be right at the lower limit, so he moves the stops outward. But at 8:00 a.m., he picks up one part and measures it. Is there a need to adjust the stops? Certainly not. The mean is very close to the nominal and nearly every piece falls within the limits. The first batch shows evidence of stable variation ( a normal distribution ). The sideways histogram represents the distribution of those 30 parts measurements, as compared to the nominal and upper and lower limits of the specification. An example of a Type I error is an operator who adjusts the stops on a turret lathe after taking one hourly measurement. Type II error - saying a process is stable when it is unstable.īoth of these errors occur when we don’t have a method of identifying assignable causes - when we aren’t thinking statistically about the data.Type I error - saying a process is unstable when it is stable.It also provides a way to avoid the two types of errors that occur when attempting to control a process: The x & R chart is extremely efficient at this. Since the parts coming off a process may be infinite in number, we need a way to establish and monitor this operating level and variation without measuring every part. The rationale for x & R ChartsĪ control chart is used to establish the operating level and variation of a process. Since all are similar in methods of usage and analysis, only x & R charts will be treated in depth. There may be specific situations where sigma charts, median charts, and charts of individuals have some advantages over x & R charts but in most applications, an x & R chart will do as well or better. ![]() The x & R chart is the most versatile of control charts for variables. This section describes how to make and analyze x & R charts, also known as Shewhart Control Charts.
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