## Control Chart For Mean and Range (MR-CHART)

The basic idea in all quality control charts is to select a sample from a production process at equal intervals of time and record some quality characteristic. The most common quality characteristic is the mean of each sample. If the process is under control, the series of sample means should vary about the population mean in a random manner. That is, we should expect some natural variation in any process and there should be no real assignable cause to this variation. If the process is in control, almost all sample mean values should fall within control limits, almost always defined as the mean plus or minus 3 standard deviations. The standard deviation is a measure of the variation of a process. If all sample observations are constant, the standard deviation is zero; as variation increases, the standard deviation grows. The control charts do not measure the standard deviation directly. Instead, the range (high value minus low value) of each sample is used as a simpler measure of variation. To establish control limits, the range is automatically converted to a standard deviation.
It is important to understand that the control chart is a management-by-exception tool. If a sample mean falls outside the control limits, there is a very small probability that this happened due to randomness or chance alone. In fact, with control limits set at 3 standard deviations, the probability is less than 1% that the sample mean occurred due to chance. There is a very large probability, more than 99%, that the sample mean is due to an assignable cause and an investigation should be conducted.

The control charts in SOM are classified as either variable or attribute charts. Variables are measurements on a continuous scale such as inches or pounds. What types of variables can be monitored with the variables control charts? Anything that can be measured and expressed in numbers, such as temperature, dimension, hardness number, tensile strength, weight, viscosity, etc. Variables are monitored in the MR-CHART worksheet for the mean and range of samples and in the I-CHART for individual observations. Attributes are discrete data such as the number of items in the sample that are defective or the number of defects in one unit of product. The P-CHART and CU-CHART models are available for attributes data.