Control charts are not perfect tool

Control charts are not perfect tools for detecting shifts in the process distribution because they are based on sampling distributions. Two types of error are possible with the use of control charts. A type I error occurs when the conclusion is made that the process is out of control based on a sample result that falls outside the control limits, when in fact it was due to pure randomness. A type II error occurs when the conclusion is that the process is in control and only randomness is present, when actually the process is out of statistical control.These errors can be controlled by the choice of control limits. The choice would depend on the costs of looking for assignable causes when none exist versus the cost of not detecting a shift in the process. For example, setting control limits at { three standard deviations from the mean reduces the type I error because chances are only 0.26 percent that a sample result will fall outside of the control limits unless the process is out of statistical control. However, the type II error may be significant; more subtle shifts in the nature of the process distribution will go undetected because of the wide spread in the control limits. Alternatively, the spread in the control limits can be reduced to { two standard deviations, thereby increasing the likelihood of sample results from a non-faulty process falling outside of the control limits to 4.56 percent. Now, the type II error is smaller, but the type I error is larger because employees are likely to search for assignable causes when the sample result occurred solely by chance. As a general rule, use wider limits when the cost for searching for assignable causes is large relative to the cost of not detecting a shift in the process distribution.SPC methods are useful for both measuring the current process performance and detecting whether the process has changed in a way that will affect future performance. Consequently, we first discuss mean and range charts for variable measures of performance and then consider control charts for attributes measures.