Reading Assignment:

Download and read Chapter 10 in Essentials of Quality With Cases and Experiential Exercises.  Review the Discussion Questions at the end of the chapter to be sure that you understand what you have read.

Process control charts can only provide evidence for a process being either in or out of control. Control charts say nothing about the ability of the in-control process to produce products which are within specifications. In fact it is entirely conceivable for a process to be in statistical control and producing many defective parts.

Consider a process that produces yard sticks.  The process consistently produces yard sticks that are 40 inches long.  The yard stick length is in control as determined by the use of x-bar and range charts.  Unfortunately, the specification (target value) for the yard stick is 36 inches (i.e. there are 36 inches in a yard).

Analysis of the ability of the in-control process to produce products which meet the specifications is the job of process capability study.  Two commonly used measures of process capability are C_p, when the process is centered on the nominal value, and C_pk when the process is not centered on the nominal value.  Both of these measures compare the specification width to the normal process variation (as measured by 3 standard deviations above and below the mean).  It is important to note that we use the standard deviation of the process (individuals) to calculate process capability rather than the standard deviation of the sampling distribution (sample means) which we use to calculate x-bar control chart limits.

For attributes, we use p-bar, the average proportion defective for the process, as a measure of process capability.

Remember, that measures of process capability are only valid if the process is in-control when the data are collected.  It is possible to calculate a "trial process control index" for an out of control process by eliminating the out of control point(s), checking to see if the remaining data are in control, then calculating the index.  Often, by removing one out of control point and recalculating the new control chart limits another point will drift out of control requiring additional adjustment.  The trial process control index should be used only as a prediction of the capability of a process once statistical control is achieved.

Click here to access a free Cpk calculator.

Answer Discussion Questions 10-11 at the end of Chapter 10 of the text.

Do Problems 2, 11, 15 at the end of Chapter 10 of the text.

Do Experiential Exercise 3 at the end of Chapter 10 of the text.