Eng. Mgt. 385 Statistical Process Control Chapter 4: Why The Control Chart Works

Control Charts Were all these samples drawn from the same bowl? Is there one universe from which these samples appear to come? Do these figures indicate a stable pattern of variation? Is this variation the result of a constant-cause system? Do these measurement show statistical control? –If the answer is no, the decision is the “hunt for assignable causes of variation, find it, and fix it. –If the answer is yes, then leave the process alone. –The decision on the establishment of the limits, that is -/- z , is one of economic balance. –What is the cost to hunt for trouble that is not there, or not look when trouble actually is there? –3  limits strike a decent balance.

Control Charts Control charts, when set up properly, help to establish visual stability of a process. Stability indicates one universe is present. Control charts for averages are established in general by:  +/- z  x where  x =  /  n  +/- 3  x limits roughly indicate points will be expected outside of the limits.27% of the time, an event that is unlikely. Hence if a point is outside of the control limit, it indicates, but does not guarantee an assignable cause of variation. Points outside of the r chart or s chart, also indicate an assignable cause of variation, though not necessarily to the level of the control chart for averages.

Formulas For Control Charts Equations for 3-Sigma limits are shown in Table 4.1, page 123. Note that the method has  and  known or assume,  and  estimated from X and R,  and  estimated from X and s Tables D, E, and F, in the appendix utilize the appropriate factors, based on the sample size. Estimates of the process standard deviation can be made from the grand range or grand standard deviation of sample data.

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