TABLE OF CONTENTS Due to the simplicity of its design the index, C p cannot reflect the tendency of process centering (targeting) and thus gives no indication of the actual process performance. In order to account for the deviations of process mean from the target value, several indices, similar in nature to C p, have been proposed over the years. These indices attempt to account for the magnitude of process variance as well as for the process departures from the target value. One of such indices is C pk defined as:
where as above USL is the upper specification limit, LSL is the lower specification limit, ? is the process mean and ?is the process standard deviation. Utilizing the algebraic identity min{a,b}=(a + b) ? a ?b / 2, the definition of the index C pk can alternatively be written as:
where as above d =(USL ? LSL) / 2 is half of the length of the specification interval and m=(USL + LSL) / 2 is the mid-point between the lower and the upper specification limits. The C p and C pk indices are directly related by the process capability indices k or C a, i.e.:
Note that if ? were outside the specification range, C pk would be negative, and the process would then be inadequate for controlling the values of X. The...
