15 research outputs found

### Desirability to characterize process capability

Over the past few years continuously new process capability indices have been developed, most of them with the aim to add some feature missed in former process capability indices. Thus, for nearly any thinkable situation now a special index exists which makes choosing a certain index as difficult as interpreting and comparing index values correctly. In this paper we propose the use of the expected value of a certain type of function, the so-called desirability function, to assess the capability of a process. The resulting index may be used analogously to the classical indices related to Cp, but can be adapted to nearly any process and any specification. It even allows a comparison between different processes regardless of their distribution and may be extended straightforwardly to multivariate scenarios. Furthermore, its properties compare favorably to the properties of the ?classical? indices. --

### A note on a multivariate analogue of the process capability index C_p

A simple method is given to calculate the multivariate process capability index C_p* as defined by Taam et al. (1993) and discussed by Kotz & Johnson (1993). It is shown that using this index is equivalent to using the smallest univariate C_p-value to determine the capability of a process

### Desirability to characterize process capability

Over the past few years continuously new process capability indices have been developed, most of them with the aim to add some feature missed in former process capability indices. Thus, for nearly any thinkable situation now a special index exists which makes choosing a certain index as difficult as interpreting and comparing index values correctly. In this paper we propose the use of the expected value of a certain type of function, the so-called desirability function, to assess the capability of a process. The resulting index may be used analogously to the classical indices related to C , but can be adapted to nearly any process and any specification. It even allows a comparison between different processes regardless of their distribution and may be extended straightforwardly to multivariate scenarios. Furthermore, its properties compare favorably to the properties of the "classical" indices

### A note on a multivariate analogue of the process capability index C p

A simple method is given to calculate the multivariate process capability index C p * as defined by Taam et al. (1993) and discussed by Kotz & Johnson (1993). It is shown that using this index is equivalent to using the smallest univariate C p -value to determine the capability of a process. The index MVC p * Analogously to univariate process capability indices also multivariate capability indices relate the allowed process spread, i.e. some measure of the specification width, to the actual process spread, i.e. some measure of the process variation. The specification for the i th quality variable X i is usually given by the triple of lower specification limit LSL i , target value T i and upper specification limit USL i . For the p quality characteristics a multivariate normal distribution with mean vector and positive definite covariance matrix S = = ( ) , . . s ij i j p 1 is commonly assumed. The natural generalization of the univariate capability index C p would be t..

### A note on a multivariate analogue of the process capability index C_p

SIGLEAvailable from TIB Hannover: RR 8460(1998,7) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

### A note on the behaviour of the process capability index C_p_m_k with asymmetric specification limits

The properties of C_p_m_k in the presence of asymmetric specification limits are discussed. It is shown that C_p_m_k tends to zero as the process variation increases and vice versa. Furthermore, if the process variation is small, C_p_m_k has its maximum near the target value but the maximum moves towards the specification midpoint as the variation increases. This is a desirable property as for large variation the percentage of items inside the specification limits is larger if the process mean is equal to the specification midpoint than if it is equal to the target value. Attention is drawn to the fact that for small process variations there is a shoulder in the graph of C_p_m_k when the process mean is equal to the specification midpoint. (orig.)Available from TIB Hannover: RR 8460(1997,12) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman