TY - JOUR
ID - 119805
TI - A note on the generalized indices of process capability
JO - International Journal of Research in Industrial Engineering
JA - RIEJ
LA - en
SN - 2783-1337
AU - Gauri, S. Kumar
AU - Pal, S.
AD - Statistical Quality Control and Operations Research Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India.
AD - Statistical Quality Control and Operations Research Unit, Indian Statistical Institute, 110, Nelson Manickam Road, Chennai- 600029, India.
Y1 - 2020
PY - 2020
VL - 9
IS - 3
SP - 286
EP - 303
KW - Generalized PCI
KW - Goodness of generalized PCI
KW - normal process
KW - Poisson Process
KW - binomial process
DO - 10.22105/riej.2020.237520.1137
N2 - Process capability indices are widely used to assess whether the outputs of an in-control process meet the specifications. The commonly used indices are , , and . In most applications, the quality characteristics are assumed to follow normal distribution. But, in practice, many quality characteristics, e.g. count data, proportion defective etc. follow Poisson or binomial distributions, and these characteristics usually have one-sided specification limit. In these cases, computations of or using the standard formula is inappropriate. In order to alleviate the problem, some generalized indices (e.g. index, index, index and index) are proposed in literature. The variant of these indices for one-sided specification are and , and ¸ and , and respectively. All these indices can be computed in any process regardless of whether the quality characteristics are discrete or continuous. However, the same value for different generalized indices and or signifies different capabilities for a process and this poses difficulties in interpreting the estimates of the generalized indices. In this study, the relative goodness of the generalized indices is quantifying capability of a process is assessed. It is found that only or gives proper assessment about the capability of a process. All other generalized indices give a false impression about the capability of a process and thus usages of those indices should be avoided. The results of analysis of multiple case study data taken from Poisson and binomial processes validate the above findings.
UR - https://www.riejournal.com/article_119805.html
L1 - https://www.riejournal.com/article_119805_0acf48cbbf99aa5cfca2df0617a0b369.pdf
ER -