Testing capability indices for manufacturing processes with asymmetric tolerance limits and measurement errors

Abstract

Abstract. Most research works related to process capability indices assume no gauge measurement errors. However, such an assumption inadequately reflects real situations even when advanced measuring instruments are employed. If we do not take into account these errors, conclusions drawn from process capability are therefore unreliable. In this paper we study the sampling distribution of capability indices C p (u, v) in the presence of measurements errors, and when small subsamples data are collected from past "in-control". We show that using a critical value without taking into account these errors, severely underestimates the α-risk which causes a less accurate testing capacity. To improve the results we suggest the use of an adjusted critical value, and we give a Maple program to get it. An example in a nougat manufactory is presented to illustrate this approach.

Process Capability Evaluation Using Capability Indices as a Part of Statistical Process Control

“…In many cases, asymptotic tolerances are used for quality characteristics. How to go about evaluating the process capability in such a case is given by, e.g., Pearn and Wu [78], Grau [79].…”

Conformity and statistical tolerancing

“…Indeed, each of the preceding conformity criteria can be expressed using the traditional capability indicators [5,6] 9 associated with a characteristic (Y, n, R): 6 A given part is actually conformed if these characteristics meet the tolerance intervals. One-part conformance is therefore a binary problem modulo the measurement process.…”

“…It should be noted that if the characteristics are, on average, at nominal or at the center, there is no evidence that the resultant characteristic is on average at nominal or center. 5 Factor h > 0 is a weighting factor introduced to ease certain constraints of the quadratic tolerancing [13]. If h = 6, it is the quadratic tolerancing strictly speaking and when h ¼ 2 ffiffi ffi 3 p , it is called probabilistic tolerancing.…”

Testing capability indices for one-sided processes with measurement errors

“…Mittag [8] was the first author to link capability indices and measurement errors. For the C p , C pk , C P U , C P L , C pm , C pmk and C p (u, v) indices, Pearn and Liao [9][10][11], Pearn et al [12], Hsu et al [13], Grau [14,15] establish reliable lower confidence bounds and reliable critical values to estimate and test the process capability with gauge measurements errors.…”