Assessment of Cpm in the presence of measurement errors

Amit K Baral,M.Z Anis

doi:10.2991/jsta.2015.14.1.2

Abstract

With the advent of Taguchi's loss function, the concept of target and sticking to the target to achieve better process performance has become widely accepted. In practice, while estimating process performance, the gauge measurement error is not taken into consideration. In the real world scenario this hardly happens since measurement errors cannot be avoided in most of the manufacturing processes. Ignoring this measurement error while estimating the process capability may often lead to unreliable/wrong decision about the capability of the process under study. Therefore, in this work we apply the method of Generalized Confidence Interval (GCI) to measure the process capability index ܥ ௣௠ in presence of measurement errors. In this study, an exhaustive set of simulation has been conducted to assess the performance of the GCI method in terms of expected value of generalized lower confidence limit (ܮ ௣௠) and Coverage Probability (CP). The efficacy of dealing with the measurement error has been found satisfactory in this model. Finally it can be concluded that GCI method seems to be quite satisfactory for measuring process capability when the measurement errors are present; as well as when measurement error is negligible.

Highlights

Process Capability Indices (PCIs) have been widely used in quality assurance for quite sometimes
A substantial majority of research works on process capability analysis that has appeared in the literature do not take into account measurement errors
If the producers do not take into account the effects of the gauge capability on estimating and testing process capability, it may often lead to incorrect decisions and resulting serious loss

Summary

Introduction

Process Capability Indices (PCIs) have been widely used in quality assurance for quite sometimes. Levinson [25] should be credited for bringing the focus on gauge It was Mittag [29] who first discussed the effects of measurement errors on the performance of the four most basic process capability indices. Pearn and Liao [35] studied the estimation and testing of and in the presence of measurement error and obtained adjusted lower confidence bounds and critical values for true process capability. In a similar vein Hsu et al [18] studied the third generation index in the presence of measurement errors The result of these analyses clearly emphasize that the presence of measurement errors in the data severely affects the assessment of process capability. We have used the concept of Generalized Confidence Interval (GCI) to determine process capability of the Taguchi Index in the presence of measurement errors.

The index

Process Capability measures with measurement errors

Numerical Results and Calculations

Case Study

Conclusion