Michael Perakis

A process capability index that is based on the proportion of conformance

In this paper a new process capability index is proposed, which is based on the proportion of conformance of the process and has several appealing features. This index is simple in its assessment and interpretation and is applicable to normally or non-normally distributed processes. Likewise, its value can be assessed for continuous or discrete processes, it can be used under either unilateral or bilateral tolerances and the assessment of confidence limits for its true value is not very involved, under specific distributional assumptions. Point estimators and confidence limits for this index are investigated, assuming two very common continuous distributions (normal and exponential).

A Process Capability Index for Discrete Processes

Perakis and Xekalaki 2002, A process capability index that is based on the proportion of conformance. Journal of Statistical Computation and Simulation, 72(9), 707–718. introduced a process capability index that is based on the proportion of conformance of the process under study and has several appealing features. One of its advantages is that it can be used not only for continuous processes, as is the case with the majority of the indices considered in the literature, but also for discrete processes as well. In this article, the use of this index is investigated for discrete data under two alternative models, which are frequently considered in statistical process control. In particular, distributional properties and estimation of the index are considered for Poisson processes and for processes resulting in modeling attribute data. The performance of the suggested estimators and confidence limits is tested via simulation.

On the Implementation of the Principal Component Analysis – Based Approach in Measuring Process Capability

The use of principal component analysis in measuring the capability of a multivariate process is an issue initially considered by Wang and Chen (1998). In this article, we extend their initial idea by proposing new indices that can be used in situations where the specification limits of the multivariate process are unilateral. Moreover, some new indices for multivariate processes are suggested. These indices have been developed so as to take into account the proportion of variance explained by each principal component, thus making the measurement of process capability more effective. Copyright

On the relationship between process capability indices and the proportion of conformance

Abstract The proportion of conformance of a process, i.e. the probability of producing within the specification area, is related to the majority of the most commonly used process capability indices (PCIs). In this article, the relationship of the four most widely used indices, i.e. Cp, Cpk, Cpm and Cpmk to the proportion of conformance is examined in the case of normal processes. Results known in the literature are presented along with several new ones. Various plots, revealing interesting aspects of these relationships are also provided.

Estimation of differences between process capability indices C pm or C pmk for two processes

In this article, the estimation of the difference between the values of process capability indices C pm or C pmk for two processes is considered. Point estimators of such types of differences are defined, separately for each of the two indices, and their distributional properties are investigated. Formulae for the moments, the expected value, and the variance of these estimators are derived as well. Moreover, the assessment of confidence intervals for the true values of the differences of either C pm or C pmk is described using three alternative bootstrap techniques. The performance of these intervals seems to be rather satisfactory, as shown via simulation. It should be noted that the assessment of such confidence intervals has real practical value, since it can be implemented to several problems arising in real-world applications, such as the selection of the superior between two candidate suppliers of an industry.

On a Process Capability Index for Asymmetric Specifications

Abstract Among the process capability indices considered in the literature C pm is one of the most widely used, despite the fact that its performance often becomes unsatisfactory in the case of processes with asymmetric specifications, i.e., processes whose target value is not located at the midpoint of the specification area. In this article, a new index that is a variant of C pm , is introduced and shown to overcome this deficiency. In particular, the proposed index performs satisfactorily for processes with symmetric or asymmetric specifications. Moreover, the article compares the suggested index with the existing indices for asymmetric specifications, investigates the distributional properties of its estimator under the assumption of normality and deals with the assessment of confidence intervals using three bootstrap methods. The coverage achieved by each of these methods is investigated via simulation.

Assessing the Proportion of Conformance of a Process from a Bayesian Perspective

A Bayesian technique for assessing the posterior probability that the proportion of conformance of a normally distributed process exceeds a particular value is suggested. Both exact and approximate formulae for the assessment of this probability are derived.

On Certain Indices for Ordinal Data with Unequally Weighted Classes

In this paper, some new indices for ordinal data are introduced. These indices have been developed so as to measure the degree of concentration on the “small” or the “large” values of a variable whose level of measurement is ordinal. Their advantage in relation to other approaches is that they ascribe unequal weights to each class of values. Although, they constitute a useful tool in various fields of applications, the focus here is on their use in sample surveys and specifically in situations where one is interested in taking into account the “distance” of the responses from the “neutral” category in a given question. The properties of these indices are examined and methods for constructing confidence intervals for their actual values are discussed. The performance of these methods is evaluated through an extensive simulation study.

On a comparison of the efficacy of various approximations of the critical values for tests on the process capability indices CPL, CPU, and Cpk

Abstract In this article several formulae for the approximation of the critical values for tests on the actual values of the process capability indices CPL, CPU, and Cpk are provided. These formulae are based on different approximations of the percentiles of the noncentral t distribution and their performance is evaluated by comparing the values assessed through them from the exact critical values, for several significance levels, test values, and sample sizes. As supported by the obtained results, some of the presented techniques constitute valuable tools in situations where the exact critical values of the tests are not available, since one may approximate them readily and rather accurately through them.

On an Improvement in Confidence Limits for the Proportion of the Conformance

This paper presents a modification of a method for constructing approximate lower confidence limits for the proportion of conformance of normally distributed processes, which was proposed by Wang and Lam (1996). The proposed method is very simple and its implementation does not require the use of special tables. In addition, as verified via simulation, it leads to confidence limits with coverage much closer to the nominal in comparison to the method of Wang and Lam (1996).