Capability Testing Based on C pm with Multiple Samples

Numerous process capability indices have been proposed in the manufacturing industry to provide unitless measures on process performance, which are effective tools for quality improvement and assurance. Most existing methods for capability testing are based on the distribution frequency approaches. Recently, Bayesian approaches have been proposed for testing capability indices C p and C pm but restricted to cases with one single sample. In this paper, we consider estimating and testing capability index C pm based on multiple samples. We propose accordingly a Bayesian procedure for testing C pm . Based on the Bayesian procedure, we develop a simple but practical procedure for practitioners to use in determining whether their manufacturing processes are capable of reproducing products satisfying the preset capability requirement. A process is capable if all the points in the credible interval are greater than the pre-specified capability level. To make the proposed Bayesian approach practical for in-plant applications, we tabulate the minimum values of C * (p) for which the posterior probability p reaches various desirable confidence levels

Process capability and data contamination

DOI nefunkční (4.5.2018)Purpose: The paper centres on process capability and its relation to data contamination. Process capability may be distorted due to imprecise data. The paper analyses to what extent capability changes reflect problems in data so that the changes can be attributed to data sampling rather than the true performance of the process. This is important because it is usually much simpler to increase the precision of data sampling than the process itself. Methodology/Approach: The paper has two major parts. In part one, effect of data contamination on the observed process characteristic is analysed. The effect is analysed using data obtained from simulated random drawings and the chi-squared test. In the other part, reaction of capability to data contamination is observed. The capability is measured by a univariate capability index. Findings: Regarding the sensitivity of the index to contamination, it is different depending on the capability before the contamination. This leads to conclusions about when the company using the index should focus more on the way the data is measured, and when it should focus more on improving the process in question. The analysis shows that if the company is used to high levels of capability and records its drop, it is worth analysing its measurement system first, as the index is at higher levels more sensitive to data contamination. Research Limitation/implication: The study concerns a single univariate index, and the contamination is modelled with only several probability distributions. Originality/Value of paper: The findings are not difficult to detect, but are not known in practice where companies do not realize that problems with their process capability may sometimes lie in the data they use and not in the process itself.Web of Science213615

Possibilities of using graphical and numerical tools in the exposition of process capability assessment techniques

Purpose: The paper focuses on how the problem of process capability assessment can be handled when taught, using convenient numerical and graphical means. The contents of the paper results from the authors' own academic and practical experience, which suggested that many important steps are overlooked in the process of selecting and using capability indices. Methodology/Approach: Selected problems in capability assessment are illustrated with suitable examples and graphs. Findings: The authors' experience is reflected in the paper, aiming to emphasize what matters and how, and what does not. Also, a new capability index is introduced. Research Limitation/implication: The style in which the problems are analysed may serve as a guide for further studies in the field and capability index applications. Originality/Value of paper: The paper also contains, aside from specific examples, some more advanced techniques, and is therefore accompanied by software readouts, since computer support is required in such cases. Category: Conceptual paperWeb of Science232331

A New SVDD-Based Multivariate Non-parametric Process Capability Index

Process capability index (PCI) is a commonly used statistic to measure ability of a process to operate within the given specifications or to produce products which meet the required quality specifications. PCI can be univariate or multivariate depending upon the number of process specifications or quality characteristics of interest. Most PCIs make distributional assumptions which are often unrealistic in practice. This paper proposes a new multivariate non-parametric process capability index. This index can be used when distribution of the process or quality parameters is either unknown or does not follow commonly used distributions such as multivariate normal

List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units