Kernel Density Estimation and Metropolis-Hastings Sampling in Process Capability Analysis of Unknown Distributions

2012 ◽  
Author(s):  
Wenzhen Huang ◽  
Ankit Pahwa ◽  
Zhenyu Kong
Keyword(s):  
Density Estimation ◽  
Kernel Density ◽  
Process Capability ◽  
Kernel Functions ◽  
Process Capability Analysis ◽  
Normality Assumption ◽  
Capability Indices ◽  
Capability Analysis ◽  
Future Extension ◽  
Strong Normality

Strong normality assumption is associated with widely used process capability indices such as cp, cpk. Violation of the assumption will mislead the interpretation in applications. A nonparametric method is proposed for density estimation of any unknown distribution. Kernels are used for density estimation and metropolis-hastings (M-H) algorithm is adopted to generate samples from the density. M-H sampling provides a tool to accommodate different kernel functions and flexibility of future extension to multivariate cases. Conformity (yield) based indices (yp, y) are adopted to replace cp, cpk. These indices can be conveniently assessed by the proposed kernel density based M-H algorithm (K-M-H). The method is validated by several simulation case studies.

scholarly journals CAPABILITY INDICES FOR CONTROL CHARTS BASED ON REGRESSION MODELS

2015 ◽  
Vol 12 (2) ◽  
pp. 234
Author(s):  
Fernanda Siqueira Souza ◽  
Danilo Cuzzuol Pedrini ◽  
Carla Schwengber Ten Caten
Keyword(s):  
Quality Improvement ◽  
Control Charts ◽  
Regression Models ◽  
Process Capability ◽  
Process Capability Analysis ◽  
Capability Indices ◽  
Capability Analysis ◽  
Simulated Process

Process capability analysis is extremely important for optimization and quality improvement. It verifies whether the process under analysis is capable of producing items within engineering and customers’ specifications. The use of capability indices when assumptions are not satisfied leads to erroneous conclusions, compromising the study and analysis of the process, jeopardizing the fulfillment of requirements from management or external customers. Aiming at filling a gap identified in the literature, the main contributions of this work are: (i) proposition of capability indices for processes monitored through control charts based on regression models, for symmetric and asymmetric specifications; and (ii) comparison of the proposed indices with traditional capability indices through a simulated process.

scholarly journals Analisis Masalah Kualitas pada M/C Crank Shaft M2 dengan Menggunakan Tool Capability Process di PT XYZ, Pegangsaan Dua, Jakarta

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Gidion Karo Karo ◽  
Jessie Deborah R. Makapedua
Keyword(s):  
Process Improvement ◽  
Control Process ◽  
Process Capability ◽  
Repair Process ◽  
Process Capability Analysis ◽  
Normality Test ◽  
Quality Control Process ◽  
Capability Indices ◽  
Capability Analysis

<p>Process Capability is a tool that is often used in the process of quality improvement, especially for process improvement. This study uses a process capability analysis on crank shaft production line 2 for motorcycles. By using normality test data and process capability indices for calculation of Cp/Cpk, shows that most of the data obtained are not normally distributed, so need to transform the data into normal, which can then be followed by the calculation of process capability. For the calculation of Cp/Cpk, it was found that there were some machines that still need to get tight control to meet the specification. It shows that mass production is still less stable. In order to meet the specifications, it is necessary to improve the quality of the repair process to reduce the variation in the process.</p><p>Keywords: Process Capability, Quality Control, Process Improvement</p>

scholarly journals Analyzing of Process Capability Indices based on Neutrosophic Sets

2021 ◽  
Author(s):  
Selin Yalçın ◽  
Ihsan Kaya
Keyword(s):  
Automotive Industry ◽  
Process Capability ◽  
Process Capability Indices ◽  
Neutrosophic Sets ◽  
Modeling Uncertainty ◽  
Inaccurate Information ◽  
Process Capability Analysis ◽  
Capability Indices ◽  
Capability Analysis ◽  
Human Thinking

Abstract Process capability analysis (PCA) is an important statistical analysis approach for measuring and analyzing the ability of the process to meet specifications. This analysis has been applied by producing process capability indices (PCIs). \({C}_{p}\) and \({C}_{pk}\) are the most commonly used PCIs for this aim. Although they are completely effective statistics to analyze process’ capability, the complexity of the production processes based on uncertainty arising from human thinking, incomplete or vague information makes it difficult to analyze the process capability with precise values. When there is uncertain, complex, incomplete and inaccurate information, the capability of the process is successfully analyzed by using the fuzzy sets. Neutrosophic sets (NSs), one of the new fuzzy set extensions, have a significant role in modeling uncertainty, since they contain the membership functions of truth, indeterminacy, and falsity definitions rather than an only membership function. This feature provides a strong advantage for modeling uncertainty. In this paper, PCA has been performed based on NSs to overcome uncertainties of the process. For this purpose, specification limits (SLs) have been reconsidered by using NSs and two of the well-known process capability indices (PCIs) named \({C}_{p}\) and \({C}_{pk}\) have been reformulated. Finally, the neutrosophic process capability indices (NPCIs) named \({C}_{p}\) \(\left({\tilde{\stackrel{⃛}{C}}}_{p}\right)\) and \({C}_{pk}\) \(\left({\tilde{\stackrel{⃛}{C}}}_{pk}\right)\) have been derived for three cases that are created by defining SLs. Additionally, the obtained NPCIs have also been applied and confirmed on real case problems from automotive industry. The obtained results show that the NPCIs support the quality engineers to easily define SLs and obtain more flexible and realistic evaluations for PCA.

Process design and capability analysis using penthagorean fuzzy sets: surgical mask production machines comparison

2021 ◽  
pp. 1-13
Author(s):  
Elif Haktanır ◽  
Cengiz Kahraman
Keyword(s):  
Fuzzy Sets ◽  
Process Capability ◽  
Intuitionistic Fuzzy Sets ◽  
Process Capability Analysis ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Capability Indices ◽  
Capability Analysis ◽  
Tremendous Importance ◽  
Picture Fuzzy Sets

Process capability analysis (PCA) is a tool for measuring a process’s ability to meet specification limits (SLs), which the customers define. Process capability indices (PCIs) are used for establishing a relationship between SLs and the considered process’s ability to meet these limits as an index. PCA compares the output of a process with the SLs through these capability indices. If the customers’ needs contain vague or imprecise terms, the classical methods are inadequate to solve the problem. In such cases, the information can be processed by the fuzzy set theory. Recently, ordinary fuzzy sets have been extended to several new types of fuzzy sets such as intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets. In this paper, a new extension of intuitionistic fuzzy sets, which is called penthagorean fuzzy sets, is proposed, and penthagorean fuzzy PCIs are developed. The design of production processes for COVID-19 has gained tremendous importance today. Surgical mask production and design have been chosen as the application area of the penthagorean fuzzy PCIs developed in this paper. PCA of the two machines used in surgical mask production has been handled under the penthagorean fuzzy environment.

scholarly journals Process Capability Analysis in the Manufacturing of Pet Bottles

2010 ◽  
Vol 3 (S1) ◽  
pp. 531-534
Author(s):  
Maja Rujnić-Sokele ◽  
Mladen Šercer ◽  
Damir Godec
Keyword(s):  
Process Capability ◽  
Process Capability Analysis ◽  
Pet Bottles ◽  
Capability Analysis

New multivariate process capability indices for measuring the performance of multivariate processes subject to non-normal distributions

2015 ◽  
Vol 33 (1) ◽  
pp. 42-61 ◽  
Author(s):  
Jeh-Nan Pan ◽  
Chung-I Li ◽  
Wei-Chen Shih
Keyword(s):  
Process Capability ◽  
Process Capability Indices ◽  
Process Data ◽  
Multivariate Process ◽  
Multivariate Processes ◽  
Content Type ◽  
Normal Distributions ◽  
Normality Assumption ◽  
Capability Indices ◽  
Multivariate Manufacturing

Purpose – In the past few years, several capability indices have been developed for evaluating the performance of multivariate manufacturing processes under the normality assumption. However, this assumption may not be true in most practical situations. Thus, the purpose of this paper is to develop new capability indices for evaluating the performance of multivariate processes subject to non-normal distributions. Design/methodology/approach – In this paper, the authors propose three non-normal multivariate process capability indices (MPCIs) RNMC p , RNMC pm and RNMC pu by relieving the normality assumption. Using the two normal MPCIs proposed by Pan and Lee, a weighted standard deviation method (WSD) is used to modify the NMC p and NMC pm indices for the-nominal-the-best case. Then the WSD method is applied to modify the multivariate ND index established by Niverthi and Dey for the-smaller-the-better case. Findings – A simulation study compares the performance of the various multivariate indices. Simulation results show that the actual non-conforming rates can be correctly reflected by the proposed capability indices. The numerical example further demonstrates that the actual quality performance of a non-normal multivariate process can properly reflected by the proposed capability indices. Practical implications – Process capability index is an important SPC tool for measuring the process performance. If the non-normal process data are mistreated as a normal one, it will result in an improper decision and thereby lead to an unnecessary quality loss. The new indices can provide practicing managers and engineers with a better decision-making tool for correctly measuring the performance for any multivariate process or environmental system. Originality/value – Once the existing multivariate quality/environmental problems and their Key Performance Indicators are identified, one may apply the new capability indices to evaluate the performance of various multivariate processes subject to non-normal distributions.

Modelling and process capability analysis of Focused Ion Beam

2009 ◽  
Author(s):  
Stoyan Stoyanov ◽  
Ying Kit Tang ◽  
Chris Bailey ◽  
Robert Evans ◽  
Silvia Marson ◽  
...  
Keyword(s):  
Focused Ion Beam ◽  
Ion Beam ◽  
Process Capability ◽  
Process Capability Analysis ◽  
Capability Analysis

scholarly journals Process Capability Analysis in a Polypropylene Bag Manufacturing Company

2021 ◽  
Vol 25 (8) ◽  
pp. 1477-1482
Author(s):  
O.F. Odeyinka ◽  
F.O. Ogunwolu ◽  
O.P. Popoola ◽  
T.O. Oyedokun
Keyword(s):  
Control Charts ◽  
Process Capability ◽  
Production Plant ◽  
Specification Limit ◽  
Process Capability Analysis ◽  
Capability Analysis ◽  
Vertically Aligned ◽  
Lower Specification Limit ◽  
And Control

Process capability analysis combines statistical tools and control charts with good engineering judgment to interpret and analyze the data representing a process. This work analyzes the process capability of a polypropylene bag producing company. The case study organization uses two plants for production and data was collected over a period of nine months for this study. Analysis showed that the output spread of plant 1 was greater than the specification interval spread which implies poor capability. There are non-conforming parts below the Lower Specification Limit (LSL: 500,000 metres) and above the Upper Specification Limit (USL: 600,000 metres) and that the output requires improvement. Similarly, the capability analysis of plant 2 shows that the overall output spread is greater than the specification interval spread (poor capability). The output centre in the specification and overall interval are vertically aligned, thus specifying that the output from plant 2 is also process centered and requires improvement. Recommendations were made to improve the outputs from each production plant.

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