Methodological insights for industrial quality control management: The impact of various estimators of the standard deviation on the process capability index

The process capability index (PCI) evaluates the ability of a process to produce items with certain quality requirements. The PCI depends on the process standard deviation, which is usually unknown and estimated by using the sample standard deviation. The construction of confidence intervals for the PCI is also an important topic. The usual estimator of the PCI and its corresponding confidence interval are based on various assumptions, such as normality, the fact that the process is under control, or samples selected from infinite populations. The main aim of this paper is to investigate the empirical properties of estimators of the PCI, and analyze numerically the effect on confidence intervals when such assumptions are not satisfied, since these situations may arise in practice.

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Modified weighted standard deviation index for adequately interpreting a supplier’s lognormal process capability

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405418755820 ◽

2018 ◽

Vol 233 (3) ◽

pp. 999-1008 ◽

Cited By ~ 3

Author(s):

Mou-Yuan Liao ◽

WL Pearn

Keyword(s):

Standard Deviation ◽

Coverage Probability ◽

Process Capability ◽

Process Capability Index ◽

Process Performance ◽

Normal Process ◽

Efficient Tool ◽

Process Yield ◽

Capability Index ◽

Normality Assumption

The process capability index has become an efficient tool for measuring a supplier’s process performance. [Formula: see text] is one popularly used index for assessing non-normal process capability when the process violates the normality assumption. Unfortunately, this index cannot accurately reflect the process yield, so it may produce a serious result if the practitioner compares the calculated [Formula: see text] value with the capability requirement to determine whether the process meets that requirement. Hence, this study modifies [Formula: see text] to provide an adequate measure of lognormal process capability. In addition, an estimator of this modified index is also provided. Simulations show that the bias of this estimator is slight, and the coverage probability of capability testing is close to the nominal confidence. This means that our proposed method is adaptable for use.

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Confidence interval for the process capability index based on the bootstrap-t confidence interval for the standard deviation

Advances in Methodology and Statistics ◽

10.51936/vvcb8367 ◽

2014 ◽

Vol 11 (2) ◽

Author(s):

Wararit Panichkitkosolkul

Keyword(s):

Standard Deviation ◽

Confidence Interval ◽

Coverage Probability ◽

Process Capability ◽

Process Capability Index ◽

Skewed Distributions ◽

Monte Carlo Simulation Study ◽

Nominal Level ◽

R Language ◽

Capability Index

This paper proposes a confidence interval for the process capability index based on the bootstrap-t confidence interval for the standard deviation. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence interval with the existing confidence interval based on the confidence interval for the standard deviation. Simulation results show that the proposed confidence interval performs well in terms of coverage probability in case of more skewed distributions. On the other hand, the existing confidence interval has a coverage probability close to the nominal level for symmetrical or less skewed distributions. The code to estimate the confidence interval in R language is provided.

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Uniformity microsprinkler irrigation system using statistical quality control

Ciência Rural ◽

10.1590/0103-8478cr20160546 ◽

2017 ◽

Vol 47 (4) ◽

Author(s):

Maurício Guy de Andrade ◽

Marcio Antonio Vilas Boas ◽

Jair Antonio Cruz Siqueira ◽

Mireille Sato ◽

Jonathan Dieter ◽

...

Keyword(s):

Quality Control ◽

Control Charts ◽

Irrigation System ◽

Process Capability ◽

Process Capability Index ◽

Statistical Quality Control ◽

Uniformity Coefficient ◽

Statistical Quality ◽

Capability Index ◽

Shewhart Control

ABSTRACT: The objective of this study was to evaluate the use of statistical quality control tools in the analysis of the uniformity of a microsprinkler irrigation system. For the analysis of irrigation Christiansen uniformity coefficient (CUC) and the distribution uniformity coefficient (DU) were statistically analyzed by means of the Shewhart control charts and process capability index (Cp). For the experiment 25 tests were carried out with a single micro sprinkler and subsequently seven different spacing between micro sprinklers were simulated. Control charts contributed to the diagnosis of the treatments to be under control and with satisfactory uniformity outcomes. Increase in process capability index was directly proportional to the average of CUC and DU.

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Manufacturing Capability Index of 3D Printing Parts for Impact Applications

Volume 5: Biomedical and Biotechnology ◽

10.1115/imece2020-23123 ◽

2020 ◽

Author(s):

Anne Schmitz

Keyword(s):

High Resolution ◽

3D Printing ◽

Brinell Hardness ◽

Weight Bearing ◽

Impact Resistance ◽

Process Capability ◽

Process Capability Index ◽

Impact Testing ◽

Capability Index ◽

The Impact

Abstract Three-dimensional (3D) printing with high-resolution stereolithography (SLA) has grown in popularity for creating personalized medical devices. 3D printing is now starting to expand to weight-bearing components, e.g. prosthetic feet, as data on the dynamic properties impact and fatigue is published in the literature. The next step towards using 3D printing in impact applications is to assess the capability of the high-resolution SLA process to manufacture components of uniform impact resistance. Because impact testing is destructive, a surrogate measure to check a part’s viability for resisting an impact load also needs to be established. Thirteen notched Izod specimens were printed on a Form2 SLA printer using the manufacturer’s clear V4, photocurable resin. Once all the specimens were printed, washed in isopropyl alcohol, and cured with ultraviolet light, the impact resistance was quantified using a pendulum impact tester in a notched Izod configuration. Then, the hardness of the specimens was quantified using a HBW 10/250 scale. The impact resistance of the clear, SLA polymer was 0.59 ± 0.14 ft-lb/in. With an upper standard limit of 0.53 ft-lb/in, the process capability index was 0.133. Impact resistance and Brinell hardness were not correlated with a Spearman coefficient of r = −0.108, p = 0.73. Since the process capability index was less than one, 3D printing with SLA polymers is not a viable manufacturing process for creating parts of consistent impact resistance. The current technology would lead to too many rejected parts. Also, Brinell hardness and impact strength were not related. Therefore, there is no non-destructive method to spot-check these components before use.

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Performance of a Robust Confidence Interval for the Process Capability Index Cp based on the Modified Trimmed Standard Deviation Under Non-Normal Distributions

WSEAS TRANSACTIONS ON MATHEMATICS ◽

10.37394/23206.2020.19.62 ◽

2020 ◽

Vol 19 ◽

Keyword(s):

Standard Deviation ◽

Confidence Interval ◽

Process Capability ◽

Process Capability Index ◽

Robust Estimator ◽

Average Width ◽

Normal Distributions ◽

Capability Index ◽

Simulation Results ◽

Interval Estimator

In this paper, a robust interval estimator for the classical process capability index (Cp) based on the modified trimmed standard deviation (MTSD = ST ∗ ) is considered under both normal and non-normal distributions. The performance of the newly proposed process capability index interval estimator over the existing method is compared using a simulation study. As a performance criterion, we consider both simulated coverage probability and average width. Simulation results evident that the proposed confidence interval based on the robust estimator performed well for most of cases. For illustration purposes, two real-life data from industry are analyzed which supported our simulation results to some extent. As a result, the proposed method can be recommend to be used by the practitioners in various fields of industry, engineering and physical sciences.

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