Process Capability Indices Cp Research Articles

Enhancing Process Stability and Quality Management: A Comprehensive Analysis of Process Capability Indices

Process Capability Indices such as Process Capability Index (Cp) and Corrected Process Capability Index (Cpk), along with Process Performance Index (Pp) and Process Performance Corrected Index (Ppk), are most commonly used tools in quality management within manufacturing processes. They determine whether a process is capable of producing products within established tolerance limits, addressing both short-term and long-term variability. Despite widespread use, the analysis of Process Capability Indices often overlooks special variability within processes, which may lead to misleading interpretations of a process's capability, especially when the determination of tolerance limits is inadequately conducted. This article aims to verify the hypothesis that current analyses of Process Capability Indices fail to consider special variability, which could mislead the interpretation of a process's ability to meet its specifications. Statistical analyses were conducted using the Minitab software, based on dynamic viscosity measurements from the production process of solvent-based paint, to explore the implications of special variability on the interpretation of Process Capability Indices. The study revealed that while Process Capability Indices are useful for identifying quality management opportunities, their effectiveness is limited when special variability is present, often resulting in misinterpretations of a process's true capabilities. The findings highlight the need for methodologies that incorporate considerations of all forms of variability to ensure accurate process capability assessments. This gap in traditional analyses can affect the strategic decision-making in quality management, suggesting a critical area for further research and methodological development. The research confirms the need for a revised approach in analyzing Process Capability Indices, advocating for advanced methods that accurately reflect all forms of variability to improve quality management practices. Future research should focus on developing these methodologies to ensure more reliable and effective use of Process Capability Indices in quality management.

On process capability of single screw extruder for fabricating PVDF composite matrix

In this study, a single screw extruder (SSE) was used to fabricate the poly (vinylidene fluoride) (PVDF) matrix inform of filament forthe material extrusion process in line with sustainable development goal (SDG) (with a special target on the industry, innovation, and infrastructure). For industrial use, the fabricated filament must be statistically controlled from a dimensional deviation viewpoint, so an effort has been made to ascertain the process capability of SSE based on the diameter of the filament. The study's findings indicate that the fabricated PVDF composite filaments are statistically controlled, as the process capability indices (Cp and Cpk) are > 1. The best setting for the SSE (for the minimum deviation) in the case of compositions A/B and D are a screw temperature of 220 °C and a screw speed of 7 rpm. For composition C the screw temperature was 230 °C and the screw speed of 7 rpm. The controlled dimensional deviations are also presented as international tolerance (IT) grades for assembly applications.

On direct metal laser sintering of functional prototype- X and R- chart and analysis of process capability

In this study, direct metal laser sintering (DMLS) was used to fabricate the functional prototype of a stifel prosthesis. A benchmark was fabricated using 17–4 precipitate-hardened (PH) stainless steel (SS). For industrial use, the process capability of the DMLS fabricated prototypes needs to be ascertained, so an effort has been made to check the process capability by fabricating functional prototypes under the specified printing parameters. Finally, a methodology has been presented for the design, fabrication, and analysis of printed components. The result of this study suggests that the value of process capability indices (Cp and Cpk) is greater than 1. Further X and R bar charts were plotted for statistical analysis.

THE ACCURACY OF ESTIMATES OF THE PROCESS REPRODUCIBILITY INDICES WITH CONSIDERING THE NUMBER OF EFFECTIVE DEGREES OF FREEDOM OF STANDARD DEVIATION

The issue of determining the accuracy of estimates of the process capability indices Cp and Cpk based on their standard deviations is considered. At the same time, since the capability indices can only be used under conditions of a statistically stable state of the process, which from a practical point of view means the need to maintain appropriate Shewhart control charts, the values Ϭ of the indices of Cp and Cpk should be determined based on k samples (data groups), each volume n and using an estimate of the standard deviation of the process according to the studied quality characteristic Ϭ, found on the basis of intragroup variability. However, in this case, it is necessary to take into account the number of effective degrees of freedom of the estimate Ϭ, since this directly affects the values σ of the standard deviations of the estimates Cp and Cpk.

Process Capability Indices With Student Mixture Models Applied to Aircraft Engines GD&T

Abstract Usually, the process capability indices (PCIs) Cp and Cpk are used to quantify the production quality of Geometric Dimensioning & Tolerancing (GD&T). For the most popular PCIs, a strong assumption about normality is required. Many previous works provide information about misleading conclusions when we use usual PCIs without any verification of the dataset normality. In recent industrial developments, many processes increasingly complicate, and GD&T are mostly geometrical specifications. For that reason, most characteristics are not normally distributed. There are two issues when calculating PCIs with nonnormal distributions. First, we have to define PCIs that can deal with all distributions. Second, we need to determine the distribution of the dataset. To do so, we give a short review of the previous work about calculating PCIs with nonnormal distributions. Following that first part, we propose our method for nonnormal distributions. This method uses new PCIs based on the quantile of a standard normal distribution. Then, we consider an estimation method based on a Student mixture model. This allows handling nonnormal distributions, potentially with outliers, and mixture distributions, which are often treated as two different fields and are common in industrial datasets. Finally, we propose some use cases to benchmark our new PCIs and Student mixture model for aircraft engines GD&T applications.

Confidence Intervals for the Common Process Capability Index Cp of Normal Distributions

Confidence Intervals for the Common Process Capability Index Cp of Normal Distributions

Semantic-Based Assembly Precision Optimization Strategy Considering Assembly Process Capacity

Assembly precision optimization is an important means to ensure product accuracy, including two aspects: on the one hand, the relevant deviations of out-of-tolerance key characteristics are reduced to the design tolerance range; on the other hand, the deviation fluctuation range of key characteristics with a large process capability index (Cp) can be extended to achieve the balance between accuracy, process capacity, and production cost. By virtue of the accumulated experience, a fast solution can be provided for the out-of-tolerance problem. Therefore, a semantic-based assembly precision optimization method considering process capacity is proposed in this paper. By constructing an ontology model between Cp and optimization strategy, a reasonable assembly precision optimization strategy can be pushed based on product accuracy analysis results. Firstly, an assembly precision optimization semantic model is established by association between analysis results, out-of-tolerance key characteristics, assembly process, and tolerance adjustment defined with Web Ontology Language (OWL) assertions. Furtherly, according to different Cp corresponding to different assembly success rates, Semantics Web Rule Language (SWRL) rules based on Cp are constructed to the push optimization strategy. Finally, the effectiveness of the model is illustrated by an aircraft inner flap.

Utility of process capability indices in assessment of quality control processes at a clinical laboratory chain.

BackgroundTo evaluate the utility of the process capability indices C p and C pk for assessing the quality control processes at chain laboratory facilities.MethodsIn April 2020, the minimum C p and C pk values for 33 assays of a laboratory chain with 19 facilities were collected for further analysis and a total of 627 datasets (C p and C pk) were compared. In addition, standard values for C p and C pk, defined as the lowest of the top 20%, were obtained for comparison and the indices were used to determine whether precision or trueness improvements were required for the corresponding assay.ResultsA total of 627 datasets of 33 assays from 19 laboratory facilities were collected for further analysis. Based on the C p results, 329 (52.5%), 211 (33.7%), 65 (10.3%), and 22 (3.5%) were rated as excellent, good, marginal, and poor, respectively. While the corresponding results for C pk were 300 (47.8%), 216 (34.4%), 79 (12.6%), and 32 (5.1%). In addition, it was noteworthy that eight (C p criteria) and six assays (C pk criteria) were rated as excellent or good at all 19 facilities. Comparison of the process capability indices at the Jinan KingMed Center with the standard values revealed that total protein, albumin, and urea showed trueness individual improvement, precision individual improvement, and precision common improvement, respectively, while the results of other assays were stable.ConclusionProcess capability indices are useful for evaluating the quality control procedures in laboratory facilities and can help improve the precision and trueness of laboratory tests.

Process quality indices: new metrics for process quality capability with zero-loss baseline

The traditional process capability indices Cp /Cpk for evaluating process capability used in the current industry are based on the probability model of a process distribution, which makes it difficult for many processes whose actual output with non-normal distribution to apply these indices. In this paper, new process quality indices (PQI) Qp /Qpk are proposed for measuring the quality capability of the process. The new PQI are derived from Taguchi's quality loss function model and do not need to estimate the probability distribution of the process output. The traditional process capability indices Cp /Cpk are zero-defect indices, it focus on meeting the process specification requirements, while the new PQI Qp /Qpk are zero-loss indices, it focus on approaching the process target value. The construction of the new PQI is logical, simple, and practical. The PQI approach is more suitable for quality management in the Era of big data.

Investigation of production parameters for process capability analysis: A case study

Today the part of an engineer is compelled to perform manufacturing, and in addition to survey whether the product is fit for conveying the same parametric results or convey insufficient defective parts. This can be an expert by process capability considerations. However, there is an unusual impact on process capability on production expenses for any manufacturing areas. An engineer is constrained to perform generation assignment, as well as to examine whether the procedure is fit for delivering the same parametric results or create blemished segments. This can be accomplished by a statistical process capability study. In this paper, an endeavor has been made to highlight the procedure of factual resistance breaking points and its appropriateness for evaluating the process capability of Y9T caliper. The Y9T caliper influenced by different cutting parameters, for example, speed of machine; feed rate and length of cut and so on. By considering the above parameters for ordinary running conditions, the process capability indices (Cp and Cpk) for a few Cases were gotten. The procedure for ordinary conditions is in measurable control however, there is an extension for improvement of process expenses by enhancing the capability indices. There might be a possibility for enhancing process capability records of the same process through changing the process parameters likes the speed of machine, feed rate, and length of cut. The outcomes got from further cases demonstrate the change in process capability indices. The outcomes likewise demonstrate that there is a change in the manufacturing rate per batch by enhancing process capability.

Process capability analysis of binder jetting 3D printing process for fabrication of calcium sulphate based porous bone scaffolds

ABSTRACT This study aims at investigating the process capability of a 3D printer for the fabrication of porous bone scaffolds. Initially, a suitable material is identified by optimising process parameters of a 3D printer using a full factorial design approach. Then, dimensional deviation and tolerance grades of the scaffold samples are calculated. Finally, process capability indices are evaluated and the process is recentred. Out of two materials under study, VisiJet PXL Core powder is found to provide better dimensional accuracy. Tolerance grades of the samples are found to be ranged from IT3 to IT10. Maximum dimensional deviation before and after centring the process is found to be 0.47% and 0.44%, respectively. Process capability indices Cp and Cpk are greater than 1 and close to industry benchmark (Cpk ≥1.33). This indicates the process is under statistical control and capable of fabricating porous bone scaffolds suitable for in vitro or in vivo bone tissue engineering applications.

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

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.

3D printed tensile and flexural prototypes of thermoplastic matrix reinforced with multi-materials: A statistical analysis

Fused deposition modelling (FDM) is one of the established low cost 3D printing techniques for preparation of functional/ non functional prototypes from thermoplastic composite matrix (prepared as multi/ hybrid blended material). But hitherto little has been reported on multi material reinforced thermoplastic matrix in successive 3D printed layers from repeatability view point. Since the adaptability of any processing technique is dependent upon repeatability/ reproducibility (for which the process output must be statistically controlled), this work reports the statistical analysis of 3D printed tensile and flexural samples printed on FDM as functional prototypes of poly lactic acid (PLA) matrix reinforced with multi materials (poly vinyl chloride (PVC), wood dust and magnetite (Fe 3 O 4 ) powder) as functionally graded thermoplastic matrix. Further in this work functional prototypes of tensile and flexural sample were 3D printed and tested for their mechanical properties to analyze the process capability index (Cp and Cpk) along with morphological characteristics using optical images of the fractured surfaces. The result of the study suggests that the process was observed to be in statistical control as Cp and Cpk was found to be more than 1 for tensile and flexural properties. Based upon optical photo micrographs it has been ascertained that the optimized 3D printing parameters resulted into uniform morphological features (based upon surface roughness (Ra) and amplitude distribution function (ADF), peak count (PC) and bearing ratio (BR) curve).

On 3D printed scaffolds for orthopedic tissue engineering applications

This paper outlines an in vitro evaluation of 3D printed scaffold of polylactic acid (PLA) blended with hydroxyapatite (HAp) and chitosan (CS) for orthopedic tissue engineering applications. In the first stage, selected composition/proportion of PLA–HAp–CS (based on melt flow-ability, mechanical and thermal properties) was 3D printed with fused deposition modeling (FDM) process. The 3D printed scaffolds were used for process capability analysis to ascertain the industrial usability of PLA–HAp–CS composite scaffold for batch production (especially in assembly applications). Further, in the second stage, an in vitro evaluation was performed to investigate the linkages of fibroblast cells for 3D printed scaffold. The results of study outline the rapid increase in growth of fibroblast cells for FDM-printed scaffolds of PLA–HAp–CS thus ensuring its capability of supporting cell adhesion and cell proliferation. Further, the dimensional variations and Shore D hardness of 3D printed scaffolds are under statistically control, with process capability indices (Cp and Cpk ≥ 1).

On multi response optimization and process capability analysis for surface properties of 3D printed functional prototypes of PVC reinforced with PP and HAp

This paper outlines the multi response optimization and process capability analysis for surface properties of 3D printed functional prototypes of poly vinyl chloride (PVC) reinforced with poly propylene (PP) and hydroxyapatite (HAp) for possible bio-sensing applications. The process started with mechanical extrusion of filament wire with fix proportion of HAp in biocompatible polymers (PP and PVC) by using twin screw extrusion (TSE) process followed by 3D printing of functional prototypes (of standard tensile specimen as per ASTM D 638) on commercial fused deposition modelling (FDM) setup. The analysis of variance (ANOVA) has been used to study the effect of three controllable parameters of the FDM (i.e. infill percentage, layer thickness, and speed of extrusion head) on the surface roughness (Ra), hardness (H), and dimensional accuracy (ΔD) of 3D printed functional prototypes. The results of multi-response optimization suggests that parts printed at 100% infill density, 0.25 mm layer thickness and 33 mm/sec have better H, controlled Ra and ΔD. Further process capability indices (Cp and Cpk) were calculated to ensure the statistical nature of the process. The results of study suggest that for selected responses, Cp and Cpk values are ≥1, hence the 3D printed functional prototypes with in-house prepared filaments of PVC-PP-HAp meets the requirements of batch/mass production. Finally X bar and R bar charts were prepared to understand the statistical nature of the process.

On process capability comparison of hybrid and multi blend PLA matrix composite: Magnetic and surface properties view point

The poly lactic acid (PLA) matrix composites have wide self-assembly non-structural engineering applications. Some studies have reported the use of hybrid blend and multi blend PLA matrix for possible 3D printing. This work is an extension of studies reported on optimization of magnetic and surface properties for hybrid blend (PLA-50 wt%, poly vinyl chloride (PVC)-25 wt%, wood powder-5% and Fe3O4-20 wt%) and multi blend (PLA-80 wt% and Fe3O4-20 wt%) in self assembly applications. The hybrid and multi blended feedstock filaments for 3D printing has been prepared by using established conditions of twin screw extrusion (TSE) as per reported literature (i.e. barrel temperature of 170 °C, screw speed 45 rpm and extrusion load of 5 kg). For industrial applications of any process it must be statistically controlled for batch/mass production. Therefore in the present work an effort has been made for comparative process capability analysis based upon magnetic properties (obtained by vibration sample magnetometer, surface porosity (obtained by photomicrographs) and surface hardness (obtained by Shore D hardness) after preparing multi-blend and hybrid blend of PLA matrix composite as feed stock filament. The results of the study suggests that process of multi blend and hybrid blend of PLA matrix is under statistical control as the values of process capability indices (Cp and Cpk) for magnetic as well as surface properties are ≥1. Further X-chart and R-chart also signifies that both multi blend and hybrid blend PLA matrix composite predicts almost similar range of Cp and Cpk. Hence either multi blend or hybrid blend feed stock filament of PLA matrix composite may be used in batch/mass production for non-structural engineering applications.

A comparison of some modified confidence intervals based on robust scale estimators for process capability index

This paper aims to compare the performances of modified confidence intervals based on robust scale estimators with classical confidence interval for process capability index (Cp) when the process has a non-normal distribution. The estimated coverage probability and the average width of the confidence intervals were obtained by a Monte-Carlo simulation under different scenarios. Simulation results showed that the modified confidence intervals performed well in terms of coverage probability and average width for all cases. Two real-life numerical examples from industry are analyzed to illustrate the performance and the implementation of the classical and modified confidence intervals for the process capability index (Cp) which also supported the results of the simulation study to some extent.

Departmental action limits for TQA energy variations defined by means of statistical process control methods.

The purpose of this study is to define departmental action limits for energy percentage variation measured by means of step-wedge helical Tomotherapy quality assurance module. Individual charts using the Statistical Process Control techniques have been used to identify retrospectively out-of-control situations ascribable to documented actions performed on the Tomotherapy system. Using the in-control data of our analysis process capability indices (cp, cpk, cpm and cpmk) are calculated in order to document the real working condition of the Tomotherapy system. Our findings indicate use of an action limit of 1.0% for energy percentage variation difference between the measured and reference output is a good working condition of a Tomotherapy system. cp and cpk indices are suggested as good indices that correctly report the system capability. A method for calculating and reporting Tomotherapy action limits for the integrated self-checking TQA energy check was shown in this study. SPC technique has proven to be efficient in defining departmental action limits from retrospective data for TQA energy measurements, hence optimally enabling corrective improvements in the process of quality assurance.

The Quality Analysis and Optimum of Key process Based on Minitab

The quality control of weapons and equipment manufacturing enterprises is not only the foundation of development, but also the life guarantee of equipment users, and it is also a key element for combat effectiveness improvement. Aiming at the problems of high computational requirements and lack of intuitiveness in the application of SPC technology, based on the analysis of SPC principles and methods, this paper designs the SPC process and method based on minitab software, and focuses on the quality characteristics of key processes of a certain type of product. According to the analysis, the process and method proposed in the paper are feasible. The calculation results based on minitab are scientific and credible. After the process optimization is implemented by causal analysis method, the process capability index Cp can reach 1.41, compared with 0.90 before optimization, the ability to be significantly improved, combined with the control chart analysis tool, can further determine the controlled state of the production process. The results show that the quality control and quality analysis of the production process based on minitab is very necessary and feasible for distinguishing the random fluctuations and abnormal fluctuations of product quality, and providing early warning and corrective measures for abnormal conditions, which make the production process in a controlled state.

Investigations for mechanical properties and biocompatibility of SS-316L implant prepared as rapid investment casting for batch production

In this work, a detailed procedure for the development of biomedical implant (SS-316L) by combining fused deposition modeling (FDM), chemical vapor smoothing (CVS), silicon molding (SM) and investment casting (IC) for batch production has been outlined. In spite of being biocompatible and bioactive within the body, the implant must possess good surface quality and dimensional accuracy along with sufficient hardness in order to reduce the wear inside the body. So in this research work, investigations have been made on the surface finish, dimensional accuracy and hardness of the implants by varying two controllable factors of the IC process (drying time of primary coating and mould thickness). The tolerance grades for the selected dimension of the casted implants were within the allowable range as defined in UNI EN 20286-I (1995) standard of ISO. The process capability indices (Cp and Cpk) values greater than 1.33 for the surface hardness and radial dimension indicated that the proposed process is statistically controlled. Further, in order to evaluate the biocompatibility, an in vitro study was conducted to ensure the attachment of mouse embryonic fibroblasts cells (NIH-3T3) to the casted samples. The results of invitro study indicated that samples were capable of supporting cell adhesion and cell proliferation and hence can be used for tissue engineering.