Capability Indices Cp Research Articles

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.

Process Capability Comparison of Fused Deposition Modelling for ABS and Fe-Nylon (6) Feedstock Filaments

Additive manufacturing (AM) is growing at a fast pace as one of the newer manufacturing technique in which the manufactured component can be put to direct use. In the category of AM, fused deposition modelling (FDM) is one of the most common technology in which the end user product can be used directly for the purpose of evaluation. This present work is taken up to study the process capability of Fe-Nylon (6) composite based feedstock filament for investigating its stability for manufacturing. Comparison has been made between the Fe-Nylon (6) composite with the existing Acrylonitrile-Butadiene-Styrene (ABS) material. It was observed that the FDM process is equally capable for ABS and Fe-Nylon (6) composite as process capability indices (Cp and Cpk) are found to be greater than one for both the materials. The calculation of process capability of the FDM machine by using both the materials is 4.5σ or higher within the specification limits specified as per the DIN standards. Control charts and the International tolerance (IT) grades as per ISO-286 indicate that the Fe-Nylon (6) composite is equally capable of manufacturing parts within the specified tolerances.

Six-sigma application in tire-manufacturing company: a case study

Globalization, advancement of technologies, and increment in the demand of the customer change the way of doing business in the companies. To overcome these barriers, the six-sigma define–measure–analyze–improve–control (DMAIC) method is most popular and useful. This method helps to trim down the wastes and generating the potential ways of improvement in the process as well as service industries. In the current research, the DMAIC method was used for decreasing the process variations of bead splice causing wastage of material. This six-sigma DMAIC research was initiated by problem identification through voice of customer in the define step. The subsequent step constitutes of gathering the specification data of existing tire bead. This step was followed by the analysis and improvement steps, where the six-sigma quality tools such as cause–effect diagram, statistical process control, and substantial analysis of existing system were implemented for root cause identification and reduction in process variation. The process control charts were used for systematic observation and control the process. Utilizing DMAIC methodology, the standard deviation was decreased from 2.17 to 1.69. The process capability index (Cp) value was enhanced from 1.65 to 2.95 and the process performance capability index (Cpk) value was enhanced from 0.94 to 2.66. A DMAIC methodology was established that can play a key role for reducing defects in the tire-manufacturing process in India.

Proposing a two-criterion quality loss function using critical process capability indices

PurposeAverage quadratic quality loss function (QQLF) measures quality of a given process using mean shift from its target value and variance. While it has a target parameter for the mean, it lacks a target for the variance revisable for counting any progress of the process across different quality levels, above/below the standard level; thus, it appears too general. Hence, in this research, it was initially supposed that all processes are located at two possible quality spaces, above/below the standard level. The purpose of this paper is to propose a two-criterion QQLF, in which each criterion is specifically proper to one of the quality spaces.Design/methodology/approachSince 1.33 is a literarily standard or satisfactory value for two most important process capability indices Cp and Cpk, its upper/lower spaces are assumed as high-/low-quality spaces. Then the indices are integrated into traditional QQLF, of type nominal the best (NTB), to develop a two-criterion QQLF, in which each criterion is more suitable for each quality space. These two criteria have also been innovatively embedded in the plan-do-check-act (PDCA) cycle to help continuous improvement. Finally, the proposed function has been examined in comparison with the traditional one in Feiz Hospital in the province of Isfahan, Iran.FindingsResults indicate that the internal process of the studied case is placed on the lower quality space. So the first criterion of revised QQLF gives a more relevant evaluation for that process, compared with the traditional function. Moreover, this study has embedded both proposed criteria in the PDCA cycle as well.Research limitations/implicationsFormulating the two-criterion QQLF only for observations of normal and symmetric distributions, and offering it solely for NTB characteristics are limitations of this study.Practical implicationsTwo more relevant quality loss criteria have been formulated for each process (service or manufacturing). However, in order to show the comprehensiveness of the proposed method even in service institutes, emergency function of Feiz Hospital has been examined.Originality/valueThe traditional loss function of type NTB merely and implicitly targets zero defect for variance. In fact, it calculates quality loss of all processes placed on different quality spaces using a same measure. This study, however, provides a practitioner with opportunity of targeting excellent or satisfactory targets.

Enhancing tensile strength of injection molded fiber reinforced composites using the Taguchi-based six sigma approach

The paper presents a case study where the targeted tensile strength of injection moldings is required to reduce or eliminate defects and to improve the process capability index C p and C pk for an injection molding process. The six sigma methodology, DMAIC (namely, design, measure, analyze, improve, and control), was applied in the study to eliminate defects, improve process, and reduce costs. The Taguchi-based six sigma approach was applied to identify the optimized processing and material parameters that led to the targeted tensile strength of injection moldings. An orthogonal array (OA) L9 was applied in the Taguchi experimental design, with four controllable factors and one non-controllable/noise factor. The four controllable factors identified include the carbon fiber (CF) content of 5 wt%, injection speed of 10 cm3/s, holding pressure of 250 bar, and barrel temperature of 260 °C, to meet the targeted tensile strength of injection moldings. A confirmation run verified the optimal parameter settings and the improved process capability index C p and C pk. An additional experiment with the CF content of 6 wt% was conducted after analyzing the effects of CF to further reduce defect, and the final results successfully demonstrated the improvement of the injection molding process. The implication of the study is that the six sigma methodology can be effectively used to eliminate defects and improve the process capability of injection molding.

Uniformity microsprinkler irrigation system using statistical quality 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.

Estimation of process capability indices from the results of limit gauge inspection of dimensional parameters in machining industry

The process capability indices Cp , Cpk are widely used in the modern quality management as statistical measures of the ability of a process to produce output X within specification limits. The customer's requirement to ensure Cp ≥ 1.33 is often applied in contracts. Capability indices estimates may be calculated with the estimates of the mean µ and the variability 6σ , and for it, the quality characteristic in a sample of pieces should be measured. It requires, in turn, using advanced measuring devices and well-qualified staff. From the other hand, quality inspection by attributes, fulfilled with limit gauges (go/no-go) is much simpler and has a higher performance, but it does not give the numerical values of the quality characteristic. The described method allows estimating the mean and the variability of the process on the basis of the results of limit gauge inspection with certain lower limit LСL and upper limit UСL , which separates the pieces into three groups: where X , number of pieces is n 1 , where LСL ≤ X , n 2 pieces, and where X ≥ UСL , n 3 pieces. So-called Pittman-type estimates, developed by the author, are functions of n 1 , n 2 , n 3 and allow calculation of the estimated µ and σ . Thus, Cp and Cpk also may be estimated without precise measurements. The estimates can be used in quality inspection of lots of pieces as well as in monitoring and control of the manufacturing process. It is very important for improving quality of articles in machining industry through their tolerance.

Statistical control process to compare and rank treatment plans in radiation oncology: impact of heterogeneity correction on treatment planning in lung cancer.

This study proposes a statistical process to compare different treatment plans issued from different irradiation techniques or different treatment phases. This approach aims to provide arguments for discussion about the impact on clinical results of any condition able to significantly alter dosimetric or ballistic related data. The principles of the statistical investigation are presented in the framework of a clinical example based on 40 fields of radiotherapy for lung cancers. Two treatment plans were generated for each patient making a change of dose distribution due to variation of lung density correction. The data from 2D gamma index (γ) including the pixels having γ≤1 were used to determine the capability index (Cp) and the acceptability index (Cpk) of the process. To measure the strength of the relationship between the γ passing rates and the Cp and Cpk indices, the Spearman's rank non-parametric test was used to calculate P values. The comparison between reference and tested plans showed that 95% of pixels have γ≤1 with criteria (6%, 6 mm). The values of the Cp and Cpk indices were lower than one showing a significant dose difference. The data showed a strong correlation between γ passing rates and the indices with P>0.8. The statistical analysis using Cp and Cpk, show the significance of dose differences resulting from two plans in radiotherapy. These indices can be used for adaptive radiotherapy to measure the difference between initial plan and daily delivered plan. The significant changes of dose distribution could raise the question about the continuity to treat the patient with the initial plan or the need for adjustments.

Method for improving the measurement system selection depending on part and process precisions

This paper suggests a method for selecting the appropriate measurement system that at best fits to the precisions of part and process simultaneously. This method conducts a hypothesis test using the number of observations n, the probabilities of type I and type II errors, the required value of the capability index (Cp,Required) and the tolerance (Tol) of the evaluated specification to establish the corresponding critical values of the number of distinct categories (NDC∗) and the precision to tolerance ratio (PTR∗). Values of Cp,Required, NDC∗ and PTR∗ are then used to draw four quarters of plane. PTR∗ is plotted on the (Tol, σm) quarter of plane, NDC∗ is plotted on the (σm, σp) quarter of plane, Cp,Required is plotted on the (Tol, σp) quarter of plane and a 45° miter line is plotted on the (σm, σm) quarter of plane. The highest tolerable level of the measurement system variability (σm) is firstly assessed by means of PTR∗ in the quarter of plane (Tol, σm). Thereafter, the adequacy of this variability to the process precision is checked out by means of projections in the quarter of plane (σm, σm) using the miter line, thereafter in the quarter of plane (σm, σp) using NDC∗ and at last in the quarter of plane (Tol, σp) using Cp,Required. The application of the proposed method avoids both cases of over and lack of precisions of the selected measurement system regarding to the tolerance of the part and to the process variability.

Lower confidence bounds as precision measure for truncated processes

ABSTRACTProcess capability index Cp has been the most popular one used in the manufacturing industry to provide numerical measures on process precision. For normally distributed processes with automatic fully inspections, the inspected processes follow truncated normal distributions. In this article, we provide the formulae of moments used for the Edgeworth approximation on the precision measurement Cp for truncated normally distributed processes. Based on the developed moments, lower confidence bounds with various sample sizes and confidence levels are provided and tabulated. Consequently, practitioners can use lower confidence bounds to determine whether their manufacturing processes are capable of preset precision requirements.

Robust design space development for HPLC analysis of five chemical components in Panax notoginseng saponins

ABSTRACTThe present work describes the systematic development of a robust, precise, and rapid reversed-phase liquid chromatography method for the simultaneous analysis of five chemical components in Panax notoginseng saponins (PNS) using quality by design (QbD). The method was developed in two main phases: screening and optimization. During the screening phase, the most suitable stationary phase, column temperature, and flow rate were identified, while the secondary influential parameters, such as the gradient slope, the initial concentration of acetonitrile, and the initial isocratic hold of the gradient elution system were fine-tuned in the later optimization phase. In this phase, a 17-run experiment was used to examine multifactorial effects of these parameters on the critical resolution, analysis time, and peak symmetry. The Monte Carlo simulation method was successfully used to build the chromatographic design space and the process capability index Cp was introduced to evaluate the robustness of the design space. At last, the verification experiment was performed within the working design space by the accuracy profile methodology and model was found to be accurate. A robust combination of separation conditions predicted in the design space was obtained with the gradient slope of 1.6% · min−1, the initial concentration of acetonitrile of 20%, and the initial isocratic hold of 20 min, and the total analysis time was no more than 40 min. The results demonstrated that rapid separation of five components of PNS herbal extract could be achieved on the chromatographic column packed with narrow size particles at backpressures available in ordinary high performance liquid chromatography (HPLC) instruments.

SU‐F‐T‐294: The Analysis of Gamma Criteria for Delta4 Dosimetry Using Statistical Process Control

Purpose:To evaluate the sensitivity of gamma criteria for patient‐specific volumetric modulated arc therapy(VMAT) quality assurance of the Delta4 dosimetry program using the statistical process control(SPC) methodology.Methods:The authors selected 20 patient‐specific VMAT QA cases which were undertaken MapCHECK and ArcCHECK with gamma pass rate better than 97%. The QAs data were collected Delta4 Phantom+ and Elekta Agility six megavolts without using an angle incrementer. The gamma index(GI) were calculated in 2D planes with normalizing deviation to local dose(local gamma). The sensitivity of the GI methodology using criterion of 3%/3mm, 3%/2mm and 2%/3mm was analyzed with using process acceptability indices. We used local confidence(LC) level, the upper control limit(UCL) and lower control limit(LCL) of I‐MR chart for process capability index(Cp) and a process acceptability index (Cpk).Results:The lower local confidence levels of 3%/3mm, 3%/2mm and 2%/3mm were 92.0%, 83.6% and 78.8% respectively. All of the calculated Cp and Cpk values that used LC level were under 1.0 in this study. The calculated LCLs of I‐MR charts were 89.5%, 79.0% and 70.5% respectively. These values were higher than 1.0 which means good quality of QA. For the generally used lower limit of 90%, we acquired over 1.3 of Cp value for the gamma index of 3%/3mm and lower than 1.0 in the rest of GI.Conclusion:We applied SPC methodology to evaluate the sensitivity of gamma criteria and could see the lower control limits of VMAT QA for the Delta 4 dosimetry and could see that Delta 4 phantom+ dosimetry more affected by the position error and the I‐MR chart derived values are more suitable for establishing lower limits.Acknowledgement: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (No. 2015R1D1A1A01060463)

Monitoring of the Production Process in Mass Production of Dimensionally Accurate Products

The main goal of the presented paperis to assess the capability of the measurement system and then evaluate the process capability in mass production of plastic moldings. The goal is to perform the measurement of a dimension characteristic serving to assess the capability of the measuring system or measurement equipment and capability of production process. After the measurements were finished, measurement capability was evaluated through the analysis of the measurement system and capability of the production process with the help of capability indices Cp, Cpk. Based on the analysis of measurement system it will be evaluated if the capability of the measurement system is acceptable.

PENGENDALIAN KUALITAS PEMOTONGAN KAIN SATEN PADA PROSES PEMBUATAN TAS DI HOME INDUSTRI X DI KABUPATEN SIDOARJO

purchasing power, making a number of craftsmen home industry in Sidoarjo either small,medium or produced in homes facing bankruptcy. Their products are not only competingwith a medium or large industrial products that use semi-modern machinery, but alsoimported products, especially from China and Vietnam which relying on cheaper productprices. Ironically, consumers now also its orientation, to model and quality. It which notowned by the craftsman home industry, because their manual production. With thiscondition, resulted in the emergence difficulties for home craftsmen in the industry toimprove and expand its business.With the variety of backgrounds, as described above, the purpose of this researchare to provide recommendations about the quality control, cutting sateen in the process ofmaking bags in the Home Industries X.Solving problems in this research using the method to determine the source ofvariation of the process, that is using the Control Chart of X-bar (average) and R(Range). The results showed that the value of Process Capability Index (Cp) in the HomeIndustry X has a value of Cp = 0.525 <1.00. This means that the process has a lowcapability to meet the specifications of the expected measurement. As well as with size ofKane Performance Index (Cpk = 0.367) were the criteria CPL = 0.367, or CPU = 0.682<1.00, which means that the process is not able to meet the lower specification limit(LSL) and upper (USL). With this condition, it is necessary to control the use of controlchart from the X-bar and R to monitor the ongoing process from time to time, to soquickly take corrective action, if any changes which not desirable in the process ofmaking bags at Home industrial X.Kata Kunci : Pengendalian Kualitas, Indek Kapabilitas Proses (Cp), Indeks Kinerja Kane(Cpk)

이변량 정규분포 하에서 공정능력지수에 대한 점근적 상관관계에 관한 연구

The process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. Some process capability indices Cp, Cpk and Cpm have been of particular interest as useful management tools for tracking process performance. Most evaluations on process capability indices focus on statistical estimation and test of hypothesis. It is necessary to investigate their asymptotic correlationship among basic estimators Ĉp, Ĉpk and Ĉpm of process capability indices Cp, Cpk and Cpm. In this paper, we study their asymptotic correlationship for three process capability indices Ĉp, Ĉpk and Ĉpm under bivariate normal distribution BN(μx, μy , σ2 x, σ 2 y , ρ). With some nonnormal processes, the asymptotic correlation coefficient of any two respective process capability index estimators could be established.

Process-based tolerance assessment of connecting rod machining process

Process tolerancing based on the process capability studies is the optimistic and pragmatic approach of determining the manufacturing process tolerances. On adopting the define–measure–analyze–improve–control approach, the process potential capability index (C p) and the process performance capability index (C pk) values of identified process characteristics of connecting rod machining process are achieved to be greater than the industry benchmark of 1.33, i.e., four sigma level. The tolerance chain diagram methodology is applied to the connecting rod in order to verify the manufacturing process tolerances at various operations of the connecting rod manufacturing process. This paper bridges the gap between the existing dimensional tolerances obtained via tolerance charting and process capability studies of the connecting rod component. Finally, the process tolerancing comparison has been done by adopting a tolerance capability expert software.

ANALISIS KINERJA PROSES LATEX DIPPING MENGGUNAKAN TEKNIK CAPABILITY PROCESS (STUDI KASUS: PT DHARMA MEDIPRO)

The quality of product is reflected from the performance of its process. The most frequent issue that occurs in local company today -- is -- most company only focuses on the output regardless the process. It causes the difficulty that occurs in local company to compete with other company in global environment. One of the local companies that has their business shifting up significantly, with the great number of export target and actual export, is PT Dharma Medipro, which has many processes on the production of sphygmomanometer. One of the processes that critical to quality is latex dipping process, where the yield of this process that must be considered is the thickness of the bag component. In order to improve the process, we should first establish the measurement of process performance using capability process technique, which is one of the tools came from statistical process control method. The result indicates that the process is unstable with the value of capability indices Cp = 4,69 ; Cpk = -0,77 ; Cpu = -0,77 ; Cpl = 10,15 ; and Cpm = 0,28, moreover the number of part per million (PPM) that out of the spesification limit reach 912.500 units.