Fuzzy U control chart based on fuzzy rules and evaluating its performance using fuzzy OC curve

Purpose The purpose of this paper is to apply fuzzy spectrum in order to collect the vague and imprecise data and to employ the fuzzy U control chart in variable sample size using fuzzy rules. This approach is improved and developed by providing some new rules. Design/methodology/approach The fuzzy operating characteristic (FOC) curve is applied to investigate the performance of the fuzzy U control chart. The application of FOC presents fuzzy bounds of operating characteristic (OC) curve whose width depends on the ambiguity parameter in control charts. Findings To illustrate the efficiency of the proposed approach, a practical example is provided. Comparing performances of control charts indicates that OC curve of the crisp chart has been located between the FOC bounds, near the upper bound; as a result, for the crisp control chart, the probability of the type II error is of significant level. Also, a comparison of the crisp OC curve with OCavg curve and FOCα curve approved that the probability of the type II error for the crisp chart is more than the same amount for the fuzzy chart. Finally, the efficiency of the fuzzy chart is more than the crisp chart, and also it timely gives essential alerts by means of linguistic terms. Consequently, it is more capable of detecting process shifts. Originality/value This research develops the fuzzy U control chart with variable sample size whose output is fuzzy. After creating control charts, performance evaluation in the industry is important. The main contribution of this paper is to employs the FOC curve for evaluating the performance of the fuzzy control chart, while in prior studies in this area, the performance of fuzzy control chart has not been evaluated.

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Research on the quality stability evaluation and monitoring based on the pre-control chart

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-02-2013-0032 ◽

2014 ◽

Vol 31 (9) ◽

pp. 966-982 ◽

Cited By ~ 2

Author(s):

Shu Qing Liu ◽

Qin Su ◽

Ping Li

Keyword(s):

Sample Size ◽

Production Process ◽

Control Chart ◽

Control Charts ◽

Stability Evaluation ◽

Monitoring And Control ◽

Content Type ◽

Quality Stability ◽

Evaluation And Monitoring ◽

And Control

Purpose – In order to meet the requirements of 6σ management and to overcome the deficiencies of the theory for using the pre-control chart to evaluate and monitor quality stability, the purpose of this paper is to probe into the quality stability evaluation and monitoring guidelines of small batch production process based on the pre-control chart under the conditions of the distribution center and specifications center non-coincidence (0<ɛ≤1.5σ), the process capability index C p ≥2 and the virtual alarm probability α=0.27 percent. Design/methodology/approach – First, the range of the quality stability evaluation sampling number in initial production process is determined by using probability and statistics methods, the sample size for the quality stability evaluation is adjusted and determined in initial production process according to the error judgment probability theory, and the guideline for quality stability evaluation has been proposed in initial production process based on the theory of small probability events. Second, the alternative guidelines for quality stability monitoring and control in formal production process are proposed by using combination theory, the alternative guidelines are initially selected based on the theory of small probability events, a comparative analysis of the guidelines is made according to the average run lengths values, and the monitoring and control guidelines for quality stability are determined in formal production process. Findings – The results obtained from research indicate that when the virtual alarm probability α=0.27 percent, the shifts ɛ in the range 0<ɛ≤1.5σ and the process capability index C p ≥2, the quality stability evaluation sample size of the initial production process is 11, whose scondition is that the number of the samples falling into the yellow zone is 1 at maximum. The quality stability evaluation sample size of the formal production process is 5, and when the number of the samples falling into the yellow zone is ≤1, the process is stable, while when two of the five samples falling into the yellow, then one more sample needs to be added, and only if this sample falls into the green zone, the process is stable. Originality/value – Research results can overcome the unsatisfactory 6σ management assumptions and requirements and the oversize virtual alarm probability α of the past pre-control charts, as well as the shortage only adaptable to the pre-control chart when the shifts ɛ=0. And at the same time, the difficult problem hard to adopt the conventional control charts to carry out process control because of a fewer sample sizes is solved.

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Synthetic control charts with two-stage sampling for monitoring bivariate processes

Pesquisa Operacional ◽

10.1590/s0101-74382007000100007 ◽

2007 ◽

Vol 27 (1) ◽

pp. 117-130 ◽

Cited By ~ 11

Author(s):

Antonio F. B. Costa ◽

Marcela A. G. Machado

Keyword(s):

Sample Size ◽

Control Chart ◽

Control Charts ◽

Quality Characteristics ◽

Synthetic Control ◽

Two Stage ◽

Variable Sample Size ◽

Second Stage ◽

Process Disturbances

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control bivariate processes. During the first stage, one item of the sample is inspected and two correlated quality characteristics (x;y) are measured. If the Hotelling statistic T1² for these individual observations of (x;y) is lower than a specified value UCL1 the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the Hotelling statistic T2² for the sample means of (x;y) is computed. When the statistic T2² is larger than a specified value UCL2, the sample is classified as nonconforming. According to the synthetic control chart procedure, the signal is based on the number of conforming samples between two neighbor nonconforming samples. The proposed chart detects process disturbances faster than the bivariate charts with variable sample size and it is from the practical viewpoint more convenient to administer.

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A Novel Adaptive Control Chart with Variable Sample Size, Sampling Interval and Control Limits: A three Stage Variable Parameters (TSVP)

International Journal of Business and Management ◽

10.5539/ijbm.v8n2p38 ◽

2012 ◽

Vol 8 (2) ◽

Author(s):

Ali Deheshvar ◽

Hesam Shams ◽

Farshid Jamali ◽

Zohreh Movahedmanesh

Keyword(s):

Adaptive Control ◽

Sample Size ◽

Control Chart ◽

Sampling Interval ◽

Variable Parameters ◽

Variable Sample Size ◽

And Control ◽

Adaptive Control Chart ◽

Control Limits

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The Importance of Beta, the Type II Error, and Sample Size in the Design and Interpretation of the Randomized Controlled Trial

Medical Uses of Statistics ◽

10.1201/9780429187445-19 ◽

2019 ◽

pp. 357-389

Author(s):

Jennie A. Freiman ◽

Thomas C. Chalmers ◽

Harry A. Smith ◽

Roy R. Kuebler

Keyword(s):

Randomized Controlled Trial ◽

Sample Size ◽

Controlled Trial ◽

Type Ii ◽

Type Ii Error ◽

Randomized Controlled

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A Fuzzy Control Chart Approach for Attributes and Variables

Engineering, Technology & Applied Science Research ◽

10.48084/etasr.2192 ◽

2018 ◽

Vol 8 (5) ◽

pp. 3360-3365 ◽

Cited By ~ 1

Author(s):

N. Pekin Alakoc ◽

A. Apaydin

Keyword(s):

Quality Control ◽

Fuzzy Control ◽

Control Chart ◽

Control Charts ◽

Fuzzy Numbers ◽

Fuzzy Theory ◽

New Approach ◽

Shewhart Control Charts ◽

Shewhart Control ◽

Quality Control Chart

The purpose of this study is to present a new approach for fuzzy control charts. The procedure is based on the fundamentals of Shewhart control charts and the fuzzy theory. The proposed approach is developed in such a way that the approach can be applied in a wide variety of processes. The main characteristics of the proposed approach are: The type of the fuzzy control charts are not restricted for variables or attributes, and the approach can be easily modified for different processes and types of fuzzy numbers with the evaluation or judgment of decision maker(s). With the aim of presenting the approach procedure in details, the approach is designed for fuzzy c quality control chart and an example of the chart is explained. Moreover, the performance of the fuzzy c chart is investigated and compared with the Shewhart c chart. The results of simulations show that the proposed approach has better performance and can detect the process shifts efficiently.

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How Large Should the Sample Be? Part II—The One-Sample Case for Survey Research

Educational and Psychological Measurement ◽

10.1177/001316448504500210 ◽

1985 ◽

Vol 45 (2) ◽

pp. 271-280 ◽

Cited By ~ 7

Author(s):

Dennis E. Hinkle ◽

J. Dale Oliver ◽

Charles A. Hinkle

Keyword(s):

Sample Size ◽

Survey Research ◽

Effect Size ◽

Previous Article ◽

Type Ii ◽

Type Ii Error ◽

The One ◽

Sample Case

In a previous article, the authors discuss the importance of the effect size and the Type II error as factors in determining the sample size (Hinkle and Oliver, 1983). Tables were developed and presented for one-factor designs with k levels (2 ≤ k ≤ 8). However, between the time the article was submitted and its publication, the authors presented these tables at several national and regional meetings. A recurring question from colleagues attending these meetings was how these tables could be used for the one-sample case ( k = 1). Since they could not be, we were encouraged to develop comparable tables for the one-sample case. Thus, the purpose of this paper is to readdress the sample size question and to present these tables.

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