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## Publications

Publications (49)

In order to more compliance of products with customer requirements, a loss-based process capability index is proposed to evaluate manufacturing processes based on absolute error loss. The distribution complexity for the estimator of the proposed loss-based capability index hindered the scientific progress in the field of statistical inference. To c...

This article presents a general approach for quality test to make a decision based on the extended process capability indices. Usual methods in measuring the quality of a manufactured product have widely focused on the precise specification limits, but in this study the lower and upper specification limits are considered as non-precise (fuzzy). Ext...

Approximately three decades ago, the fuzzy quality was proposed by Yongting as a flexible and powerful tool to quality modeling. Furthermore, in order to more compliance of products with customer requirements, the probability of fuzzy quality was introduced as a process capability index to evaluate manufacturing processes based on the fuzzy quality...

A new kind of fuzzy random variable, named the “piecewise linear fuzzy random variable”, is introduced in this paper based on the nested random cuts. Illustrative examples are presented for better understanding of the simulation method from the piecewise linear fuzzy random variable.

Analysis of variance is an important method in exploratory and confirmatory data analysis when explanatory variables are discrete and response variables are continues and independent from each other. The simplest type of analysis of variance is one-way analysis of variance for comparison among means of several populations. In this paper, we extend...

The extension principle is one of the most fundamental principles in the fuzzy set theory. It provides a powerful technique in order to extend the domain of a classical function from real numbers to fuzzy sets. In the present paper, we propose a new program in R software to graphically show the behavior of the simplest type of the extension princip...

In statistical quality control, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of process capability estimation, when the observation and the specification limits are fuzzy rather than crisp. In other words, this paper illustrate how a researcher can use “FuzzyNumbers” Package in R soft...

Usually, the statistical estimators (or mathematical functions) are the base of scientific decision making. In applied situations, at least one of the parameters or variables of the decision function may be fuzzy valued, instead of real valued. In such vague situations, one way to perform the calculations is using extension principle approach which...

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which the hypotheses of interest are imprecise. In this paper, we recall and redefine some concepts about testing fuzzy hypotheses and then we provide a minimax approach to the problem of testing fuzzy hypotheses by using crisp...

Testing one-way analysis of variance (ANOVA) is used for experimental data analysis in which there is a continuous response variable and a single independent classification variable. In this paper, we extend one-way ANOVA to a case where observed data are imprecise numbers rather than real numbers. Several fast computable formulas are calculated fo...

Three organic fertilizers of manure sheep, sewage sludge and municipal waste were mixed with soil at the rates of 0%, and (w/w), respectively. In a greenhouse experiment, corn seed were grown on pots of 3 kg treated contaminated soils and irrigated. Sixty days after sowing, the aerial plant parts were harvested and analyzed for Cadmium (Cd) and Lea...

In testing the capability of industrial processes, the researcher considers and tests the vague hypothesis "the capability index is low" against the vague hypothesis "the capability index is high". But, two fuzzy concepts low and high are usually formulated by two crisp hypotheses in traditional quality tests. In this paper, we formulate these two...

The process capability analysis aims at measuring the capability degree of the process distribution in meeting the specification limits. Process capability indices are used to indicate the capability degree of a process. A process whose distribution falls inside the specification limits is a capable process and its capability indices are at least 1...

In some cases, the specification limits of a quality characteristic should be defined under uncertain information. In
the literature, process capability analyses have been handled by using type-1 fuzzy sets under fuzziness up to now.
In this paper, we develop the concept of type-2 fuzzy quality and use it in the calculation of process capability.
L...

In this paper, a new method is proposed for testing fuzzy hypotheses based on the following two generalized p-values: (1) the generalized p-value of null fuzzy hypothesis against alternative fuzzy hypothesis and (2) the generalized p-value of alternative fuzzy hypothesis against null fuzzy hypothesis. In the proposed method, each generalized p-valu...

In this paper, on the basis of Zadeh’s probability measure of fuzzy events, the p-value concept is generalized for testing fuzzy hypotheses. We prove that the introduced p-value has uniform distribution over (0, 1) when the null fuzzy hypothesis is true. Then, based on such a p-value, a procedure is illustrated to test various types of fuzzy hypoth...

After the fuzzy set theory was introduced and developed, many studies have been realized to combine quality control methods and fuzzy set theory. This chapter is including the categorization of most essential works on fuzzy process capability indices in the following four main categories: (1)
Lee et al.’s method and its extensions: This class deals...

Such as other statistical problems, we may confront with uncertain and fuzzy concepts in quality control. One particular case in process capability analysis is a situation in which specification limits are two fuzzy sets. In such a uncertain and vague environment, the produced product is not qualified with a two-valued Boolean view, but to some deg...

Fuzzy process capability indices establish the relationship between the actual performance and the fuzzy specification limits, which are used to determine whether a production process is capable of producing items within fuzzy specification tolerance. In this chapter we test a fuzzy process capability index
\( \tilde{C}_{p} \), where instead of pre...

There exist various methods for providing confidence intervals for unknown parameters of interest on the basis of a random sample. Generally, the bounds are derived from a system of non-linear equations. In this paper, we present a general solution to obtain an unbiased confidence interval with confidence coefficient 1 − α in one-parameter exponent...

Process capability indices provide numerical measures to compare the output of a process to client's expectations. However, most of the existing researches have used traditional distribution frequency method by using a single sample due to assess process capability. An alternative to this approach is to use the Bayesian method. In this paper, we ut...

Process capability indices (PCIs) provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The PCI C p compares the output of a process to the...

In quality control, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which specification limits are two fuzzy sets. In such a fuzzy environment, the product is not qualified with a two valued Boolean view, but to some degree depending on the quality level of the product and the strictness of the dec...

Using the pivotal quantity method, a general solution is presented to obtain an unbiased confidence interval for families of distributions involving truncation parameters. Also, we show that for these families of distributions the unbiased confidence interval is equal to the shortest confidence interval. Several examples are given to demonstrate th...

It is more appropriate that many industrial products be evaluated and qualified by an imprecise (fuzzy) quality. By this idea the products could be evaluated using two membership functions for specification limits rather than two real numbers used in classical quality control. This idea leads the researchers to be able to deal with the vague proces...

This paper deals with the problem of testing statistical hypotheses when both the hypotheses and data are fuzzy. To this end,
we first introduce the concept of fuzzy p-value and then develop an approach for testing fuzzy hypotheses by comparing a fuzzy p-value and a fuzzy significance level. Numerical examples are provided to illustrate the approac...

Most of the traditional methods for assessing the capability of manufacturing processes are dealing with crisp quality. In quality control, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which specification limits (SLs) are imprecise. In this situation, the fuzzy process capability indices (PCIs)...

The impreciseness happens in the quality control same as other statistical problems. In quality control where specification limits are better expressed by fuzzy sets, the generalized process capability indices Cp~, Cpk~ and Cpm~ can be helpful and necessary for measuring the capability. We propose a generalized form of Taguchi index Cpm~ to assess...

Fuzzy set theory models situations in which the uncertainty is due to the non-precise (fuzzy) environment. One such case is testing the hypotheses problem where hypotheses are fuzzy rather than crisp and the data are crisp. Pais and Benton (1997) [1] present a suitable amount of cadmium absorption which is more appropriate for modeling by a fuzzy s...

Analysis of variance (ANOVA) is an important method in exploratory and confirmatory data analysis. The simplest type of ANOVA is one-way ANOVA for comparison among means of several populations. In this article, we extend one-way ANOVA to a case where observed data are fuzzy observations rather than real numbers. Two real-data examples are given to...

Process capability indices (PCIs) have been proposed in the manufacturing industry to provide numerical measures on process capability, which are effective tools for quality assurance. Usual practices in measuring production quality have focused on the precise specification limits (SLs). If vagueness is involved into SLs, we face quite new, reasona...

In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper
deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first introduce the
notion of fuzzy p-value, by applying the extension principle and then present an approach for testing fuz...

In quality control, we may confront imprecise concepts. One case is a situation in which upper and lower specification limits (SLs) are imprecise. If we introduce vagueness into SLs, we face quite new, reasonable and interesting processes, and the ordinary capability indices are not appropriate for measuring the capability of these processes. In th...

Fuzzy process capability indices are used to determine whether a production process is capable of producing items within fuzzy specification tolerance. In this paper we test a fuzzy process capability index (C) over tilde (p)' where instead of precise quality we have two membership functions for specification limits. Numerical examples are given to...

Control charts are among the simplest of on-line statistical process control techniques. When the quality characteristic is a variable, the p-chart takes time to react to shifts in the production process because of its weak response to small variations in the process mean and variance. In this paper, instead of considering an item to be either conf...

Control charts are among the simplest of on-line statistical process control techniques. When the quality characteristic is a variable, the p-chart takes time to react to shifts in the production process because of its weak response to small variations in the process mean and variance. In this paper, instead of considering an item to be either conf...

In this paper, using a family of confidence intervals, we construct a triangular shaped fuzzy number as the estimator for mean lifetime as well as the estimator for reliability function of a component. We derive the explicit and unique membership functions of these fuzzy estimators. Our attention is on the case where the lifetime has an exponential...

Using a family of confidence intervals, we construct a triangular shaped fuzzy number as the estimator of mean lifetime by J. J. Buckley’s [Soft Comput. 9, No. 7, 512–518 (2005; Zbl 1079.62026); ibid., No. 10, 769–775 (2005; Zbl 1077.62051)] estimation approach. Also by two approaches [Buckley’s estimation approach and L. A. Zadeh’s extension princ...

Fuzzy process capability indices are used to determine whether a production process is capable of producing items within specification tolerance, where instead of precise quality we have two membership functions for specification limits. In practice these indices are estimated using sample data and it is of interest to obtain confidence limits for...

Process capability indices are summary statistics which measure the actual or the potential performance of process characteristics relative to the target and specification limits. In most traditional methods, precise estimation is used to assess the capability of manufacturing processes. In this paper we introduce an algorithm based on Buckley’s es...

Process capability indices are used to measure the capability of a process to reproduce items within the specified tolerance preset by the product designers or customers. After introducing fuzzy one- sided process capability indices PU C ~ and PL C ~ , we obtain fuzzy lower confidence bounds for the introduced indices, where instead of precise qual...

In this paper we present several fuzzy confidence intervals for fuzzy process capability index pm C ~ in a fuzzy process based on Roubens ranking function, where we have two membership functions for specification limits. Keyword: Triangular fuzzy numbers, Confidence Interval, Process capability indices, fuzzy statistics, Ranking function.

The notion of fuzzy process capability indices is studied b y Parchami et al. 1], where the speciication limits are triangular fuzzy numbers. In this note, their results a r e revised for the general case, where the speciication limits are L R fuzzy intervals.

Capability indices compare the actual performance of a manufacturing process to the desired performance. In practice these indices are estimated using sample data, often with quite small sample sizes. Thus, it is of interest to obtain confidence limits for actual capability index given a sample estimate. Most of the traditional methods for assessin...

Most of the traditional methods for assessing the capability of manufacturing processes are dealing with crisp quality. In this paper we dis-cuss the fuzzy quality and introduce fuzzy process capability indices, where instead of precise quality we have two membership functions for specification limits. These indices are necessary when the specifica...