On the fuzzy evaluation of measurement system analysis in a manufacturing and process industry environment : A comparative study

Article history: Received: November 26, 2017 Received in revised format: January 31, 2018 Accepted: March 14, 2018 Available online: March 14, 2018 Variation exists in all processes. There is not even a single process that is completely true. Measuring the trueness of the process is itself a process which can also imitate the process variation. Therefore, measurement system should be strong enough to wager on the trueness of the process. This paper is an attempt to indicate the true method and substantiate the use of measurement system analysis (MSA) by using it in two different environments i.e. in manufacturing as well as process industry. Also, a comparison among various analyzing techniques has been drawn for authenticating the candid method followed by an evaluation using fuzzy TOPSIS for authenticating the results of comparison. The organization’s type, also, strongly influences the performance of MSA as revealed in the conclusion of the article. The results calculated by various methods and in both environments were discussed and as a result ANOVA comes out to be the best method. The application of correct MSA is highly required which ultimately results in increased organizations’ performance. The study is one of its type and will motivate the researchers and industrialists to use and explore the new and efficient ways of MSA. © 2018 by the authors; licensee Growing Science, Canada


Introduction
Inaccuracies are everywhere and industries too, are not away from it.There are two types of causes for variations: assignable causes (Ex.: faulty design, improper layout, incapable machinery) and chance causes (Ex.: environmental conditions, vibrations, organizational culture).One can work on the assignable causes by finding the root cause and eliminating them but cannot remove chance causes completely.Here comes the importance of providing tolerance to every product and process.But what if the measuring instrument is providing unreal results?The consumer will be supplied with the Not Good (NG) products.This can seriously hamper the organization's reputation as the ultimate goal of customer satisfaction will go in vain.
There are mainly two types of industries: Manufacturing and Process.A manufacturer assembles along in a routine whereas a process manufacturer produces in a batch.Product manufacturing includes producing and assembling the individually produced items (Lots) in a sequence of operations against an order whereas the process manufacturing includes batch or continues processes and the operations are of irreversible nature.The working environment of a process industry and manufacturing industry is entirely different.Where in the manufacturing industries, the data available is of discrete nature, in the process industry it is of continuous nature.The nature of data always has a role to play when any type of analysis has to be made out of that data.Here also, in this paper, applying the MSA under both environments was a challenge and required a depictive skill.Till now three mostly used methods of MSA available are the AIAG, Wheeler's and the ANOVA.The objective of the study was to find out the most accurate and easy to use method, which can be applicable to both types of industries.First of all, starting from the basics of MSA, here is the introduction of MSA and gauge Repeatability and Reproducibility (R&R).

Measurement System Analysis
MSA is a scientific and objective method of analyzing the validity of a measurement system.It is a systematic discipline (Jones, 2013) & a tool that quantifies equipment variation, appraiser variation & the total variation of a measurement system.To address actual process variability, the variation due to the measurement system must first be identified and separate out from the process (Göndör & Koczor, 2010).It is required to be sure that measurement system function independently and correctly 100% of time; otherwise, there is a risk of flaws in data.MSA can be and should be applied to each and every process because bad measurement system can cause to scrap good products and ship bad products.The possible types of variations and their check are as shown in Fig 1.

Gauge Repeatability & Reproducibility Study
Gauge R&R is a statistical tool that measures the amount of variation in the measurement system arising from the measurement device and the people taking the measurement (Kaushik et al., 2012;Smith et al., 2007).The purpose of gauge R&R study is to ensure that measurement system is sound.When measuring the product of any process, there are two sources of variation: the variation of the process itself and the variation of the measurement system.The purpose of conducting the gauge R&R is to be able to distinguish the former from the latter, and to reduce the measurement system variation if it is excessive (Zanobini et al., 2016).The measurement error is one of the most important yet overlooked and misunderstood aspects of any measurement process (Hajipour et al., 2013).When implementing any statistical method that relies on data, it is important to be sure that the systems collect that data accurately and precisely & follow the real conditions (Kooshan, 2012).For measurement systems that result in quantitative measurements such as weight, concentration, or strength, it is important to determine the magnitude of any error in the resulting measurements (Dearden, 2014).Gauge repeatability and reproducibility analysis addresses the issue of precision and accuracy of measurement (Awad et al., 2009).The purpose of repeatability and reproducibility experiments is to determine the proportion of measurement variability that is due to (1) The items or parts being measured (part-to-part variation), (2) The operator or appraiser of the gauges (reproducibility), and (3) Errors (unreliability's) in the measurements over several trials by the same operators of the same parts (repeatability).
In the ideal case, all variability in measurements will be due to the part-to-part variation, and only a negligible proportion of the variability will be due to operator reproducibility and trial-to-trial repeatability.

Automotive Industries Action Group (AIAG) Method
The AIAG was founded in 1982 and publishes a no. of documents including the MSA manual, in which various steps of the analysis process are described.Also it provides some of the tables carrying the values for different constants/Correction Factors (d2, D4 and d2*) used during the calculation.Various step followed under this method are as follows: 1. Find the Average range and corresponding Upper range limit (URL).None of the ranges in the tab le should exceed this limit.

Wheeler's Method
This method was suggested by Donald J Wheeler in 2009 (Wheeler, 2009).The method is a modification of the AIAG method and uses proportions in place of percentage as used in AIAG method.Also the method is a corrected version of AIAG in statistical and trigonometric terms.The various constants/correction factors used are same as used in the previous section.Various step followed under this method are as follows: 1 Find the Average range and corresponding Upper control limit.None of the ranges in the Table should exceed

MSA by Analysis of Variance (ANOVA) Calculation by Minitab software
Apart from the two methods describe above, MSA can also be done by ANOVA.ANOVA stands for analysis of variation.It is an experimental design technique that looks at no. of variables at a time.
ANOVA offer statistics on interactions between samples and appraisers.With an ANOVA, we can vary the number of samples, appraisers, trials, and even the number of measurement devices to get a more accurate picture of the variation in the measurement system.It allows us to get an accurate estimate of variances.It is used to help regulate which of the variables under study have a statistically noteworthy influence on the process output.Calculations using ANOVA are more complex than those with other techniques.Therefore, it is best to use a computer with DOE software for the calculations.
A standard 2-factor ANOVA format is used for examining measurement systems.Factor A is used to designate the parts or samples.Factor B represents the appraisers.The number of levels for each factor is a function of the number of samples and the number of appraisers.Following are the terms that are calculated theoretically.Direct results can be calculated easily by using a software.In determining the credibility of measurement system, two different environments were chosen.In first case, a study from a manufacturing industry and in second case, a study from a process industry, is taken.Every organization wants to improve the quality of its product and aim to reduce process variability and waste (defects/nonconformities), ultimately improve business performances.First of all, a manufacturing industry is taken into consideration.The industry is having a turnover of INR 4.5 Crores and hence comes under the category of small scale industry (SSI).It is manufacturing sheet metal parts of varying thickness.These sheet metal parts are being supplied to large manufacturing units who further use these parts in manufacturing various other important parts of automobiles.So thickness is very critical factor which is being measured by a Vernier Calliper.Although many advance and accurate instruments can be used for measuring sheet thickness but Vernier calliper was being used as the resources of the industry were limited.Also, in such SSIs, due to not much management support, less importance is given to these type of work (MSA) and are often regarded as non-productive work.

Manufacturing Industry
Five parts of different thickness were taken to analyse whether the measurement system is correct or not.Table 1 shows the actual readings of those five parts taken randomly by three different appraisers.All dimensions are in mm.Parts were coded so as to avoid the interference among the operators and to obtain exact results.The table 1 also includes various direct values {X-bar, R-bar, Upper Critical limit (UCL), Lower Critical Limit (LCL) etc.} calculated by using simple statistics.Now by using the values from table 1, 10 different terms (Repeatability, Reproducibility, Part Variation, Total variation and their proportions) were calculated by using the three different methods described under section 2 in detail.
The comparison of the readings is shown in Table 2.The comparison showed a different picture as results were surprising.The most widely used AIAG method was giving false interpretations.Fig. 2 and Fig. 3 shows the results of gauge R&R study using ANOVA.It indicates high part to part variation than repeatability, reproducibility and gauge r & r.The Fig. 2 shows number of distinct categories (NDC) as 8 which is greater than 5 means the system is capable of discriminating the parts.Total gauge R & R % study variation comes out to be 16.39 % which is less than 30.00% which indicate that measurement system is OK.

Process Industry
Secondly a process industry is taken into consideration for more elaboration of the MSA.The industry is a paper manufacturing plant having various sections.General equipment used to measure the flow of fluids in one of the pipe sections is a flow meter.The process industry presents a different scenario as compared to manufacturing industry because conducting a MSA on a flow meter and so on to the real values is a tricky situation.As the process industry is having continuous processes so the problem is one has to dismantle the flow meter from its position and replace it with another one so that work doesn't get halted.But the industry has to adhere to the work loss in changing the flow meter and again reassembling it when checked.In this case also, the checking will be done on the assumed values not on the real.The solution to the problem also comes out to be tricky one.In place of dismantling the flow meter, for such situations, another measuring device of tested accuracy and characteristics was put in series to the original instrument before Gauge R&R study so that analysis can be done on the real values.

Fig. 3. Components of Variation (Manufacturing Industry)
Table 3 shows the actual readings (m 3 /s) at varying flow rate taken by three different appraisers at random.The device is an analog type of instrument; hence the readings are in whole numbers.Arrangement was made to avoid the interference among the operators and to obtain exact results.The table also includes various direct values calculated by using simple statistics.Now, similar to the earlier process in previous case study of manufacturing industry, by using the values from table 3, 10 different terms were calculated by using the three different methods.The comparison of the results is shown in Table 4. Fig. 4 and Fig. 5 show the components of variation drew using the ANOVA by Minitab.It indicates high part to part variation than repeatability, reproducibility and gauge r & r.The Fig. 4 shows number of distinct categories (NDC) as 10 which is greater than 5 means the system is capable of discriminating the parts.

Fuzzy Evaluation
In the next step it was decided to run an evaluation test on the basis of comparison results carried out in Table 2 and Table 4 for manufacturing and process industries respectively.As the present case is similar to decision making under uncertainty with the availability of various dependent parameters, a suitable multiple attribute decision making (MADM) with fuzzy logic approach could be used (Mittal, Tewari, & Khanduja, 2017a).Various MADM approaches such as TOPSIS (Technique for order preference by similarity to ideal solution) (Chen, 2000;Hwang et al., 1993;Mittal et al., 2016;Rathi et al., 2015), VIKOR (VlseKriterijumskaOptimisacija I KompromisnoResenje) (Liu et al., 2012;Opricovic & Tzeng, 2004;Yadollahi Farsi et al., 2012), AHP (Mittal et al., 2017b;Saaty, 1990) and SAW (simple additive weighting) (Chen & Klein, 1997) etc. are available but in this case study TOPSIS was selected as it was best suited for similar case scenarios.

Fuzzy TOPSIS Methodology
This section explains the steps involved in the particular fuzzy TOPSIS approach.It includes the following steps: Step 1: Calculation of weights In the first step weightage (Wj) of each parameter is calculated.The formula for weight calculation is as follows: As the present case is of evaluation of result, weightage of each parameter is taken as equal.
Step 2: Define linguistic variables, membership function and corresponding fuzzy numbers.A set of fuzzy numbers is necessary to compare the alternatives for each parameter.

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Step 6: Calculation of weighted normalized decision matrix: * * * Crisp values are calculated by the equation described in step 4. Table 8 shows the corresponding crisp values of manufacturing and process industries.

Results & Discussions
It is visible from the comparison drawn between the three methods i.e.AIAG, Wheeler's method and ANOVA, that the readings are different.Concentrate on the last term % or Proportionate Total Variation of the Total Variation which in case of AIAG is 114.20% (Manufacturing) & Not Determined (Process) and in case of Wheeler's method and ANOVA is 100%.The % EV and %AV do not add up to %GRR and %GRR and %PV do not add up to 100% because they are not proportions.They are instead trigonometric functions and trigonometric functions do not satisfy the conditions needed for a set of ratios to be interpreted as proportions.This implies that values do not infer the correct information about the source of variation.
Also one can see the difference in case of part variation.In AIAG study it is mere 11.03 (Manufacturing) & 15.54 (Process) which is almost acceptable but in case of Wheeler and ANOVA the values are beyond acceptance.If these values are based on the adequacy of the measurement process, there is a high risk that one can make a bad decision about the process.
In AIAG method the variance of estimates and sum of individual proportions are not equal, in contrast Wheeler's & ANOVA both method suggested the variance of estimates and the sum of individual proportions are equal to the total variation.Also it is visible from the tables that sometimes, as in case of process industry, the estimate of the variances cannot be made by using AIAG method while the correct estimate can be made by using ANOVA method.
In the end, evaluation performed by fuzzy TOPSIS provided a concrete solution that ANOVA is the best suited method for analysing the measurement system in both manufacturing and process industries.
The evaluation procedure using fuzzy MADM approach is a tested and frequently used method for evaluation in cases where various dependent variables are available.
Recently more people are beginning to prefer the ANOVA method for conducting Gauge R&R studies.
The ANOVA method includes the interaction between the operators (or appraisers) and the parts.ANOVA breaks down the variance into four components: parts, operators, interaction between parts and operators and the repeatability error due to the measurement system (or gauge) itself.The interaction seldom is often insignificant and has little, if any, impact on the results.The ANOVA method, however, allows estimating the variance of the components.If one bases the % of total variation on the variance, instead of the standard deviation, can get very different results.One more disadvantage of ANOVA is that the use of software is necessary in case of a medium skilled user, as the statistics involved in the manual version is very lengthy and tedious talk that required a definite skill.But this can be taken as granted in favour of ANOVA that software is easily available and hence a certain advantage over other methods where one has to do the calculations.

Conclusion
If an organization is facing repeated quality issues, MSA is an important step that should be performed to check and confirm the current quality status of an organization, before going for a quality management technique.This paper depicts a comparative study of applying MSA by three different techniques and under two different environments.The application of MSA in a continuous system is also described, which generally proves to be tricky situation for such analysis.As it is evident from the application of three methods of MSA i.e. the AIAG, the Wheeler's and the ANOVA under the manufacturing and process environment that the ANOVA method has comes out to be the best one which can be used for any type of industry and can withheld any type of data.Evaluation by fuzzy TOPSIS also put a stamp on the results.The objective, here, was to rank the best and accurate technique for MSA and it can be seen that AIAG and Wheeler method have a certain limit to the type of data.The AIAG method does not provide the right information as explained above and can lead to the wrong interpretation and in Wheeler's method; one has to do the lots of calculation work which is not feasible in today's time bound industrial culture.Also with the availability of the computers as well as the software in the industry, definitely the ANOVA is the need of the hour.

∑∑
Thus the obtained decision matrix (Z) is shown as: technique of translating the fuzzy output to crisp value in fuzzy logic.The input for the technique is the aggregate set and the output is a single number.Following equation lead to the crisp values:

Table 2
Comparison Sheet of Various MSA Methods (Manufacturing Industry)

Table 3
Data Collection Sheet (Process Industry)

Table 4
Comparison Sheet of Various MSA Methods Fig. 4. ANOVA Calculation by Minitab (Process Industry) Two-

Table 8
Crisp Value for Manufacturing & Process IndustriesAfter applying various steps described in step 5 to 9 final TOPSIS ranks are shown in Table9.It is now evident that ANOVA attains the top ranks for both manufacturing and process industries studies.

Table 9
TOPSIS Ranks for Manufacturing and Process Industries