=Paper=
{{Paper
|id=Vol-2038/paper10
|storemode=property
|title=Neutrosophy, Method of Uncertainties Process Analysis
|pdfUrl=https://ceur-ws.org/Vol-2038/paper10.pdf
|volume=Vol-2038
|authors=Florentin Smarandache,Mirela Teodorescu
|dblpUrl=https://dblp.org/rec/conf/ercimdl/SmarandacheT17
}}
==Neutrosophy, Method of Uncertainties Process Analysis==
https://ceur-ws.org/Vol-2038/paper10.pdf
Neutrosophy, Method of Uncertainties Process Analysis
Florentin Smarandache1 and Mirela Teodorescu2
1
Math. & Sciences Dept., University of New Mexico 705 Gurley Ave., Gallup, NM 87301,
U.S.A.,
2
Neutrosophic Science International Association, New Mexico, USA,
smarand@unm.edu,mirela.teodorescu@yahoo.co.uk
Abstract. This paper presents the importance of Neutrosophy theory in order to
find a method that could solve the uncertainties arising on process analysis. The
aim of this pilot study is to find a procedure to diminish the uncertainties
induced by manufacturing, maintenance, logistics, design, human resources.
The study is intended to identify a method to answer uncertainties solving in
order to support manufacturing managers, NLP specialists, artificial intelligence
researchers and businessman in general.
Keywords: communication, neutrality, solving of uncertainties, process analy-
sis.
1. Introduction
This study is the first step of a research that points out the solving of uncertainties in
process analysis. The research is based on Neutrosophy Theory [11], a new concept of states
treatment with a generous applicability to sciences, like artificial intelligence [12],[16].
We believe that such as method would be useful for manufacturing managers, NLP
specialists, artificial intelligence researchers, other scientists interested to find a method of
uncertainties solving.
The paper is structured as follows: after a brief introduction, section 2 describes the
background related to neutrosophy applicability; section 3 discusses the annotations regarding
neutrosophy theory described in transposed in algebric structures, section 4 presents some
indicators of process stability, section 5 introduces a sample of neutrosophic interpretation on
manufacturing process, and finally section 6 depicts some conclusions and directions for the
future.
2. Previous work
2
According to the neutrosophy theory, the neutral (uncertainty) instances can be ana-
lysed and accordingly, reduced.
There are some spectacular results of applying netrosophy in practical application
such as artificial intelligence [6]. Extending these results, neutrosophy theory can be applied for
solving uncertainty on other domains; In Robotics there are confirmed results of neutrosophics
logics applying to make decisions when appear situations of uncertainty [8],[13].
The real-time adaptive networked control of rescue robots is another project that used
neutrosophic logic to control the robot movement in a surface with uncertainties for it [13].
Starting from this point, we are confidence that neutrosophy theory can help to analy-
sis, evaluate and make the right decision in the process analysis taking into account all sources
that can generate uncertainty, from human being (not appropriate skill), logistics concept, lack
of information, programming automation process according requirements, etc.
3. The Fundamentals of Neutrosophy
The specialty literature reveals that Zadeh introduced in 1965 the degree of member-
ship/truth (t), the rest would be (1-t) equal to f/ false, their sum being 1, so it was defined the
fuzzy set.
Why was it necessary to extend the fuzzy logic? Because a paradox, as proposition,
cannot be described in fuzzy logic; and because the neutrosophic logic helps make a distinction
between a „relative truth‟ and an „absolute truth‟, while fuzzy logic does not.
As novelty to previous theory, Smarandache introduced the degree of indetermina-
cy/neutrality (i) as independent component, defining 0<= t+i+f <= 3.
This theory was revealed in 1995 (published in 1998) when he defined the neutro-
sophic set, [11].
In manufacturing process analysis, it can appear a situation like this: an automation
complex workstation, endowed with robots, which has to processes different parts with appro-
priate auxiliary components with deciding option for LH (left hand part) or RH (right hand
part); this represents an uncertainty. Operator must take the appropriate aux component and to
put it on robot tool.
If operator chooses the appropriate aux component of 2 possibilities:
Operator NT value
O1 T 75%
I 50%
F 0%
The robot can process that part and send it forward, in cycle time.
3
Fig. 1 Workstation
If the same operator chooses the wrong component of 2 possibilities:
Operator NT value
O1 T 10%
I 50%
F 90%
the process is stopped because the robot doesn‟t recognize the component, this status is un-
certainty, it is waiting for attention, manual intervention; process indicators such as OEE,
MTTR, MTBF are changed, efficiency decreased.
As much as the uncertainty increases, supposing that an operator has to select the
right part from more than 2 possibilities:
Operator NT value
O1 T 10%
I 70%
F 90%
Percentage of wrong choice increase, so it is important to solve/decrease the uncer-
tainty.
Logistics represents the department that supply the chain just in time (JIT) and just in
place (JIP).
In case of delivering wrong parts (another code), in the wrong place, parts with de-
fects, it is obvious that the operator induce at his turn confusion/uncertainty. In this situation it
is a great concern who, what, how to intervene to diminish the confusions/uncertainties.
4. Indicators for Process Stability Measuring
In automation systems equipment operate in cycles of time defined as sum of states:
cycling time (machine is in cycling/operating), starved time (machine finished cycle tine but
previous station cannot deliver part), blocked time (machine finished cycle time but cannot
deliver the part to the next station because it is in cycle), waiting aux part time (machine pro-
cess the part in addition with an auxiliary part that is not present), waiting attention time (ma-
chine is in fault and wait for operator to make decision), repair in progress (machine is in re-
pairing), emergency stop (general stop for whole station), bypass (station is not operating,
skip), tool change (machine needs to change tool), setup (time for parameters changes), break
4
time (break for operators lunch time), no communications (network communication error) (see
Fig. 2).
These statuses are defined in PLC (programmable logic controller) for process analy-
sis and evaluation. Related on these statuses are proceeded also the maintenance indicators.
Fig. 2 The structure of a machine cycle time.
The OEE (Overall Equipment Effectiveness)
is measured as:
(Availability) *(Performance)*(Quality)
where:
Availability is OEE Metric that represents the percentage of scheduled time that the
operation is available to operate. Often is referred as Uptime.
Performance is OEE Metric that represents the speed at which the Work Center runs
as a percentage of its designed speed.
Quality is OEE Metric that represents the Good Units produced as a percentage of
the Total Units Started.
Definition of a failure - failure is declared when the equipment does not meet its de-
sired objectives. Therefore, we can consider any equipment that cannot meet mini-
mum performance or availability requirements to be “failed”. Similarly, a return to
normal operations signals the end of downtime or system failure, is considered to be
“non-failed”.
Mean Time to Repair (MTTR) is the mean time of the facility in the status of “Re-
pair”, and it is calculated as:
MTTR = Repair in Progress Time (min)/ Repair in Progress Occurrences.
Mean Time Between Failures (MTBF) shows the amount of time the machine
spends in production time as a percentage of all the states except Break and No Communica-
tions.
MTBF = (Time in Auto / Total Time) x 100,
where:
Time in auto = Cycling Time + Blocked Time + Starved Time + Waiting Auxiliary Time +
Bypass Time,
and
5
Total Time = Cycling Time + Blocked Time + Starved Time + Waiting Auxiliary Time +
Bypass Time + Tool Change Time + Waiting Attention Time + Shutdown Time + Emergency
Stop Time + Set Up Time.
Failure Metrics
Time between failures
Time to repair Time to failure
Process
System failure Resume Process Operations System failure
Fig. 3 Failure milestones.
A process is stable when there is no variability in the system, when the outcome is by
design, as expected [14], [15].
The systems variation we are talking about in this study refers to uncertainty, confu-
sion that can occur in various situations in the manufacturing process that, can lead to another
product than expected one, or a scrap.
In a process, practically can occur such situations when we are put in a position of
uncertainty that leads the process variation to instability, to errors.
Below are presented two methods of analysis, evaluation and correction of the pro-
cess: the Ishikawa diagrams and Pareto chart.
Ishikawa diagrams (also called fishbone diagrams, cause-and-effect diagrams) are
causal diagrams created by [2] that shows the causes of a specific event [17], [7].
Common uses of the Ishikawa diagram (see Fig.4) are product design and quality de-
fect prevention, to identify potential factors causing an overall effect. Each cause or reason for
imperfection is a source of process variation. Causes are usually grouped into major categories
to identify the sources of variation such as: people, methods, machines, materials, measure-
ments, environment [7].
Fig. 4 Ishikawa diagram
Related to these categories can be extended to detailed items like anyone involved
with the process, how the process is performed and the specific requirements for doing it, poli-
cies, procedures, rules, regulations and laws, any equipment, computers, tools, etc. required to
6
accomplish the job, raw materials, parts, pens, paper, etc. used to produce the final product,
data generated from the process that are used to evaluate its quality, the conditions, such as
location, time, temperature, and culture in which the process operates [4], [5].
Pareto analysis is a statistical technique in decision-making used for the selection of
a limited number of tasks that produce significant overall effect. It uses the Pareto Principle
(also known as the 80/20 rule) the idea that by doing 20% of the work you can generate 80% of
the benefit of doing the entire job (see Fig.5).
Step 1: Identify and list problems – that occur in manufacturing process with the
highest frequency and concern the process.
Step 2: Identify the root cause of each problem – for each issue it is important to
identify the fundamental cause. The used methods can be: Brainstorming, 5 Whys, Cause and
effect analysis, and Root cause analysis.
Step 3: Score problems – scoring each problem depends on the sort of problem that
it has to be solved, for quality, safety, efficiency, and cost.
Step 4: Group problems together by root cause – similarly problems belong to the
same group.
Step 5: Add up the scores for each group – assign scores to each group of prob-
lems.
Step 6: Take action – is the moment to deal with the top priority problem, group of
problems and also the purpose that you want [1].
5. Neutrosophy, Method of Uncertainty Solving
For a manufacturing process we identify some sources that influence effectiveness
indicators. Using Pareto charts it was described the process (see Fig.5.)
Process Analysis
30 120.00%
25 100.00%
25 100.00%
Relative Cumulated 96.72%
91.80%
frequency frequency
Frequency % % 20 78.69% 80.00%
Procedures errors 25 40.98% 40.98%
Operators errors 12 19.67% 60.66%
Bad parts 11 18.03% 78.69% 15 60.66% 60.00%
12 Frequency
Missing parts 8 13.11% 91.80% 11
Equipment fault 3 4.92% 96.72% Relative frequency %
10 40.98% 40.00%
Others 2 3.28% 100.00% 8 Cumulated frequency %
Total 61
5 3 20.00%
2
40.98% 19.67% 18.03% 13.11% 4.92% 3.28%
0 0.00%
Pareto Chart
Fig. 5 Pareto chart
In this example, there are few issues that appear in process analysis such as procedures
errors, operator errors, bad parts, missing parts, equipment faults, etc. According to Pareto
principle, examining “operator errors” we can make the decision that reducing this cause of
errors, the parameters of the system can be improved. Refining the operator errors issue by IT
application, automation system, operators training, it results reducing human decision on pro-
cess.
7
100 Neutrosophic interpretation according to issues
90 90
80 80
75
IT 70 70
Training Automation Logistic
Application 60
lack low errors
poor 50 50 50
T 20 25 35 10 40 40
35 T I F
I 80 75 50 70 30 28
25
F 50 40 28 90 20 20
10 10
0
Training Automation IT Logistic
lack low Application errors
poor
Fig.6 Neutrosophic interpretation of the process by issues
Neutrosophic interpretation according to T, I, F
100 90
90 80
T I F 75
80 70
Training lack 20 80 50
70
Automation low 25 75 40
60 50
IT Application poor 30 40 30
50 40 40
Logistic errors 10 70 90
40 30 30
30 25
20
20 10
10
0
T I F
Training lack Automation low IT Application poor Logistic errors
Fig.7 Neutrosophic interpretation of the process by (T, I, F)
During the refining process procedure, we observed that operator errors issue, generated also
the decrease of all others errors of the manufacturing process (see Fig.8.)
Refined Process Analysis
20 120.00%
18
18 100.00%
100.00%
Relative Cumulated 16 94.59%
frequency frequency 89.19%
14
Frequency % % 81.08% 80.00%
Procedures errors 18 48.65% 48.65% 12
Missing parts 7 18.92% 67.57% 67.57%
Bad parts 5 13.51% 81.08% 10 60.00%
Frequency
Equipment fault 3 8.11% 89.19% 48.65%7
8 Relative frequency %
Operators errors 2 5.41% 94.59%
40.00%
Others 2 5.41% 100.00% 6 5 Cumulated frequency %
Total 37
4 3
2 2 20.00%
2
48.65% 18.92% 13.51% 8.11% 5.41% 5.41%
0 0.00%
Pareto Chart
Fig. 8 Refined Pareto chart
The data of Neutrosophic interpretation show also this situation. Important is that un-
certainty I and false F values decreased and true T value increased (see Fig.9 and Fig.10).
8
Refined Neutrosophic issues
100
90
IT Logistic 85
Training Automation 80
Application errors T
T 60 90 85 10 60 60
I
I 30 10 5 20
40 F
F 25 5 9 20
30
25
20 20
10 9 10
5 5
0
Training Automation IT Logistic
Application errors
Fig.9 Refined Neutrosophic issues
Refined Neutrosophic T, I, F process
100 90
T I F 90 85
Training 60 30 25 80
Automation 90 10 5 70 60
IT Application 85 5 9 60
Logistic errors 10 20 20 50
40 30
30 25
20 20
20 10 10 9
10 5 5
0
T I F
Training Automation IT Application Logistic errors
Fig.10 Refined Neutrosophic (T, I, F)
6. Conclusions and Future Work
We presented a way of correcting the uncertainties arising in process analysis apply-
ing neutrosophy theory.
This result can drive us to use the neutrosophy theory for solving the uncertainty, ex-
tended in IT applications, logistics, and human resources.
In the future work we will be oriented to find an algorithm to achieve the objectives
to improve the percentage of stable statuses, to reduce the neutrality/uncertainty.
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