Human–Machine Systems Reliability: A Series–Parallel Approach for Evaluation and Improvement in the Field of Machine Tools

Abstract

Machine workshops generate high scrap rates, causing non-compliance with timely delivery and high production costs. Due to their natural characteristics of a low volume, high-mix production batches, and serial and parallel configurations, generally the causes of their failure are not well documented. Thus, to reduce the scrap rate, and evaluate and improve their reliability, their system characteristics must be considered. Based on them, our proposed methodology allows us to evaluate the system, subsystem, and component–subsystem relationship by using either the Weibull and/or the exponential distribution. The strategy to improve the system performance includes reliability tools, expert interviews, cluster analysis, and root-cause analysis. In the application case, the failure sources were found to be mechanical and human errors. The component maintenance/setup, institutional conditions/attitude, and subsystem process/operation were the machine factors that presented the lowest reliability indices. The improved activities were monitored based on the Weibull β and η parameters that affect the system reliability. Finally, by using a life–effort analysis, and the method of comparative analysis of two sequential periods, we identified the causes that generated a change in the Weibull parameters. The contribution of this methodology lies in the grouping of the tools in the proposed application context.

1. Introduction

Reliability theory allows us to analyze failures that occur in the components of a system over time; therefore, its application crosses diverse areas of knowledge, including health sciences [1,2,3], social sciences [4,5], engineering and technology [6,7,8], and industry in general [9]. In the industrial sector, the concept of reliability is used in maintenance, where it is necessary to keep machines in good working condition, under statistical control, and even avoiding variation. However, complex tools are needed to achieve these goals due to random variables.

Moreover, in manufacturing where computer numerical control (CNC) equipment plays an essential role in production, high reliability is desirable. Unfortunately, determining the system’s reliability is complex. Existing research studies mainly focus on univariate degradation data or multiple correlated data, which might not be accurate in equipment reliability assessments [10]. Li et al. [11] investigated the early failure of the Main Drive Systems of Computerized Numerical Control machine tools and developed a Bayesian network model to conduct a comprehensive reliability analysis. Li et al. [12] adopted a Bayesian network predictive analysis to model and analyze the reliability characteristics, such as failure probability, failure rate, and mean time to failure, of a floating offshore wind turbine. Bobbio et al. [13] proposed improving the analysis of dependable systems by mapping fault trees into Bayesian networks. Guo et al. [14] introduced a degradation-analysis-based reliability assessment method for CNC machine tools under performance testing by considering unit non-homogeneity. Langeth and Portinale [15] discussed the properties of the modeling framework that makes BNs particularly well suited for reliability applications and pointed to ongoing research that is relevant to practitioners in reliability. Mi et al. [16] focused on the reliability analysis of a complex multi-state system (MSS) based on the Bayesian network (BN) method using the Dempster–Shafer (DS) evidence theory to express the epistemic uncertainty in the system, considering a complex redundant system and introducing a modified β parametric factor for the reliability analysis.

Huai-Wei et al. [17] proposed a novel Failure Mode and Effects Analysis (FMEA) model based on multi-criteria group decision-making that integrates a rough best–worst method for machine tool risk analysis. Adamyan and He [18] presented a methodology that can be used to identify the failure sequences and assess the probability of their occurrence in a manufacturing system. Bai et al. [19] proposed a modified fatigue damage accumulation model to precisely predict lifetimes of aero-engine materials according to an interaction factor that is able to quantitatively map damage interactions introduced by high cycle fatigue and low cycle fatigue loads.

Dundulis et al. [20] present an overall framework for the estimation of the failure probability of pipelines based on the results of a deterministic–probabilistic structural integrity analysis, the corrosion rate, the number of defects, and failure data. A method for estimating the reliability of a wind power system based on modeling and analysis was developed by Erylmaz and Kan [21]. In Fan et al. [22], the evaluation of a small sample was applied in a CNC grinding machine evaluation based on Bayes theory. In terms of the production of CNC machine tools, due to the use of big data technology, CNC machine tools have been rapidly produced on a large scale, which has played an important role in the upgrading of CNC machine tools and the improvement of their quality and efficiency [23].

In Li et al. [24], the fuzzy theory was employed to represent uncertainties involved in prediction. Reliability prediction under fuzzy stress with and without fuzzy strength is conducted by using a dynamic stress–strength interference model that takes types of cycles of aero-engines into consideration. Taking into account the fuzziness associated with the failure probability of hydraulic systems, a fuzzy fault tree was proposed by integrating fuzzy set theory into the conventional fault tree analysis method.

Mi et al. and Vineyard et al. [25,26] describe failures and repair rate characteristics as well as distribution data for a typical flexible manufacturing system (FMS) that is in use in a manufacturing plant in the United States. Data included mechanical, hydraulic, electrical, electronic, software, and human failures as well as repairs. The data were also fit with appropriate theoretical distributions.

For this case, we present a methodology to evaluate and improve the reliability of the man–machine system in a machine tool workshop by considering the system characteristics, particularly those presented by the machine shops of Chihuahua city. Workshops of this metal-mechanic sector work with a low-volume production system and high-mix batches. These, by using the same machine, can manufacture parts of different materials for different customers. Therefore, a great variety of cutting tools and the use of different operations are needed. Consequently, failures that occur in the machine tool can be generated by several factors, which in our proposed methodology are conveniently addressed as a component, a component–system relationship, or a subsystem, to reduce the scrap rate and to improve the system reliability.

Although the man–machine system’s evaluation is complex due to the interaction of the system’s elements, its reliability evaluation consists of determining the reliability of each component-subsystem relationship by applying the probability rules that apply according to the series–parallel configuration, and then by computing the whole system’s reliability. The application of the methodology to a regional man–machine system enables us to use the Weibull and exponential distributions to determine the reliability of the addressed component–subsystem combinations and the subsystems themselves. Finally, by implementing the proposed methodology the causes of critical failures were addressed and improved. This was done by considering that failures of mechanical and human origin are the major contributors to the system’s failure (by a case study), and that the component maintenance/setup and institutional conditions/attitude are subcauses with a greater impact on the presence of failures in the machine tool. These components interacting with the subsystem process/operation and the machine were the factors that presented the lowest reliability indices. Once they were improved, the improvement actions were monitoring using their related Weibull β and η parameters.

2. Materials and Methods

Machining shops in the metal-mechanical sector operate as batch production systems with a high mix and a low volume. Conventional and CNC machine tools are included in the system, which presents as a common problem the generation of high scrap rates, which affect the ability to comply with the delivery times committed to customers and produce an increase in production costs. Another characteristic of this machine shop is that there is no culture of recording incidents related to the defects or failures that occur; therefore, there is no systematic analysis and follow-up of them. The interaction of the elements of the system makes it complex and affects its reliability.

The evaluation of the reliability of the man–machine system consists of determining the appropriate reliability by modeling each component of the system, applying the rules of probability according to its configuration, and computing the system’s reliability. The components within a system can be related in the following two primary ways: serial configuration and parallel configuration. In serial reliability, all components must function for the system to operate correctly. In the case of a parallel (redundant) configuration, at least one component must be functioning for the system to operate correctly [27].

For this case, the methodological design consists of four phases: an operational context, a human–machine system design, the reliability evaluation model, and some improvement methods. They are presented in Figure 1. The four phases for the evaluation and improvement of the reliability of the human–machine system from Figure 1 range from the system approach and production system definition to the human–machine system design, reliability assessment, and improvement methods. These phases were developed using a system approach, reliability engineering concepts, root-cause analysis techniques, and some probability and statistical concepts. Some other methodologies, such as Bayesian networks, fuzzy theory, rates of failures and repairs, and data distributions, have also been found to be useful to evaluate the reliability of different kinds of systems. However, they have not focused on evaluating the reliability of a complex and flexible system with a series–parallel configuration using some statistical models with the same configuration, such as the one presented in this publication. A description of these four phases will be presented in the following subsections.

3. Case Study. The Applied Evaluation Processes

3.1. Phase 1: Operational Context

Preliminary research was conducted to identify the different kinds of Conventional and Numerical Control machines used in machine shops and the required knowledge and responsibilities.

Table 1. Some of the machines, knowledge, and responsibilities considered.

Machine	Knowledge	Responsibility
Milling	Measurement	Take care of yourself
Griding	Geometric tolerances	Machine care
Machining center	Machine and tools	Order
Turnstile	Materials	Precision

shows some of the machines, knowledge, and responsibilities considered in this research. In addition to identifying the machinery, knowledge, and responsibilities, it was necessary to investigate the functions and activities developed to manufacture parts. Some of them are shown in

Table 2. Some functions and activities considered for the production system.

Function	Activity
Production control	Plan the quantity of parts to be manufactured.
Shipment	Packing and shipping of parts
Quality control	Inspection of material and parts manufactured
Quotes	Quote orders

. Then, based on functions and relationships, a Production System of the machine tools model was developed.

Functions, activities, and relationships (production systems). Using interviews with experts from the machine shop, the Production System of the machine tools was developed based on the workshop functions, activities, and relationships. This model is presented in Section 3. Some other models were developed using a system approach.

Models for the system approach. A system approach was used to analyze the production system as an open system. The inputs of the system and the outputs were identified in order to understand how it operates. Figure 2 shows the production system with an open system approach. Figure 2 shows how the customer requirements or inputs activate functions and activities and relationships between them. The influence of internal and external factors affects the functioning of the system, as well as the entropy or tendency to disorder. The outputs of the system are the manufactured pieces. Some quality and reliability indices were required to generate the guideline to improve the system.

Activities and functions and the relationships between them were helpful in establishing the Production System of the human–machine system presented in Figure 3.

3.2. Phase 2: Human–Machine System

A human–machine system for the machine tool was designed in this phase. The procedure was as follows:

Data collection. To obtain uniform and consistent information, first, a standardization of the terminology used to identify the failures that occurred and the assignment of their causes and sub-causes were performed using the following materials and methodology:

• An awareness interview was conducted with operators, technicians, designers, programmers, and managers to establish a diagnosis that facilitated the survey’s design.
• The survey was designed and applied to identify the terminology used in the presence of failures, when they occurred in the area, the causes and sub-causes that originated them, and the places where they occurred.
• Based on the standardized terminology and the survey’s results, a relationship matrix was created. Based on the name of the failure and the assigned causes and sub-causes in the different areas, the used terminology was standardized and used to create a catalog of visual aids.
• A database was designed in excel that records the failures, causes, and sub-causes. They were recorded according to their (standardized) name, production date, part number, and standardized type of failure.

Classification and analysis of data. Once the information was collected in the database and it was standardized, for the analysis of the failures, a classification was performed to identify the causes, classify them, determine the place where they were detected, and determine the sub-causes of the failure. Each failure’s classification was carried out with the information from the three participating machining workshops. To carry out this activity, the participation of production, quality, and engineering personnel from the three machine shops considered was required. The procedure followed is described below.

Detection of failures that occurred in the machine tool area. Detection of the failures in the machine tool area in the three machine shops was conducted in order to use only standardized failures. Some examples of these failures are great height, pores, large groove dimension, groove out of tolerance, bad grips, and chopped materials.

Identification of causes and sub-causes of failures and the places where the failures occurred. The failures that occurred in the machining area were analyzed based on their causes, sub-causes, and where they occurred using the root-cause analysis (RCA) [28,29,30,31]. The sub-causes of failure were listed and classified by groups or clusters and the place where the failure occurred. As a result, the six sub-causes used in this research are called components and the six places where the failures occurred are called subsystems. With them, a proper and adequate classification was obtained to develop a relationship matrix.

Matrix of component–subsystem relationships. Using the classification of faults through the cluster technique and root-cause analysis (RCA), a relationship matrix between components and subsystems was constructed, identifying the component and subsystem relationship. This matrix is presented in

Table 3. Matrix of the component–subsystem relationship.

Subsystems	Sub-Causes/Components
	Maintenance/Setup	Admission Profile	Institutional Conditions/ Attitude	Information/ Communication	Calibration	Supplier
Machine	X	X	X	X		X
Tool	X	X	X	X
Process/Operation	X	X	X	X
Measurement/ Instrumentation	X	X	X	X	X
Programming/Design		X	X	X
Material		X	X			X

, showing that Admission Profile and Institutional Conditions/Attitude are present in every one of the six subsystems. Maintenance/Setup, Supplier, Calibration, and Information/Communication only influenced some blocks.

This matrix resulting from the component–subsystem relationship is the basis of the model of the human–machine system for the machine tool given in Figure 4. Considering Figure 4, a serial–parallel system approach as an adequate configuration to evaluate the system’s reliability was developed. It is important to mention that, for this research, the term “reliability” refers to the probability of finding a product without failures for which it must be scrapped.

3.3. Phase 3: Reliability Evaluation Models

To evaluate the reliability of the human–machine system, some statistical models were formulated using a serial–parallel system approach, some concepts of reliability engineering, and statistics. According to these statistical models, it was necessary to have a database that recorded failures that occurred over time.

Recording of product failures. When a failure is recorded, the sub-cause of failure and the place where the failure occurred are also analyzed. A list of the six components (sub-causes) and subsystems (where the failure occurred) is conveniently included to facilitate this analysis.

Table 4. Database used to collect and analyze failures that occurred in machine tools.

Date	Machine	Part Number	Failure #	QTY. Failures/Day	Total Failures/Day	Time to Failure	Cause	Subsystem	Component
jan/06	MT	138	37	5			Operation	3	1
jan/06	MT	138	19	2	7	0.73684	Adjustment	3	1
jan/07	MT	138	33	1			Adjustment	3	1
jan/07	RS3	591	16	1			Program setting	3	1
jan/07	TMO	18	33	1			Adjustment	3	1
jan/07	RAB	584	24	1	4	0.42105	Adjustment	3	1
jan/08	RS3	591	16	2	2	0.21053	Program setting	3	1
jan/09	LOP	82	6	1	1	0.10526	Tool selection	3	1
jan/12	MT	954	19	1			Adjustment	3	1
jan/12	RS3	563	19	1	2	0.21053	Adjustment	3	1
jan/13	LM	131	4	1	1	0.10526	Tool selection	2	1
jan/14	R2	121	8	1			Adjustment	3	1
jan/14	R2	246	8	1			Adjustment	3	1
jan/14	TUI	563	21	1	3	0.31579	Mat handling	3	3

shows the database used to collect the product failure information and its respective analysis. The database from Table 4 was obtained from the scrap report by a machine, and it was helpful in failure control and the identification of component–subsystem relationships.

Standardization and systematization of terminology. The process of standardization of the terminology used to feed the database consisted of the following:

• An awareness interview was conducted with operators, designers, and managers to establish a diagnosis to help design the survey.
• The survey was designed and applied in each one of the three machining workshops to identify the terminology used by each person involved in the different functions, the failures found in the products in each area, the causes and sub-causes of the failures, and the places where failures occurred.
• A matrix of relationships was constructed between the areas involved using the terminology identified in the application of the surveys in the different areas of the machine shops, reducing terms to obtain a standardization of the terminology used.

It is important to ensure (through the commitment of the main actors in each machine shop) that the information-gathering process is carried out periodically and without interruption, and that the analysis of the collected data is constantly monitored (as required by the designed database). It is the responsibility of each machine shop that participates in this activity.

Determination of the periodicity of the analysis of the information. We previously selected the periodicity with which the analysis of the information collected would be carried out (monthly, weekly, daily, etc.), depending on the response time we wanted to obtain and the amount of data available for the analysis and evaluation of reliability.

Evaluation of the reliability using a statistical model. For this research, reliability is understood as the probability that the man–machine system works appropriately or does not produce defective parts after some time. The basis of the reliability evaluation is the defective parts that have been manufactured in the machine tool area. The subsystems considered are machines, tools, processes, measurement/instrumentation, programming/design, and materials, and the components considered are maintenance, admission profile, institutional conditions/attitude, information/communication, calibration, and supplier.

Evaluation of the reliability of a component–subsystem combination. The first step in evaluating the reliability of a component–subsystem combination is to perform a goodness-of-fit test to determine the theoretical distribution that best describes the failure’s behavior and its parameters. Here, the parameter estimation was performed by using the Weibull ++ Software. For data that follow a Weibull distribution, the reliability of each component–subsystem combination is evaluated by using Equation (1a). For data that follow an exponential distribution, their reliability is evaluated by using Equation (2).

$$\mathit{R}\left(\mathit{t}\right)={\mathit{e}}^{-\left\{\frac{\mathit{t}}{\mathbf{\eta }}\right\}}{}^{\mathbf{\beta }}$$

(1a)

In the Weibull reliability function given in Equation (1a), R(t) is the reliability index, β is the shape parameter, and η is the scale parameter. In Equation (1b) is given the instantaneous Weibull time-dependent risk function.

$$\mathit{h}\left(\mathit{t}\right)=\frac{\mathbf{\beta }}{\mathbf{\eta }}{\left(\frac{\mathit{t}}{\mathbf{\eta }}\right)}^{\mathbf{\beta }-1}$$

(1b)

From Equation (1b), notice that because, for the Weibull distribution, the instantaneous risk is dependent on time, then any failure mode whose probability depends on time should be modeled by using the Weibull distribution. In particular, observe that the time-dependent behavior implies that the event is generated by a non-homogeneous Poisson process (see [Rine] for details), and, consequently, the exponential distribution should not be used to represent time-dependent events. The exponential distribution does not depend on time, and it is generated by a homogeneous Poisson process. In Equation (2), the exponential reliability is given, where λ is the non-time-dependent risk function.

$$\mathit{R}\left(\mathit{t}\right)={\mathit{e}}^{-\mathbf{\lambda }\mathit{t}}$$

(2)

Evaluation of the reliability of a subsystem. The evaluation of the reliability of a subsystem affected by one or more components that participated in the failure of the product assumes that components have a series configuration within the subsystem, as they are independent and not mutually exclusive. The statistical model of Equation (3) is used to evaluate the reliability of a subsystem with a series configuration. In Equation (3), Rs is the reliability of the subsystem, and R_i is the reliability of the component–subsystem relationship.

$${\mathit{R}}_{\mathit{s}}={{\displaystyle \prod }}_{\mathit{i}=1}^{\mathit{n}}{\mathit{R}}_{\mathit{i}}$$

(3)

Evaluation of the reliability of the human–machine system. To evaluate the reliability of the human–machine system, the assumption is made that the subsystems have a parallel configuration since they are independent and mutually exclusive. Using the statistical model of Equation (4), the reliability index of the human–machine system is evaluated. It is worth mentioning that the subsystems that do not have any component affecting them will have a reliability of 1 and will not affect the calculation of the system’s reliability, given by

$${\mathit{R}}_{\mathit{S}}=1 -{{\displaystyle \prod }}_{\mathit{i}=1}^{\mathit{n}}\left(1-{\mathit{R}}_{\mathit{i}}\right)$$

(4)

In Equation (4), R_S is the reliability of the man–machine system, and R_i is the reliability of the subsystem. The equation for its calculation assumes a parallel system. The reliability index obtained by the statistical models represented by Equations (1)–(4) represents the probability of not finding defective parts to be scrapped after a period t. Depending on the reliability obtained, it may be necessary to identify the lowest reliability presented in the system and perform improvement actions, such as those presented in the next section.

3.4. Phase 4: Improvement

In this phase, two methods that can help to improve the reliability of the human–machine system in the machine tool area are applied. These methods depend on the type of origin of the failures that occurred and their effect on the system’s reliability. Failures were analyzed to identify their origin. A case study was used for this purpose, so the data that appear were obtained from a machine shop.

Origin and contribution of failures. The analysis consists of a classification of kinds of failures by origin using a cluster analysis to detect the kinds of origins of failures in the machine tool area according to similar characteristics of each identified failure that occurred in the machine tool.

Table 5. Classification of kinds of failure by origin.

Mechanical	Mechanical	Mechanical	Human Error	Heat Treatment	Material	Unexpected Event
3	15	31	1	43	26	42
4	18	35	2	49	30	45
5	19	37	10	50	33
6	20	38	16	51	34
7	21	40	17	52	58
8	22	41	27	53
9	23	46	32	55
11	24	47	36	56
12	25	48	39	57
13	28		44
14	29		54

shows this classification. Table 5 shows that the failure origins identified were mechanical, human error, heat treatment, material, and unexpected event and that failures of a mechanical origin were most common in the machine tools.

The frequency of each kind of failure by origin is presented in

Table 6. Frequency of kinds of failures by origin.

Origin	Qty. of Failures	Relative	Cumulative
Mechanical	31	53.45%	53.45%
Human Error	11	18.97%	72.42%
Heat treatment	9	15.51%	87.93%
Material	5	8.62%	96.55%
Unexpected event	2	3.45%	100.00%
Total	58	100.00%

. Through the Pareto Diagram shown in Figure 5, we identified the sources of failure that most affected their appearance and made the greatest contribution to or had the highest impact on the reliability of the man–machine system. Table 6 shows that the origin with the highest number of failures is the mechanical type, with 31 out of 58 (53.54%). Using data from Table 6, a Pareto Diagram of the origins of failures and their contribution from Figure 5 was drawn. In Figure 5, failures of mechanical and human-error origin are vital causes, with 72.4% of the contribution. In contrast, failures of heat treatment, material, and other origin were identified as trivial causes, with a 27.6% contribution to the failures in the products of the machine tool area. After identifying that the failures of both mechanical and human-error origin contribute most to the appearance of failures in the products, two improvement methods, namely monitoring the parameters β and η of the Weibull distribution for time-dependent failures, such as those of a mechanical origin, and monitoring the parameter λ of the exponential distribution for non-time-dependent failures, were developed.

Monitoring of Parameters between Two Sequential Periods

The objective of monitoring the parameters is to identify the lowest reliabilities in the human–machine system during two sequential periods. A case study from a machine shop was carried out to develop this method. The steps were as follows:

Component–subsystem relationships present in failures. This refers to the time to failure generated by a specific component–subsystem combination from a data distribution, either Weibull or exponential, with their corresponding parameters.

Table 7. Component–subsystem relationships presented in the failure analysis and their parameters from 25 to 30 January 2021.

	Weibull		Exponential
Combination	β	η	Λ
1, 1	1	3.1667
1, 6	1	9.5
2, 1	1	9.5
3, 1	1.0688	3.1268

and

Table 8. Component–subsystem relationships presented in the failure analysis and their parameters from 17 May to 28 May 2021.

	Weibull		Exponential
Combination	β	η	Λ
1, 1	3.4615	7.9737
1, 6	2.18399	7.19726
2, 1	1.52633	5.32846
3, 1	1.90918	2.34728
3, 3			1/9.5

show the parameters for each component–subsystem relationship presented in the failure analysis for the period from 25 January to 30 January 2021 and for the period from 17 May to 28 May 2021, respectively. These parameters were helpful in evaluating the reliability of each component–subsystem relationship and they were obtained using the software Weibull ⁺⁺.

Evaluation of the reliability of component–subsystem relationships. To evaluate the reliability from the period of 25 January to 30 January 2021, the statistical model represented by Equation (1) (Weibull distribution) was used because only failures of mechanical origin were present. To evaluate the reliability from the period of 17 May to 28 May 2021, both the Weibull distribution (Equation (1a)) and the exponential distribution (Equation (2)) were used because there were failures of mechanical and human-error origin.

Table 9. Reliability for the component–subsystem relationships during five time periods from 25 to 30 January 2021.

Periods	R1,1	R1,6	R2,1	R3,1	R3,3
1 h	0.7292	0.9	0.9	0.645	0.7292
3 h	0.3877	0.7292	0.7292	0.2683	0.3877
5 h	0.2061	0.5907	0.5907	0.1111	0.2061
7 h	0.1096	0.4786	0.4786	0.0464	0.1096
9 h	0.0583	0.3877	0.3877	0.0193	0.0583

shows the reliability indices for the component–subsystem relationships present in the machine tool during the period of 25 January to 30 January 2021 for five time periods considered within the 9.5-h shift.

Table 10. Reliability for the component–subsystem relationships during five time periods from 17 to 28 May 2021.

Periods	R1,1	R1,6	R2,1	R3,1	R3,3
1 h	0.6478	0.7382	0.7509	0.4437	0.9000
3 h	0.2718	0.4023	0.4234	0.0871	0.7292
5 h	0.1141	0.2193	0.2387	0.0171	0.5907
7 h	0.0478	0.1195	0.1346	0.0033	0.4786
9 h	0.0200	0.0651	0.0759	0.0006	0.38776

shows the reliability indices for the component–subsystem relationships present in the machine tool during the period of 17 to 28 May 2021 for five time periods considered within the 9.5-h shift.

Evaluation of the reliability of the subsystems and the man–machine system. Using Equation (3), which considers a series configuration, the reliabilities of the subsystems that contributed to the failures were evaluated. Considering Equation (4), which considers a parallel configuration, the reliability of the man–machine system was evaluated.

Table 11. Reliability of the subsystems and the man–machine system during five time periods for the period from 25 to 30 January 2021.

Periods	R1	R2	R3	RS
1 h	0.6563	0.9	0.645	0.9878
3 h	0.2827	0.7292	0.2683	0.8579
5 h	0.1218	0.5907	0.1116	0.6807
7 h	0.0524	0.4786	0.0464	0.5289
9 h	0.0226	0.3877	0.0193	0.4131

shows the reliability indices of the subsystems that contributed to the failures and the reliability indices of the man–machine system for five time periods considered within the 9.5-h shift during the period from 25 to 30 January 2021.

Table 11 shows that, in the 7-h period after the start of the shift, in subsystem 1 (machine), the probability that there were no failures for scrap was 5.24%, while in subsystem 2 (tool) it was 47.86% and in subsystem 3 (process/operation) it was 4.64%. The lowest reliability was obtained for subsystem 3. Regarding the reliability of the man–machine system, the analysis showed a probability of 52.89% that no scrap failures would occur in the 7-h period after the shift started.

Table 12. Reliability of subsystems and the man–machine system during five time periods for the period from 17 to 28 May 2021.

Periods	R1	R2	R3	RS
1 h	0.4782	0.7509	0.3990	0.9219
3 h	0.1094	0.4234	0.0635	0.5191
5 h	0.025	0.2387	0.0101	0.2653
7 h	0.0057	0.1346	0.0016	0.1409
9 h	0.0013	0.0759	0.0002	0.0773

shows the reliability indices of the subsystems present in the failure analysis and the reliability indices of the man–machine system for five time periods considered within the 9.5-h shift during the period from 17 May to 28 May 2021. Table 12 shows that in the 7-h period after the start of the shift, in subsystem 1 (machine), the probability that there were no failures for scrap was 0.57%, while in subsystem 2 (tool) it was 13.46% and in subsystem 3 (process/operation) it was 0.16%.

The lowest reliability was obtained for subsystem 3. Regarding the reliability of the man–machine system, the analysis showed a probability of 14.09% that no scrap failures would occur in the 7-h period after the shift started. Once the lowest reliabilities of the subsystems (process/operation) and the components (maintenance/setup) were identified, to determine which component or components had an influence on the low reliability, the causes that generated it, the origin of these causes, and the actions to be taken, we performed a FMEA analysis. The recommended actions were documented as a work instruction. This action is described below.

Failure Mode and Effect Analysis (FMEA). The analysis developed in the previous section for the case study yielded the causes that generated the low reliability of the subsystem (process/operation) and the components (maintenance/setup and institutional conditions/attitude). With this information as an input, we generated a FMEA analysis with a work team of two operators, one maintenance technician, and the production supervisor.

Table 13. FMEA analysis used to control and monitor activities.

Activity	Potential Failure Mode	Potential Effect of Failure	Sev	Potential Causes/Failure Mechanism	Oc	Current Process (Detection)	Det	RPN
Check the condition of the tool.	Tool in bad condition/damaged	Excess of burrs	3	Inability to calculate tool life expectancy.	2	None	2	12
			3	The machinery for sharpening is not available	2	None	5	30
Perform set-up of tools.	Wrong tool	Scrap	7	Operator’s error	2	None	3	42
Load the material into the machine.	Incorrect material	Scrap	7	Warehouseman’s error	1	None	7	49
	Incorrect location	Scrap	6	Operator’s error	2	None	2	24
Assembly, welding, and polishing.	Pores	Noncompliance with specifications (error/scrap)	7	Material contamination	5	None	2	70
			9	Tungsten contamination	5	None	2	90
			7	Incorrect gas flow	3	None	2	42
			7	Fixture dirt	5	INS204 base assembly and fabrication	2	70

shows the FMEA analysis used to control and monitor the activities that affect the reliability of the man–machine system.

Table 13 presents some activities identified as being of a mechanical and human-error origin. The corresponding activity for assembling, welding, and polishing, whose defect was the presentation of porous pieces due to contaminated tungsten, was the one that presented the highest NPR value. This particular action was monitored and controlled, as a work instruction, to prevent recurrence as shown in Figure 6. The work instruction presented in Figure 6 was used to reduce or eliminate failures due to this failure mode and evaluate the system’s improvement.

Monitoring of the parameters β and η and the parameter λ for activities with critical failures. The relationship between the reliability index and the Weibull β and η parameters shown in Equation (1a) is unique; for fixed t and R(t) values, unique β and η values exist. For activities that depend on time, addressed here as failures generated by a mechanical source, we propose to monitor the system’s reliability by monitoring the corresponding β and η parameters. Therefore, since the parameter β represents the dispersion of the logarithm of the failure times, then when its value is lower compared with the previous period, the log-dispersion among the failure times will increase, implying that no improvement was made; that is to say, the higher the β value the lower the log-dispersion. Similarly, since η represents the product strength, then the higher the η value the better the product strength, implying that if its value is lower compared with the previous period, no improvement was made.

On the other hand, for failures generated by human errors, by considering that human errors do not depend on time, their reliability was monitored by monitoring the λ parameter of Equation (2). Consequently, because λ is the inverse of the mean time to failure, if its value is lower compared with the previous period, then this implies that no improvement was made.

We started from the identification of the critical problem (FMEA analysis), as in the case of the cutting tool. Referring to the unidentified wear of the edge, we propose that an analysis of the life–strength relationship be carried out and a model be generated as a way of solving the problem. A specific material, a cutting tool, and a process/machine that were identified as critical were considered. From

Table 14. Machine efforts were recorded for roughing with the cutting tool according to the number of cycles per part.

C	9	18	27	36	45	54	63	72	81	90	99	108	117
X	7–16	7–21	7–19	4–19	6–17	5–17	4–13	4–17	5–10	4–14	4–19	4–12	2–19
Y	5–10	5–12	4–11	4–9	3–10	3–10	2–10	4–9	2–10	4–13	3–10	3–10	2–10

C, cycles per piece; X, Effort S (%); Y, Effort S (%).

, the critical wear failure of the edge of the cutting tool was considered, whose NPR value is 30. Thus, to determine the parameters β and η, the minimum and maximum forces generated by the machine were measured. Then, by using the method proposed in [32], the Weibull shape (β) and scale (η) parameters were determined based only on the observed maximal (σ₁) and minimal (σ₂) applied effort. The method’s efficiency was based on the following facts:

(1)

The square root of σ₁/σ₂ represents the base life on which the Weibull lifetimes are estimated;

(2)

The mean of the logarithms of the expected lifetimes (g(x)) is completely determined by the determinant of the analyzed stress matrix;

(3)

The Weibull distribution is a circle centered on the arithmetic mean (μ), and it covers the entire span of the principal stresses;

(4)

σ₁/σ₂ and g(x) completely determine the σ_1i and σ_2i values, which correspond to any lifetime in the Weibull analysis; and

(5)

σ₁/σ₂ and η completely determine the minimal and maximal lifetime, which correspond to any σ_1i and σ_2i values. Additionally, the β and η parameters are used when the stress is either constant or variable.

Life–effort relationship analysis as a method for improving the reliability of the man–machine system in the machining area. The data in Table 14 aim to generate a model of the life–effort relationship between the cutting tool used in the manufacturing process of different steel parts in the CNC machining center. The model was built as follows. The % strength represents the excess effort to which the machine is subjected in order to carry out the operation on the part for the x and y axes.

Table 15. Machine efforts recorded for the z axis, for drilling, according to the number of cycles per part.

C	9	18	27	36	45	54	63	72	81	90	99	108	117
Z	27–29	27–29	26–28	26–28	27–29	26–28	26–28	27–29	22–28	27–29	27–29	27–29	27–29

C, cycles per piece; Z, Effort S (%).

shows the values captured from the screen of the machining center board referring to the effort generated in the z axis for drilling the pieces with a 3/8″ drill according to the number of accumulated cycles.

Table 16. Machine efforts recorded for the z axis, for drilling, according to the number of cycles per part.

C	1	2	3	4	5	6	7	8	9	10	11	12	13
Z	23–25	23–25	24–26	23–25	23–25	24–26	23–24	25–28	23–28	25–29	25–29	24–29	22–25

C, cycles per piece; Z, Effort S (%).

shows the values captured from the screen of the machining center board referring to the efforts generated in the z axis for drilling the pieces with a 1/4″ center drill according to the number of accumulated cycles.

A comparison among Table 14, Table 15 and Table 16 shows that efforts presenting the most variation occur when roughing the part on the x axis, which range from 4% to 21%. Second, there are efforts in roughing the part on the y axis, which range from 2% to 13%. The efforts exerted on the z axis to drill the pieces, with two types of drill bits, range from 22% to 29%.

Considering the most significant variation in the effort values, corresponding to that exerted on the x axis (minimum 4% and maximum 21%), these values were used to calculate the parameters β and η given in

Table 17. Calculation of the β and η parameters using the minimum and maximum values of resistance.

i	Y	R(t)	toi	Applied Effort	Minimal Resistance
1	−3.4034833	0.9673	0.06751	0.619	135.764
2	−2.491662	0.9206	0.13899	1.274	65.942	Max=	21
3	−2.0034632	0.8738	0.20460	1.875	44.796	Min=	4
4	−1.6616459	0.8271	0.26821	2.458	34.172	Beta=	1.26264954
5	−1.3943983	0.7804	0.33143	3.038	27.653	Eta=	9.16515139
6	−1.1720537	0.7336	0.39525	3.622	23.189	From the maximum range of values:
		0.704	0.43644	4.000	21.000	3.146	Standard deviation
7	−0.9793812	0.6869	0.46040	4.220	19.907	1.4353	Variation
8	−0.8074473	0.6402	0.52756	4.835	17.373
9	−0.6504921	0.5935	0.59739	5.475	15.342	22.435	Upper limit for resistance
10	−0.5045088	0.5467	0.67061	6.146	13.667	19.565	Lower limit for resistance
11	−0.3665129	0.5	0.74806	6.856	12.252
12	−0.2341223	0.4533	0.83075	7.614	11.032
13	−0.1052851	0.4065	0.92000	8.432	9.962
	0	0.3679	1.00000	9.165	9.165
14	0.0219284	0.3598	1.01752	9.326	9.007
15	0.1495258	0.3131	1.12572	10.317	8.142
16	0.279845	0.2664	1.24811	11.439	7.343
17	0.4159621	0.2196	1.39018	12.741	6.593
18	0.562502	0.1729	1.56126	14.309	5.870
19	0.7276158	0.1262	1.77937	16.308	5.151
20	0.9293107	0.0794	2.08757	19.133	4.390
21	1.2296598	0.0327	2.64818	24.271	3.461

according to [28]. Additionally, the 95% confidence interval was constructed in order to monitor the maximal machine resistance. Table 5, Table 6, Table 7, Table 8, Table 9, Table 10, Table 11, Table 12 and Table 13 are given In Table 17.

The above-mentioned analysis was performed by using the Weibull parameters fitted from the data as

$$\mathbf{\beta }=\frac{-4\mu y}{0.0954\ln \left({\mathsf{\sigma }}_1/{\mathsf{\sigma }}_2\right)}$$

(5)

$$\mathbf{\eta }=\sqrt{{\mathsf{\sigma }}_1{*\mathsf{\sigma }}_2}$$

(6)

where ${\mathsf{\sigma }}_1$ and ${\mathsf{\sigma }}_2$ are the maximum and minimum efforts at which the machine is performing, and $\mu y$ is the mean of the median rank approach estimated from the elements of the Y vector determined by using the sample size from Piña-Monarrez et al., [32] given as

$$\mathbf{n}=\frac{-1}{ln\left(R\left(t\right)\right)}$$

(7)

The n elements of the Y vector used to estimate $\mu y$ were determined based on the median rank approach as

$$Y_i=\ln \left(-\ln \left(1-\frac{\left(i-0.3\right)}{\left(n+0.4\right)}\right)\right)$$

(8)

From these Y elements, the corresponding standardized base lifetime $t_{0i}$ values that allowed us to determine both the applied effort and its corresponding minimal resistance (see Table 17) are given as

$$t_{0i}= \exp \left\{\frac{Y_i}{\beta }\right\}$$

(9)

Therefore, from Equations (5), (6), and (9) the applied effort and the minimal resistance are given as

$$Applied effort=\eta *t_{0i}$$

(10)

$$Minimal resistance=\eta /t_{0i}$$

(11)

Finally, the mean and standard deviation for the maximum values of resistance and the corresponding 95% confidence interval are given as

$${\mathsf{\mu }}_{max}={{\displaystyle \sum }}_{i=1}^n\frac{\max values of resistance}{n}$$

(12a)

$${\sigma }_{max}=\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(\frac{\max value of resistance-{\mathsf{\mu }}_{max}}{n-1}\right)}^2}$$

(12b)

$$CI={\mathsf{\mu }}_{max}\pm \left(\frac{1.96}{\sqrt{n}}\right)$$

(13)

As shown Table 17, the corresponding reliability indicator was established for each machine resistance. For a machine that has a minimum resistance of 21% over its nominal value, it has a reliability of 0.704 (the minimum resistance that the machine must have to have this reliability). When the effort is 9.1651 (η) and the process has a resistance of 21, the reliability is 0.7040. When the resistance is higher, the reliability is higher too. This method consists of monitoring the critical value of 21% through the confidence interval, hoping that the maximum value of the machine effort does not exceed the upper limit of 22.4353. It is also possible to evaluate whether the maximum efforts produced by the machine exceed the standard efforts considered in the confidence interval.

4. Results

Phase 1: Operational Context. The importance of the participation of different functions and activities developed by operators and technicians in the machine tool, the responsibility they have when performing their functions, as well as the possession of sufficient knowledge, skills, and abilities to efficiently and effectively develop the use of conventional and semi-automated CNC machines and tools, without forgetting the fundamental aspects of safety, formed the fundamental basis for establishing the production system of the machine tool. Regarding the Production System of the machine tool, Figure 3 helped to identify the relationships between functions and activities involved in the production system and made it possible to identify the human–machine interactions within the production system, which were considered when establishing the human–machine system.

Phase 2: Human–Machine System of the machine tool. The component–subsystem relationship is the basis of the model shown in Figure 4. Admission Profile and Institutional Conditions/Attitude were present in every one of the six subsystems. Maintenance/Setup, Supplier, Calibration, and Information/Communication only influenced some blocks. The serial–parallel configuration of this system helped us analyze and assess the system’s reliability.

Phase 3: Reliability evaluation models. With the evaluation of the reliability indices for the component–subsystem relationships, comparing Table 10 and Table 11, the component–subsystem relationships with the lowest reliability values were 3,1 and 1,1, referring to Process/Operation Maintenance/Setup and Machine Maintenance/Setup, respectively, being Maintenance/Setup the common component affecting the reliability. Regarding the evaluation of the reliability for subsystems, Table 12 shows that in the 7-h period after the start of the shift, in subsystem 1 (machine), the probability that there were no failures for scrap was 5.24%, while in subsystem 2 (tool) it was 47.86% and in subsystem 3 (process/operation) it was 4.64%. The lowest reliability was obtained for subsystem 3. Table 13 shows that in the 7-h period after the start of the shift, in subsystem 1 (machine), the probability that there were no failures for scrap was 0.57%, while in subsystem 2 (tool) it was 13.46% and in subsystem 3 (process/operation) it was 0.16%. The lowest reliability was obtained for subsystem 3. Subsystem 3 (process/operation) was the most common subsystem affecting the reliability. Regarding the reliability of the man–machine system, Table 12 shows a probability of 52.89% that no scrap failures would occur in the 7-h period after the shift started. Regarding the reliability of the man–machine system, Table 13 shows a probability of 14.09% that no scrap failures would occur in the 7-h period after the shift started, with the second period having the lowest human–machine system reliability.

Phase 4: Improvement. Table 14 (FMEA) presents the corresponding activity for assembling, welding, and polishing, whose defect is the presentation of porous pieces due to contaminated tungsten, which presented the highest NPR value. A comparison between Table 15, Table 16 and Table 17 shows that the efforts presenting the most variation occurred when roughing the part on the x axis, which range from 4% to 21%. Second, there are efforts in roughing the part on the y axis, which range from 2% to 13%. The efforts exerted on the z axis to drill the pieces, with two types of drill bits, range from 22% to 29%. Considering the most significant variation in the effort values, corresponding to that exerted on the x axis (minimum 4% and maximum 21%), the corresponding reliability indicator was established for each machine resistance as shown in Table 17. For a machine that has a minimum resistance of 21% over its nominal value, it has a reliability of 0.704 (the minimum resistance that the machine must have to have this reliability). When the effort is 9.1651 (η) and the process has a resistance of 21, the reliability is 0.7040. When the resistance is higher, the reliability is higher too. The proposed method consists of monitoring the critical value of 21% through the confidence interval, hoping that the maximum value of the machine effort does not exceed the upper limit of 22.4353. Table 17 shows the maximum resistance that the machine must have to obtain a certain degree of reliability. It is also possible to evaluate whether the maximum efforts produced by the machine exceed the standard efforts considered in the confidence interval.

5. Discussion

The results obtained were congruent with the hypotheses formulated. From them, one hypothesis was raised: the man–machine system of the machining area is defined from the component–subsystem relationship if the non-conforming parts present in the machine tool have been considered, analyzed, and classified for a specific period. Its validation was supported by the structured analysis of the collected information, which allowed us to obtain the conditions to be analyzed with the series–parallel system approach. Another hypothesis raised was: the reliability of the man–machine system can be accurately evaluated from the component–subsystem relationship if the used statistical model considers the subsystems and the component–subsystem relationship that have a series–parallel system configuration. Monitoring the reliability of components and subsystems and probability distribution parameters improves the reliability of the man–machine system of the machining area if it is complemented with tools for the identification of failure modes, such as the FMEA, and actions are taken based on it.

In our case, we presented a methodology to evaluate and improve the reliability of the man–machine system in a machine tool workshop by considering the system characteristics presented in workshops of Chihuahua city. Our proposed methodology can be used to conveniently assess the component–subsystem relationship, the subsystems, and the system to detect the lowest reliability. These allow us to reduce the scrap rate and to improve the system’s reliability. Regarding the evaluation of the reliability of a man–machine system, the tools used by other authors do not consider the establishment of an evaluation model based on a man–machine system designed with the characteristics of a specific machine tool area that aims to reduce scrap. Additionally, the tools proposed to improve the man–machine system are based on the assumptions of the Weibull and exponential distributions for the analysis of failures of mechanical and human-error origin as they were the most common kinds of origin.

Other authors have applied the Weibull and exponential distributions in different contexts, methodologies, and tools from the perspective of reliability. Their research work is explained below in order to highlight their different contributions that contrast with the contribution of this research work, both in the context of the application and in the methodology used, but having in common the process reliability perspective. Zhang, Xie, and Tang [33] presented a study of efficiency using robust regression methods over the ordinary least-squares regression method based on a Weibull probability plot. The emphasis was on the estimation of the shape parameter of the two-parameter Weibull distribution. Both the case of small data sets with outliers and the case of data sets with multiple-censoring were considered. Maximum-likelihood estimation was also compared with linear regression methods. Simulation results showed that robust regression is an effective method for reducing bias and performs well in most cases.

Flores, Torres, and Alcaraz [34] analyzed three technological alternatives to produce electricity and compress gas in offshore crude oil processing facilities to be installed in Mexico. The comparison of alternatives was performed based on system reliability estimations by using the “reliability block diagram” method. The fundamental concepts of systems reliability theory were pointed out, and the reliability model was defined as a parallel arrangement with redundancy in passive reserve and without maintenance for any component.

Assuming that Weibull time-to-fail distributions cannot be correctly estimated from field data when manufacturing populations from different vintages have different failure modes, Rand and McLinn [35] investigated the pitfalls of ongoing Weibull parameter estimation and analyzed two cases based upon real events. Assessment of the mixed population at each month of calendar time resulted in an increasing Weibull shape parameter estimate at each assessment. When the two populations were separated and estimated properly, a better fit with more accurate estimates of Weibull shape parameters resulted.

Pascual and Zhang [36] proposed control charts for monitoring changes in the Weibull shape parameter β. These charts were based on the range of a random sample from the smallest extreme value distribution. The control chart limits depended only on the sample size, the desired stable average run length (ARL), and the stable value of β. They derived control limits for both one- and two-sided control charts. They were unbiased with respect to the ARL. Pascual and Zhang discuss sample size requirements when estimating the stable value of β from past data. The proposed method was applied to data on the breaking strengths of carbon fibers. For this case, the authors recommended one-sided charts for detecting specific changes in β because they were expected to signal out-of-control sooner than the two-sided charts.

Guevara, Valera-Cárdenas, and Gómez-Camperos [37] proposed a methodology to assess the reliability factor in the management of industrial equipment designing. The complexity of several industrial procedures and the equipment required establishes that not all of an asset’s failure patterns may be easily handled through maintenance service activities done after its manufacture and use. To avoid all kinds of high-impact failures when using the product, there must be a stage of elimination by removing some maintenance needs, and it should be done considering their own foundations from the very first moment when the asset is designed and produced. These failures might emerge in production, quality, safety, the environment, and costs, among others, which are hard to identify and control. All this requires different concepts and tools in industrial maintenance and service and the engineering of reliability during the design phase.

Piña-Monárrez [38] proposed conditional Weibull control charts using multiple linear regression. Because, in Weibull analysis, the key variable to be monitored is the lower reliability index (R(t)), and because the R(t) index is completely determined by both the lower scale parameter (η) and the lower shape parameter (β), a pair of control charts to monitor a Weibull process were proposed based on the direct relationships between η and β with the log-mean (μx) and the log-standard deviation (σx) of the analyzed lifetime data. Moreover, because of the fact that, in Weibull analysis, right-censored data are common, and because they introduce uncertainty into the estimated Weibull parameters, in the proposed charts, μx and σx are estimated based on the conditional expected times of the related Weibull family. After that, both μx and σx are used to monitor the Weibull process. In particular, μx was set as the lower control limit to monitor η, and σx was set as the upper control limit to monitor β. Numerical applications were used to show how the charts work.

Ferreira and Silva [39] analyzed the parameter estimation for the Weibull distribution with right-censored data using the EM algorithm. Maximum-likelihood estimation (MLE) is a method for estimating the parameters of a statistical model for given data set. This method allowed the authors to estimate the unknown parameters of a statistical model. These parameters were obtained by maximizing the likelihood function of the model in question. The estimation of the parameters of the Weibull distribution by the maximum-likelihood method based on information from a historical record with right-censored data showed this difficulty. The solution used the Expectation Maximization (EM) algorithm.

Although the Weibull distribution for B = 1 mimics the exponential distribution, both distributions are different and behave differently. This fact is due to the Weibull distribution being generated by a non-homogeneous Poisson process in which the risk depends on time, and the exponential distribution is based on a Poisson process in which the risk does not depend on time (a lack of memory property). Based on this fact, we used the Weibull distribution for components and subsystems whose failure mode is mechanical. Due to the mechanical stress that accumulates damage over time, the failure risk depends on time as in the Weibull distribution (or the non-homogeneous Poisson process). On the other hand, by considering that human errors do not depend on time, we used the exponential distribution for components and subsystems whose failure mode is human error (the Poisson process).

This is an innovative contribution because it is based on the participation of the failures in different machining areas. The man–machine system proposed was designed based on the causal relationship between the failures occurring in different machining areas, where the components represent the sub-causes of failures and the subsystems represent the places where failures occur. The series–parallel configuration given to this system allowed us to find statistical models to evaluate the reliability of the component–subsystem relationship (Weibull and exponential distributions), of the subsystems (serial configuration), and of the man–machine system (parallel configuration). No man–machine systems were found to have been configured in a serial–parallel manner based on the participation of the failures.

The Weibull and Exponential distributions were used due to the fact that, at the beginning of the research, it was assumed that the random variables involved in the failures within the man–machine system had a Weibull distribution and an exponential distribution. As the study developed, it was found that failures of mechanical and human-error origin were the most frequent occurrences in the machining area, proving these assumptions to be correct. The Weibull distribution is suitable for representing failures of mechanical origin because they are time-dependent, and the exponential distribution represents failures of human-error origin, which are not time-dependent.

To monitor two sequential periods that have an exponential distribution in one of their component–subsystem relationships, it is only a matter of checking whether their reliability has improved or not and to act on the affected component. This is not the case with the Weibull distribution, where its parameters must be monitored to check whether the reliability has improved with the actions taken. Some proposed improvement actions, such as the use of the life–effort model, may help when the failure is caused by cutting tool wear.

Because, in Weibull analysis, the shape parameter β characterizes the aging of the system, then in the Weibull reliability analysis the used β value plays a key role in accurately determining the reliability R(t) of the analyzed product. Moreover, because in practice β cannot be accurately estimated, then it is generally selected from historical data or from a baseline (a similar product). The estimation of the Weibull scale parameter η depends on both the estimated β value and on the desired R(t) index. The η parameter of the stress distribution is estimated by using R(t) = 0.9535 with n as an integer.

6. Conclusions

The failure analysis of a man–machine system is flexible because it allows us to include any quantity of components, systems, and component–subsystem relationships for the analyzed period. Once the man–machine system had been designed, using the series–parallel system approach proposed to assess the reliability of the man–machine system turned out to be efficient. The man–machine system and the statistical models can be adapted to any company in the metal-mechanic sector with low-volume and high-mix production whose operations are carried out on conventional and CNC machine equipment that utilizes the characteristics of batch production. The man–machine system reliability indicators provide useful information that can be monitored over time. Due to the unique relationship between the Weibull parameters and the reliability index, monitoring the Weibull parameters is an effective way to improve the reliability of the system, the components, and the subsystems.

Limitations of the proposed methodology include the lack of records related to failures and, therefore, the analysis of data. In some cases, the same failure was registered with a different name (standardization) and the data collection process was not continuous (systematization). The information in this paper can be used as the basis for the development of a process to improve the reliability of machine shops considering the lower reliability indices.

Considering that Industry 4.0 works together with machines in innovative and highly productive ways, and due to the dependence of the reliability evaluation on the ability of the operator, the technician, and the programmer to determine the causes and sub-causes of failure, to strengthen this research it would be convenient to automate the information captured in the databases as well as the monitoring of improvement actions. Industry 4.0 is an area of great entrepreneurship, where technologies are used to promote new models. Industry 4.0 is also a space of new opportunities, creativity, and innovation. In response to the problems presented by the machining workshops in Chihuahua City, the digitalization of connected Industry 4.0 is a good option because it means lower production costs, faster lead times, and greater responsiveness to customer demand. Customer expectations have changed due to the advent of connected devices and platforms. The needs in production volume have changed from mass production to customized production, which is happening at an accelerated pace. The introduction of digital technologies in manufacturing processes implies the need for systems to operate and manage broadband information and IT infrastructure, as well as buildings and traffic systems. Digital transformation of the industrial sector with automation, data sharing, uploading to the cloud, Big Data, artificial intelligence, the Internet of Things, and technological techniques can be used to achieve smart industrial and manufacturing goals by interacting with people, new technologies, and innovation. The basis of our proposal is the analysis of the failures that occur in the machine tool, which is obtained from a database containing Big Data. Then, automation of the database with the manufacturing processes of the company, the use of artificial intelligence (algorithms) during development for task performance, and on-demand manufacturing for customized prototypes and parts in short-run productions (smart factories) must be considered.

Innovative applications in Smart Cities. Innovation is a driver of the development of current and future Smart Cities. Innovation, understood as newness, improvement, and spread, is often promoted by Information and Communication Technologies (ICTs) that make it possible to automate, accelerate, and change the perspective of the way that economic and “social good” challenges can be addressed. In economics, innovation is generally considered to be the result of a process that brings together various novel ideas to affect society and increase competitiveness. In this sense, the economic competitiveness of future Smart City societies is defined as an increase in consumers’ satisfaction given by the right product price/quality ratio. Therefore, it is necessary to design production workflows that maximize the resources used to produce products and services of an appropriate quality. Companies’ competitiveness refers to their capacity to produce goods and services efficiently (decreasing prices and increasing quality), making their products attractive in global markets. Thus, it is necessary to achieve high productivity levels that increase profitability and generate revenue. Beyond the importance of stable macroeconomic environments that can promote confidence and attract capital and technology, a necessary condition to build competitive societies is to create virtuous creativity circles that can propose smart and disruptive applications and services that can spread across different social sectors and strata. Smart Cities are willing to create technology-supported environments to make urban, social, and industrial spaces friendly, competitive, and productive contexts in which natural and material resources can be accessible to people and citizens can develop their potential skills in the best conditions possible. Since countries in different geographic locations and with different natural, cultural, and industrial ecosystems must adapt their strategies to these conditions, Smart City solutions are materialized differently. This study shows an example of an experience where industrial planning, urban planning, and health and sanitary problems are addressed with technology, leading to disruptive-data- and artificial-intelligence-centered applications. By sharing research experiences and results that, to date, have mostly been applied in Latin American countries, the authors and editors show how they have contributed to making cities and new societies smart through scientific development and innovation.