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# Statistical Tolerances

Statistical tolerance is a method of execution using certain statistical principles as a basis, which is applied to determine tolerances form a two-sided viewpoint.

1.2.1.10.1 Applications

In cases where multiple individual parts or members are assembled in a single unit, the final value, using this technique, occurs only when the dimensions of all the individual sectors are located at the bottom or above the limits range. This technique is most commonly used in mechanical, electronics, and chemical industries where components or factors are assembled which increase the connection or involve structural subtraction. Also, this technique is used in computer simulation for determining optimal tolerances.

Calculation of the total statistical tolerances is based on a single tolerance set of a total tolerance, which would be smaller than the overall estimate gained by arithmetic. Therefore, giving a general dimensional tolerance using wider tolerances is made possible with simpler and less costly production methods for single dimensions; this feature can be an important advantage in many cases.

In general, the following prerequisites are needed for applying this technique to be feasible:

• • Real single dimensions should be considered as non-correlated random variables
• • The dimensional chain must be linear and have at least four members
• • Single tolerances should be given in order of magnitude
• • The distribution of single chain dimensions must be clear

If any of the above prerequisites are ignored, the analytical value of the application of this technique is lost. That is to say, the production of individual dimensions should be controlled and continuously monitored.

# Time Series Analysis

The analysis of time series incorporates a set of methods for studying a batch of counting observations. This set includes:

• • Punctuation of times series
• • Finding delay patterns
• • Finding periodic or seasonal patterns
• • Forecasting future observations

1.2.1.11.1 Applications

Time series analysis is used to describe patterns of data in order to identify the set of points that should be reviewed. This technique is also used to create adjustments and to understand patterns of change besides specifying the points of change. The analysis is a technique used to predict future values (performance patterns over time) with the upper and lower limits defined as the prediction distance. As a result, the method can be applied to a vast range of time-consuming processes. For example, the issue of supplier assessment, the process of complaints by customers, the forecast of the procurement or repair of parts and related costs, the estimation of future energy consumption for production, and service collections are among the most important uses of the technique in question. This technique is used to set the process toward targets with the least variables. An example of the use of this method is in selecting and working with the desired quality suppliers (of an appropriate assessment score) so that the product’s quality is maintained and/or a certain level of product supply is targeted to retain the market demand.

Analyzing time series is most useful in the following cases: Planning, controlling engineering, identifying process changes, creating predictions, comparing planned performances of a process with certain criteria, and measuring the effect of some interventions or external operations. This technique provides an insight into causative patterns, and can be used further to distinguish systematic causes from specific causes. Another application of this method is to aid understanding of how a process would behave under certain conditions, and what settings would be needed for its effective implementation.

Different techniques used to estimate time series, depending on the number of periods considered for the data, yield different responses. Add to this the nature of the data, the purpose, and the characteristics of the analysis, and the related costs should also be taken into account to achieve the desired result. Otherwise, the obtained results would be misleading.

1.2.1.11.4 A Summary of the Direct Application of the Statistical Techniques in Some Industries During the Last Decade

There are many examples of statistical techniques being used in industrial applications; they are described below.

In a comprehensive research study, design of experiments (DOE) was introduced as a powerful statistical technique for collecting QET and statistical tools. The authors of the study found that the desirable features in the integrity of processes are indicated for organizations that invoke ISO9001 and concentrate on the characteristics and trends of processes and products for attaining the measurement results. In other words, the innovation of this research lay in the application of DOE to measure the impacts of various factors on the process of a quality management system. In this study, the authors investigated the history of applications and the benefits of DOE, and the way the results are analyzed (Karbasian and Rostamkhani, 2017).

Innovative research revealed that the statistical process control (SPC) proves very effective in relation to the productivity calculations of construction companies (Espinosa-Garza et al., 2017).

In a valuable research project, the industrial production losses were fully assessed through DOE, SPC, and process capability indices (PCI) (Bounazef et al., 2014).

Research at the Malek Ashtar University of Technology in Iran, introduced statistical techniques as a tool for the mathematical branch of quality engineering. The statistical techniques were considered and applied by executive managers of quality management systems. Choosing these techniques and their application were entirely determined by the level of the organization's performance, where the requirements and recommendations of the quality management system are taken into account. Certainly, using a statistical techniques approach in quality engineering is a powerful, advantageous, and practical tool as it utilizes both the scientific aspect and the modern framework leading to organizational productivity. In the concluding part of their research, they explained the crucial and major benefits of statistical techniques as follows (Karimi Gavareshki et al., 2014):

• • Finding the root cause of problems
• • Quick solution to qualitative problems
• • Augmenting customer satisfaction
• • Attaining sustainability and capability in quality control processes
• • A profitable tool for continuous improvement
• • Creating awareness of qualitative situations, observation, and follow-up
• • Creating data from quality management process
• • Sustainable development of quality
• • Supporting regular quality measurements and eliminating previous problems
• • Developing existing products or processes
• • Standardization and verification of all processes

In the aforementioned research, for the strategic issues related to ISO9001, at least ten key indices are defined, and for these ten indices, ten effective statistical techniques are considered as input variables. This forms the main basis in statistical analyses for both the working procedures of the Defense Industries Organization (DIO) and the performance of the Maham Group (MG) in Iran. The detailed functional model is presented as a final result of this study in Table 1.1.

In another research project, the generalized application of reliability concepts to outsourced supply chain networks was investigated. The authors introduced a new model in their research dealing with manufacturing lines with reworking and multiple parallel approaches, the results of which can be generalized to outsourced supply networks. Further, the results of this study, intending to ensure the optimized arrangement of outsourced supply chain networks, show the technique can be used to create a strong decision-making process for high-productivity manufacturing (Abbasi and Rostamkhani, 2014).

TABLE 1.1

Detailed Functional Model for the Effective Employment of Statistical Techniques in QMSa

 Related statistical techniques Related indices Strategic issues Simple bar charts Pareto charts Dispersion charts Statistical hypothesis tests Sampling and regression Design and analysis of experiments Reliability analysis Statistical process control charts Time series analysis 1. Getting customer feedback 2. Analyzing, investigating, and finding root causes of customer complaints (prioritizing corrective actions in early stages) 3. Analysis of customer satisfaction in the context of cause and effect relationship (to measure the effect of a particular cause on customer satisfaction). 4. Evaluation of the average customer satisfaction score Phase 1. Estimated sample number (customer) Phase 2. Investigating the organization's claims in the average customer satisfaction rating Phase 3. Measuring the effectiveness of corrective actions to increase customer satisfaction toward strengthening the above measures, and proceeding toward TQMb Increasing customers’ satisfaction Process capability analysis Design and analysis of experiments Reliability analysis Statistical process control charts Time series analysis Sampling and regression Statistical tolerances Conformity to product requirements in order of priority: 1. Observing customers’ requirements, in an explicit or implicit manner 2. Compliance with the design requirements of the organization, including design standards 3. Compliance with health, safety, and environmental regulations (HSE)C 4. Compliance with state laws 5. Other agreement requirements Product conformity Statistical process control charts Process capability analysis Independent hypothesis test Design and analysis of experiments Histogram charts Time series analysis Sampling and regression Phase 1. Assessing process trends in terms of being controlled or not. (confirming or not confirming the initial operation of the process) Phase 2. Checking the status of output processes under controlled conditions (to determine the desirability of the output of controlled processes) Phase 3. Measuring the nature of the process performance even under controlled conditions as well as desirability of their output Phase 4. Analysis of the relationship between different factors (such as periods, etc.) as sources of turbulence with process performance Assessing and analyzing features of processes and products

(Continued)

TABLE 1.1 (CONTINUED)

Detailed Functional Model for the Effective Employment of Statistical Techniques in QMS3

 Related statistical techniques Related indices Strategic issues Time series analysis Histogram and trend charts Reliability analysis Sampling and regression Supplier status assessment includes: Phase 1. Initial identification of suppliers Phase 2. Choosing top suppliers Phase 3. Periodic control of suppliers Phase 4. Identifying weaknesses and strengths of suppliers Phase 5. Development and improvement of suppliers' capacity Reinforcement of suppliers a Quality Management System b Total Quality Management c Health, Safety, and Environment

## The History of Research in Non-Statistical Techniques

There are many non-statistical techniques that do not fall into a specific category. In the following section, however, the important and applicable non-statistical techniques are introduced as:

• • Quality function deployment (QFD)
• • Value engineering (VE)

QFD, a customer-focused approach for designing and improving product quality— the most common implementation tool in this technique—contains the following four matrices:

• • Product planning matrix
• • Product design matrix
• • Process design matrix
• • Process control matrix

Analysis of value function is the essence of VE aiming at identifying profitable areas for future studies. According to the definition provided in the standard ENl 2973:2000, function analysis reflects the impact of a product or implementation of a product. Also, this function analysis includes performance identification with expressing performances with logical tools. In this research, after a comprehensive overview of the history of important applications of QFD and VE techniques, non- statistical techniques were found to be the most significant techniques in quality engineering from 2008 to 2015. We have provided a table at the end of this review which makes the literature review in this regard a satisfactory one. Over recent years, we have witnessed individual applications from QFD and VE based on Lean and agile models in industrial companies. In this research, the combinatorial QFD and VE following a Lean approach as research methodology was explained. In other words, it is for the first time that the power of these non-statistical techniques is being illustrated in the form of integrated situations for control tests in product design (Karimi Gavareshki et al„ 2017).

The value stream mapping (VSM) process allows one to create a detailed visualization of all steps in the work process. It is the representation of the flow of goods from a supplier to a customer through each organization. The primary purpose of creating a value stream map is to show the places where we can improve our process by visualizing both its value-adding and wasteful steps.

Workflow analysis (WFA) is a review of all sub-processes related to a specific operation. It can include plans to eliminate the inefficiencies and to optimize the efficiency of sub-processes.

Many industrial companies and firms have integrated strategic management tools with non-statistical techniques. The high flexibility of non-statistical techniques, for instance the fact that they can be developed, has convinced a majority of experts in various fields of management to apply them in their organizations (Rezazadeh et al„ 2017).

The simplicity and accessibility of non-statistical techniques have encouraged their use by many experts in the economics and business sectors (Zhou, 2016). Moreover, the capability of non-statistical techniques to be used for interpreting such interdisciplinary issues as project management (PM) has created a strong background for analyzing different aspects of PM (Fisher, 2014).

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