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Posted: February 10th, 2022
Total Quality Management
Sigma is a statistical or mathematical measure of data dispersion that is used in statistics and mathematics. It is a metric that makes use of prior data and information aspects in order to determine how the process is projected to perform in the future, according to the definition. If a given collection of data has a normal probability distribution, Sigma can be used to calculate the number of defects that can be predicted in the process over a given period of time. Sigma is one of the most important instruments that businesses may employ to maintain quality management in their operations. Six Sigma is a data-driven technique that aids in the resolution of problems and the maintenance of high quality. The technique incorporates a number of mathematical and statistical principles, such as normal distribution curves, into its design. The curve makes use of data to anticipate the likelihood of a particular result in the firm. Because of this, it provides corporate managers with insight into what should be expected in the future and which route to take in order to achieve high quality in both processes and goods.
Statistical Process Management (Sigma) is a concerned process approach meant to improve the performance of a corporation by advancing specific areas and key processes of the organization. When it comes to improving operations and procedures, Six Sigma applies two basic techniques. IDOV and DMAIC are the approaches employed. Process or product developments can be of two types: either designing a new product or process from scratch, or improving an existing product or process (Wang et al., 2019). When it comes to improving an existing product or process, companies and enterprises always turn to the DMAIC technique for guidance. The IDOV approach, on the other hand, will always be used by the organization when entirely overhauling an existing process in order to build a completely different product. As a result, the approaches described above greatly assist the organization in ensuring improved quality in their operations and processes.
Quality management systems based on Sigma have sparked interest in a wide range of industries, including retail, healthcare, business process outsourcing, and others. In order to ensure that key goods and services satisfy the set standards and that the customer’s expectations are met, cutting-edge strategies are developed to completely analyze them (Evans & Lindsay, 2014). With the ever-increasing demand for high-quality goods, Six Sigma quality management has risen to the top of the priority list for businesses around the world in order to increase their chances of survival and success. As a result, six Sigma assesses products and processes to ensure that they perform and are of high quality.
It has been suggested that variability or variation should be included in the summary statistics. In most cases, it is used to depict the degree of dispersion or spread of the data sets in question. When calculating the dispersion of the data set’s values and how close or how far each number is from the data set’s central tendency, it is helpful to have this information. It is preferable for a good process to have as little variation as feasible. The lower the level of volatility, the better the process is. Six Sigma methods are designed to reduce variation in a product or process in order to improve their quality and make them more efficient (Voehl et al., 2019). In statistics, there are various different types of variation measures. Variance, standard deviation, and interquartile range are only a few of the relevant measurements from six Sigma. Using all of these indicators, it is possible to determine the normal distribution curve and improve the overall quality control of the product.
The mean or average values of the data are always quoted by managers and other professionals. In order to summarize the set of data, they employ the central tendency. For example, most schools always calculate the mean or average score of a class, and businesses may calculate the average time it takes to deliver products to a customer. Despite the fact that central tendency metrics may be valuable to businesses, it is generally agreed that variance has a substantial impact on the final customer. In the case of a school, for example, parents will be unhappy in the institution and will not care about the class’ mean score if their children perform below the mean. In the same way, if a consumer does not receive the desired good or service within one hour, he or she will not be concerned about the average product delivery time of 30 minutes. Customers frequently look for consistency in the way services and products are delivered to them. If customers are aware that a particular shop will supply their product in 30 minutes, they will always expect it to be delivered in 30 minutes. In order to avoid client displeasure, any delay, even if it is only 10 or 15 minutes, should be avoided at all costs. When a customer orders anything from a store that promises to deliver their items in 50 minutes, they will not anticipate it to arrive before that time frame is met. It is certain that they will be happy and more satisfied if a product is delivered within 45 minutes of ordering it. As a result, quantifying variance is critical for the business because it contributes to increased customer satisfaction.
For the purpose of determining variance in statistics, the following four variables are used: standard deviation, range, variance, and the coefficient of variation.
Sample Standard Deviation (s)
Population Standard Deviation (σ)
Variation in Normal Distribution
The normal distribution shape is highly dependent on µ & σ.
When distribution moves to the right or left, µ will change.
Changes in σ lead to a decrease or increase in width.
The Practical Normal Distribution Rule
Data distribution is considered normal when;
µ±1σ = 68%
µ±2σ = 95%
µ±3σ = incorporates all values under that area
The diagram below represents the Normal Distribution curve with S = 7
The standard deviation is 1.3
The chart portrays the data variation from the mean. In the chart, the distribution is bell-shaped.
Mean = 7
Standard Deviation = 68 % of data
Standard Deviation = 95 % of Data
Standard Deviation = 99.7% of data
Increase in Standard Deviation Mean Value Z value
-3 3.1 0.0034
-2 4.4 0.0415
-1 5.7 0.1861
0 7 0.3069
1 8.3 0.1861
2 9.6 0.0415
3 10.9 0.0034
From the table, when the mean value is 7, the standard deviation increases to 0
Goalpost mentality is the belief that attaining objectives is typically and equally acceptable. This attitude states that if a person or an organization sticks to a certain goal, they will always think about it and achieve it. Goalpost mentality is highly associated with meeting the company’s specifications. It means giving all results are within the goalposts (the specification). Managers using the goal post approach assumes all is well when all the project or process specification are fully met. They always believe that nothing more should be done or said about that particular product when an outcome is within the project specification. Studies have shown that many managers and scientists still adopt the conventional goalpost mentality (McConnell, Nunnally, & McGarvey, 2011). They ignore the variability in key product characteristics mainly because it meets all the needed specifications. This is an extreme but common mistake many organizations always make. They focus on meeting the product or process specification and not the variation.
Goalpost mentality always gives producers false hope of satisfying the needs of their customers as it focuses on the specification of the product. The mentality of many organizations is such that when the product meets a given standard or specification, they do not need any further improvement on the characteristic. Usually, these companies always treat any outcome outside the set standards or specification as a special or conveyable variation cause. The goal post mentality is always a great mistake to a company as it does not pursue new developments that may enhance the product quality (Berger, Maurer, & Celli, 2018). The companies using this approach are always content with the set standards that do not pursue any other advancement in the product or process. As a result, the end customer may be dissatisfied with their products.
The perfect way of looking at the performance capability is by putting great consideration o variations. As mentioned above, variations enhance product quality and customer satisfaction. Even though all results appear to fulfil specifications, variation is not free. It consumes time, capital, and other resources (Geng & CMfgE, 2016). When a large part of technical personnel’s time is spent analyzing data, time that could have been spent enhancing the process and product is squandered. In highly regulated sectors like pharmaceutical and aviation, reducing variance by attaining a stable state and minimizing variability is very important. Close enough isn’t good enough, and fulfilling specs isn’t enough.
Process Capability Index
Process capability index is a mathematical tool that allows a process to produce quality products while remaining within the specified limits required by clients. Cpk measures the manufacturer’s capability to maintain its processes within the targeted and specified limits ordered by the consumer. It aids in determining the average performance of the process. Also, Cpk aids in the prediction of process performance in the future.
Control charts monitor process variability and provide tools for correcting it. It aids in keeping the process within statistical constraints.
The goal of creating this chart is to examine how the process operates to meet target limitations and when the process exceeds those limits. The table below represents the sample mean, lower and upper control limits to maintain the track of process performance.
Standard Deviation is 0.955
Sample Number Sample Mean (X-Bar) X double Bar UCL (+3σ) LCL (-3σ)
1 280.6 280.5 283.3 277.6
2 280.3 280.5 283.3 277.6
3 278.6 280.5 283.3 277.6
4 281.0 280.5 283.3 277.6
5 278.8 280.5 283.3 277.6
6 280.7 280.5 283.3 277.6
7 281.0 280.5 283.3 277.6
8 279.6 280.5 283.3 277.6
9 279.8 280.5 283.3 277.6
10 280.7 280.5 283.3 277.6
11 279.6 280.5 283.3 277.6
12 281.7 280.5 283.3 277.6
13 280.8 280.5 283.3 277.6
14 281.4 280.5 283.3 277.6
15 282.0 280.5 283.3 277.6
16 281.7 280.5 283.3 277.6
17 280.5 280.5 283.3 277.6
18 279.8 280.5 283.3 277.6
19 281.4 280.5 283.3 277.6
20 279.6 280.5 283.3 277.6
The above chart indicates that the upper control limits have been defined as UCL X-Bar =X-Double Bar+3σ, and likewise;
LCL X-Bar=X-Double Bar-3σ.
The graph portrays that the production value is within lower and upper control limits while the density is up to the targeted line (X-double bar)
Range control Chart
The goal of creating this chart is to maintain track of process performance so that the performance range remains within the set upper and lower control limits. It will also detect any anomalous trends, such as a trend line that exceeds the UCL Range Limit (Vidya, Niavand, & Haghighat, 2014). The table below portrays sample number, range, upper and lower control limits, and Range Bar.
Sample Number Sample range (R) R-Bar UCL LCL
1 5.5 4.95 10.46 0
2 4.5 4.95 10.46 0
3 4.0 4.95 10.46 0
4 6.5 4.95 10.46 0
5 6.0 4.95 10.46 0
6 6.5 4.95 10.46 0
7 5.0 4.95 10.46 0
8 4.0 4.95 10.46 0
9 3.0 4.95 10.46 0
10 4.5 4.95 10.46 0
11 5.5 4.95 10.46 0
12 4.5 4.95 10.46 0
13 4.0 4.95 10.46 0
14 6.5 4.95 10.46 0
15 6.0 4.95 10.46 0
16 6.5 4.95 10.46 0
17 5.0 4.95 10.46 0
18 4.0 4.95 10.46 0
19 3.0 4.95 10.46 0
20 4.5 4.95 10.46 0
Standard Deviation = 1.13
D4 when n=5 2.114
D3 when n=5 0 (In manufacturing industry, up to n=6, D3 remains 0)
UCL R = D4 x R-Bar
UCL R = 2.114 x 4.95 UCL R = 10.46
LCL R = D3 x R-Bar LCL R = 0 x R-Bar
Specification Tolerance Level and Process Capability Indices
Customers’ needs are referred to as customer specifications. The customer has some product requirements that the producer must meet. Failure to satisfy the customer’s specifications might result in the customer’s departure (Sorensen, 2016). A process may be operating within its control limitations, but there is another dimension to consider: client specifications, frequently disregarded by production concerns. The company must maintain track of its production process capabilities to satisfy the criteria of client specifications/requirements.
Involving in a quality improvement allows employees in a manufacturing organization to apply and assimilate essential professional capabilities in their daily operations. Employees and managers will acquire professional capabilities like managing complexity, ensuring high quality of the product manufactured, and training in human factors. For employees in manufacturing industries, it is an opportunity to enhance their skills of producing highly advanced products, improve their presentation skills, and develop leadership and time management skills essential in moving end-customer needs (Ross, 2017). Also, it helps develop a perfect relationship between employees in a firm. For managers and supervisors in the firm, engaging in quality management gives them a chance to address enduring concerns about how services and systems are delivered and enhance their leadership to improve skills. Therefore, to enhance quality in the manufacturing industry, the following considerations must be fully taken into account:
The first step in improving quality in a company is by involving stakeholders. When leading a quality management project, the manager must ensure that the topic is properly laid down and all the member properly understands their roles. The manager will determine whether the existing matter can be amended for change to be followed using quality improvement methodology. They must consider whether the improvement plan is in line with the national and local requirements to ensure support from other organizations. As such, the manager should run a search of the existing literature to explore the available proofs and determine whether there is any evidence concerning the impact, quality, benefit, and cost-effectiveness of a similar approach of change undertaken somewhere else (Mizuno & Bodek, 2020). Therefore, the manager must involve all the stakeholders at every stage of development to ensure quality improvement approaches are attained. This activity requires time, energy, and money, as well as the development of a communications plan; otherwise, even the best-planned initiative may fail. Frequent reviews and evaluations of data analysis, employing the ‘plan, do, study, act’ cycle and ‘adapt, adopt, adjust’ methodologies, as well as ongoing management of the team and stakeholders, are critical to keeping a project on track, preserving the team’s vitality, and engaging all stakeholders.
Figure 1Flow chart of SPC Implementation Plan
The second step is conducting a thorough groundwork. Managers must always spend time investigating the approaches that have been tried and tested somewhere else and those that worked. They must determine how they can fully use the available resources to ensure the quality and performance of their product reaches its maximum limit. Managers should not waste much time recreating the already available product. A constant measurement is an essential tool for product quality enhancement. There is no perfect measure; data will always be vulnerable to mistakes but strive to limit this by collecting data in a regular manner. The manager must always be prepared of having setbacks. Even seemingly basic adjustments might be difficult to put in place. It is critical to think about how you’ll retain your resilience in the face of failures and how they will keep yourself and your team motivated when things don’t go as planned. The companies must understand that quality improvement is not all about knowing the methodology. It is all about having a vision, cultivating relationships, and leading a group. Even though it may seem self-evident, they should not overlook the necessity of establishing a clear goal from the start. This offers your team a clear sense of purpose and guarantees that your efforts are focused on a common goal. It’s all too simple for your goal to continue to grow and eventually feel out of reach.
Berger, P. D., Maurer, R. E., & Celli, G. B. (2018). Introduction to Taguchi methods. In Experimental Design (pp. 449-480). Springer, Cham.
Evans, J. R., & Lindsay, W. M. (2014). An introduction to Six Sigma and process improvement. Cengage Learning.
Geng, H., & CMfgE, P. E. (2016). Quality: Inspection, Test, Risk Management, and SPC. Manufacturing Engineering Handbook, Second Edition.
McConnell, J., Nunnally, B. K., & McGarvey, B. (2011). Meeting specifications is not good enough-the Taguchi loss function. Journal of Validation Technology, 17(2), 38.
Mizuno, S., & Bodek, N. (2020). Management for quality improvement: The seven new QC tools. Productivity press.
Ross, J. E. (2017). Total quality management: Text, cases, and readings. Routledge.
Sorensen, C. E. (2016). The relationship of growth mindset and goal-setting in a first-year college course. South Dakota State University.
Vidya, R., Niavand, H., & Haghighat, F. (2014). What is the calculation the Quality costs using the ABC Method the order application in TQM. International Journal of Science & Engineering Research, 5(9). Retrieved from https://www.ijser.org/researchpaper/What-is-calculation-the-Quality-Costs-Using-the- ABC-Method.pdf
Voehl, F., Harrington, H. J., Mignosa, C., & Charron, R. (2019). The lean six sigma black belt handbook: tools and methods for process acceleration. Productivity Press.
Wang, X., Wen, D., Wang, W., Suo, M., & Hu, T. (2019). Application of biological variation and six sigma models to evaluate analytical quality of six HbA1c analyzers and design quality control strategy. Artificial cells, nanomedicine, and biotechnology, 47(1), 3598-3602.
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