Reflection Final Paper

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Lean Manufacturing

Department of Industrial Engineering –

New Mexico State Unviversity

Dr. Delia J. Valles-Rosales

MODULE 4

Variance Reduction SPC (Statistical Process Control))

What is Statistical Process Control?

According to the ASQ: “Statistical process control (SPC) is defined as the use of statistical techniques to control a process or production method. SPC tools and procedures can help you monitor process behavior, discover issues in internal systems, and find solutions for production issues. Statistical process control is often used interchangeably with statistical quality control (SQC).”

https://www.youtube.com/watch?v=LdhC4ziAhgY

https://asq.org/quality-resources/statistical-process-control

Total quality management (TQM) is a people focused management system that aims at continual improvement in customer satisfaction. According to Mason B. and Antony J., Statistical Process Control (SPC) is a technique used within the TQM framework for reducing variation in processes that we deal with everyday [1]. It is a powerful technique to control, manage, analyze and improve the performance of a process by eliminating special causes of variation in processes such as tool wear, operator error, errors in measurements, use of improper raw materials, and so on. Reference[2] is also defined as a powerful collection of problem-solving tools useful in achieving process stability and improving capability through education on variability. It is also a technique developed based on Shewhart’s conception of process variability, which is widely applied not only in manufacturing processes but also in service operations. In order to survive in a competitive market, improving quality and productivity of products is a must for any company. SPC techniques have been widely recognized as effective approaches for process monitoring and diagnosis. It provides use of the statistical principals and techniques at every stage of the production. SPC aims to control quality characteristics on the methods, machine, products and equipment, both for the company and operators with the magnificent seven.There are two kinds of variations that occur in all manufacturing processes, which cause subsequent variations in the final product. The first is known as the common cause of variation and consists of the variation inherent in the process as it is designed. It may include variations in temperature, properties of raw materials, strength of an electrical volt and so on. The second kind of variation is known as a special cause of variation and happens less frequently than the first. Since checking quality of a product in the sewing section using 100% inspection is time consuming and expensive, in this paper, the authors have great interest in implementing appropriate SPC tools in the sewing section of Silver Spark Apparel Limited, to enhance process performance for quality products.

https://sciendo.com/pdf/10.1515/aut-2017-0034

. Pareto Chart: It can be used to display categories of problems graphically, so that they can be properly prioritized. ii. Cause-and-Effect Sheet: It organizes and displays the relationships between different causes for the effect that is being examined and helps to organize the brainstorming process. iii. Scatter Diagram: It is used to uncover possible cause-andeffect relationships. iv. Flow Chart: It is a type of diagram that represents an algorithm, workflow or process, showing the steps as boxes of various kinds, and their order by connecting them with arrows. v. Histogram: It is a snapshot of the variation of a product or the results of a process. vi. Check sheets: These are simply charts for gathering data. When check sheets are designed clearly and cleanly, they assist in gathering accurate and pertinent data, and allow the data to be easily read and used. vii. Control Charts: These are graphical devices that aid in process control and make it easy to identify points and processes that are out of control, without using complicated statistical tests.

https://sciendo.com/pdf/10.1515/aut-2017-0034

https://www.yourpedia.in/wp-content/uploads/2019/06/Quality-Gurus-and-their-contribution.pdf

SPC was pioneered by W. A. Shewhart in the early 1920s. In 1939, he created the basis for the control chart and the concept of a state of statistical control, through carefully designed experiments.[3] He discovered that some process variation in manufacturing data is natural to the process, while others display uncontrolled variation that is not present in the process causal system. W. E. Deming later applied SPC methods in the US during the World War II, thereby, successfully improving the quality in the manufacturing of munitions and other strategically important products. Deming also introduced SPC methods to Japanese industries after the war. The methods were practiced by many manufacturing and service organizations. Sultana F. et al.[4] tried to show machine breakdown frequencies and time duration of making cigarettes, as well as the major causes of those breakdowns by using SPC. Semel F. J. et al.[5] indicated implications, not only to manufacturing and quality but also to research programs and product development. https://sciendo.com/pdf/10.1515/aut-2017-0034

https://learnmech.com/what-is-statistical-process-control-qc-tools/

https://www.simplypsychology.org/type_I_and_type_II_errors.html

McLeod, S. A. (2019, July 04). What are type I and type II errors? Simply psychology: https://www.simplypsychology.org/type_I_and_type_II_errors.html

A statistically significant result cannot prove that a research hypothesis is correct (as this implies 100% certainty). Because a p -value is based on probabilities, there is always a chance of making an incorrect conclusion regarding accepting or rejecting the null hypothesis (H0).

Anytime we make a decision using statistics there are four possible outcomes, with two representing correct decisions and two representing errors.

The chances of committing these two types of errors are inversely proportional: that is, decreasing type I error rate increases type II error rate, and vice versa.

How does a Type 1 error occur?

A type 1 error is also known as a false positive and occurs when a researcher incorrectly rejects a true null hypothesis. This means that your report that your findings are significant when in fact they have occurred by chance.

The probability of making a type I error is represented by your alpha level (α), which is the p-value below which you reject the null hypothesis. A p-value of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis.

You can reduce your risk of committing a type I error by using a lower value for p. For example, a p-value of 0.01 would mean there is a 1% chance of committing a Type I error.

However, using a lower value for alpha means that you will be less likely to detect a true difference if one really exists (thus risking a type II error).

How does a Type II error occur?

A type II error is also known as a false negative and occurs when a researcher fails to reject a null hypothesis which is really false. Here a researcher concludes there is not a significant effect, when actually there really is.

The probability of making a type II error is called Beta (β), and this is related to the power of the statistical test (power = 1- β). You can decrease your risk of committing a type II error by ensuring your test has enough power.

You can do this by ensuring your sample size is large enough to detect a practical difference when one truly exists.

Why are Type I and Type II Errors Important?

The consequences of making a type I error mean that changes or interventions are made which are unnecessary, and thus waste time, resources, etc.

When you perform a statistical test a p-value helps you determine the significance of your results in relation to the null hypothesis.

The null hypothesis states that there is no relationship between the two variables being studied (one variable does not affect the other). It states the results are due to chance and are not significant in terms of supporting the idea being investigated. Thus, the null hypothesis assumes that whatever you are trying to prove did not happen.

The alternative hypothesis is the one you would believe if the null hypothesis is concluded to be untrue.

The alternative hypothesis states that the independent variable did affect the dependent variable, and the results are significant in terms of supporting the theory being investigated (i.e. not due to chance).

How do you know if a p-value is statistically significant?

A p-value, or probability value, is a number describing how likely it is that your data would have occurred by random chance (i.e. that the null hypothesis is true).

The level of statistical significance is often expressed as a p-value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

Methods and Philosophy of SPC - 7 Tools

Methods and Philosophy of SPC - Check Sheet

Methods and Philosophy of SPC - Pareto Chart

Methods and Philosophy of SPC - Magnificent SEVEN: Cause and Effect Diagram

Methods and Philosophy of SPC - Defect Concentration Diagram

Methods and Philosophy of SPC - Scatter Diagram

Statistical Methods - Quality Improvement and Control

Control Charts for Variables - Control of Both Mean and Variability

U chart

Process characteristics of measurements

What type of data?

P chart

I- chart

- R chart

- S chart

2-10

>10

defects

defectives

attribute

continuous

Types of Control Charts

There are continuous and discrete control charts, but they differed because of the capability of measuring the quality characteristics of a product.

- p Charts: For defectives – sample size variables.

- np Charts: For defectives – sample size fixed.

- c Charts: For defects – sample sized fixed.

- u Charts.: For defects – sample size varies.

Variable (Continuous) Control Charts

- X bar and R Charts: When data is readily available.

- Run Charts: Limited single-point data.

- X-MR Charts: Individual moving range.

- X bar and S Charts: when sigma is readily available.

- EWMA Chart

Attribute (Discrete) Control Charts

Identifying Variation

It is considered inherent to the process or random and not controllable. If this is the only cause present, the process is considered stable or “in control”.

01.

Chance Causes:

Two important points:

Assignable causes

It varies due to external influences. If this is present, the process is considered “out of control”.

(common-cause)

(Special causes)

Monitoring processes

1. Define what needs to be controlled or monitored.

Control charts can be used to check and monitor the statistics of a process.

General step-by-step approach for the implementation of a control chart:

2. Determine the measurement system that will supply the data.

3. Establish the control charts.

4. Properly collect data.

5. Make appropriate decisions based on control chart information

Aspects of Control Charts

1. Identifying Variation

2. Learning

more about

the process

Control chart components

Data

Center Control limit

Upper Control Limit

Certerline: Shows where the process avarage is centered or the central tendency of the data

UCL and LCL describes the process spread.

(UCL)

Lower Control Limit

(LCL)

and R charts

Step 1:

Define the problem

Use quality tools to determine the general problem.

Step 2:

Select a quality characteristic to be measured

Identify a characteristic to study, typically choose characteristics which are creating quality problems. For example, part length or any other variable.

Step 4:

Collect the data

Run the process and gather the initial data. Subgroups are generally between 20-25 samples. Each time a subgroup of sample size n is taken, an average is calculated for the subgroup and plotted on the control chart.

Choose homogeneous groups which means parts produced under the same conditions, by the same machine, same operator, etc.

Step 3:

Choose a subgroup size to

be sampled

and R charts

The Centerline is the population mean (). The is the grand average of the subgroup averages (), and the number of samples.

Step 5:

Determine trial Centerline

and R charts

However, it can be determined an alternative value for the standard deviation.

To determine the upper and lower center limits, we must use the next two equations.

Step 6:

Determine trial Control

limits – Chart

and R charts

The range charts shows the spread or dispersion of the individual samples within the group. Similar calculations as x-bar charts, but two different variables and .

Control limits for the chart:

Step 7:

Determine trial Control

limits – R Chart

and R charts

Step 9:

Revise the Charts

Calculations must be revised to make sure points are in or out of control limits. Also, the point removal process has to be supported by an assignable cause.

When a process performance falls within the control limits, it is considered stable or under control. Also, it is important to analyze how points are spread and patterns that determine problems in the process.

Step 8:

Examine the process

Step 10:

Achieve the purpose

The goal is to decrease the variation inherent in a process overtime. In fact, as the process is improved, the spread of the data will continue decreasing, which mean quality improves.

and R charts

Collect Preliminary Data

Estimate

Establish control limits

Check Preliminary Data

Future Monitoring

Update Estimation

Eliminate the outliers due to Assignable Causes

In control

Out of control

Pareto chart

Pareto chart is graphical tool that helps to break a big problem down into its parts and identify which parts are the most important (Stojčetović, Šarkoćević, Lazarević, & Marjanović, 2015).

The bars are arranged in descending order of height from left to right, which means the categories represented by the tall bars on the left are relatively more significant than those on the right (“Basic Tools for Process Improvement PARETO CHART,” n.d.).

A Timeline Works Well

Record the data.

Step

Order the data.

Step

Label the vertical axis.

Step

Analyze the diagram.

Step

Label the horizontal axis.

Step

Plot the bars.

Step

Add up the counts.

Step

Add title, legend, and date.

Step

Add a cumulative line.

Step

Example (Pareto Chart)

Home improvement loan Balance	$2,870
Visa	$2,340
Mastercard	$2,100
Car Loan	$1,800
School tuition (monthly)	$1,200
Husband´s car loan	$900

A 32-year-old woman recently inherited $10,000 and would like to apply it to some of her bills. Here is what she owes:

To do the Percent calculation divide amount by Total and multiplied by 100. Then, to obtain the Cum.% calculation, add the previous cell value to the current cell until getting 100.

To graph this data, look for the Pareto Chart icon in the insert tab in Excel. Select the category, amount, and Cum.% columns to obtain the next graph.

Histogram

A histogram is a popular choice for displaying continuous data. It looks similar to a bar chart, but in a histogram, the bars touch each other. Bars in histogram do not have the same width, but frequently they are. The vertical axis represents a scale rather than simply a series of labels, and the area of each bar represents the proportion of values that are contained in that range (Boslaugh, 2012).

Features of a Histogram Graph

Title

Axes

Bars

Scale

It summarizes the information of the histogram chart.

A histogram has two axes, the vertical ad the horizontal axis. The vertical shows the frequency, and the horizontal indicates the class intervals.

They are considered the body of a histogram chart, which visualizes the data set.

This is a set of numbers used to measure or quantify the dataset on the graph.

Types of Histogram Graphs

Example (Histogram)

Suppose you have the dataset as shown below. It has the scores (out of 100) of 30 students in a subject.

Here are the steps to create a Histogram using Microsoft Excel:

Select the entire dataset.

Click the insert tab and look for this icon

In the Histogram group, click on the histogram chart icon.

By Category:

This option is used when you have text categories. For instance, if you have sales data for items such as cellphone, computer, and printer, and you want to know the total sales of each of these items.

Automatic:

This option is shown in the previous histogram chart, and it automatically decides what bins to create in the Histogram.

Here are some of the options to customize this histogram chart.

Bin Width: Here it can be defined how big the bin should be. If I type 15, it will create bins such as 28-43, 43-58, 73-88, 88-103.

Number of Bins: Here it can be defined the number of bins. It will automatically create a chart with that many bins.

All these options can be found on the right hand side of your computer once you select a bar from your histogram.

https://www.datapine.com/blog/how-to-choose-the-right-data-visualization-types/

Thanks!

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