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Statistical Control

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STATISTICAL CONTROL OF HOT SHOT PLASTIC KEYCHAINS
TBD
Webster University
BUSN6110, Operation and Project Management [ 2/1/2015 ]

Abstract
This term paper examines a case study with Hot Shot Plastics company in which statistical process control (SPC) with variable measurements using X bar and R control charts is used to determine whether the process variability is in control. Sample data are utilized to demonstrate how to use X bar and R control charts to check if all the sample points are within the control limits. Patterns on the control charts are analyzed to understand the possible reasons that the process is out of control. Keywords: [control charts, statistical process control, patterns]

Statistical Control of Hot Shot Plastic Keychains

Hot Shot Plastics is a company that produces plastic keychains. During production of plastic keychains, Hot Shot Plastics first molds the plastic material and then trims it to the required shape. The edge quality of the keychains produced is determined by the curetimes during the molding process. The curetime is the time it takes for the plastic to cool. To ensure good quality plastic keychains, Hot Shot Plastics needs to maintain a process that yields accurate and precise curetimes. It is more desirable for the curetimes to be consistent among samples. When the curetimes are repeatable and there is less variability among samples’ curetimes, the process is deemed to be accurate. The R control chart is intended to show the accuracy of the curetimes. In addition, when the curetimes are close to the desired target curetime, the process is deemed to be precise. The X bar control chart is intended to show the precision of the curetimes.
To compete with other domestic and foreign competitors effectively, it is essential for Hot Shot Plastics to achieve statistical control of the curetimes without having to invest a lot of capital for quality control. Effective application of the X bar and R control charts will enable Hot Shot Plastics to reduce production rate of defective plastic keychains and keep its quality control cost down as low as possible.
Jacobs and Chase (2013, p. 327) stated, “For industrial applications in process control involving the measurement of variables, it is preferable to keep the sample size small. Statistics suggest that 25 or so sample sets are adequate.” If Hot Shot Plastics chooses to keep the sample size and the number of samples smaller, it would be able to save more money. However, adequate SPC may not be achievable with smaller sample observation size and smaller number of samples. Hot Shot Plastics should use the right sample observation size and the right number of samples that sufficiently enable statistical control of the curetimes using X bar and R charts. Using a smaller sample size than required would be unethical, so proper training of staff members would be necessary to ensure that the SPC is correctly applied and company ethics is strictly followed.
In this case study, the primary aim is to demonstrate that statistical process control (SPC) can be effectively deployed via proper training to detect the presence of any disturbance to the process and find possible remedy via analysis of patterns in the control charts to prevent producing non-conforming products. Curetime data of twenty-five and twelve additional samples of four observations were taken when the process was assumed to be in control. Applying statistical process control (SPC) will increase product quality of plastic keychains and minimize the associated quality control cost.

Methodology
SWOT analysis of the problem
A SWOT (Strength, Weakness, Opportunity, and Threats) analysis was applied to the SPC of the curetimes. Since the objective is to achieve process control of the curetimes, favorable and unfavorable factors were identified in the following SWOT analysis.

Strengths | Weaknesses | Opportunities | Threats | Curetime samples are easily obtainable after proper training is provided. | It is difficult to precisely measure the curetimes. | If successful in achieving statistical control of curetimes using the X bar and R control charts, Hot Shot Plastics does not need to buy expensive machines, so it can keep the quality control cost significantly lower than competitors. | Competitors are investing a lot of capital to use expensive computer and laser controlled machines that produce good quality keychains. | It does not cost much to sample the curetimes. | Reading the precise curetimes are susceptible to human errors. | If successful in achieving statistical control of curetimes, Hot Shot Plastics can effectively compete with low cost offshore competitors because there will be less number of discarded defects. | Other offshore companies are eager to sell the plastic keychains at a very low price because offshore labor cost is much lower than the US. |

Causes and effects of the problem
Less accurate and precise curetimes of the plastic keychains cause less than desirable edge quality of the keychains. Poor edge quality of the keychains makes it difficult to obtain the required shape of the keychains.

Use of the X bar and R control charts in understanding of the problem
Many quality characteristics can be expressed in terms of a numerical measurement. A single continuous and measurable quality characteristic is called a variable. Control charts for variables usually lead to efficient control procedures and are used extensively.
It is a standard practice to control both the mean value and variability of the quality characteristic in dealing with a variable quality. Control of the mean quality level is usually done by using the X bar chart. The control of the process variability is done by using the R chart.
The X bar chart is developed from the average of each subgroup data. The R chart is developed from the ranges of each subgroup data. Range is calculated by subtracting the maximum and the minimum value in each subgroup.
Grant and Leavenworth (1980) computed three standard deviation (sigma) limits that allow us to easily calculate the upper (UCL) and lower control limits (LCL) for both the X bar chart and the R chart:
UCL for X bar = mean for sample means + A2 * mean for sample ranges (Rmean)
LCL for X bar = mean for sample means - A2 * mean for sample ranges (Rmean)
UCL for R = D4 * mean for sample ranges (Rmean)
LCL for R = D3 * mean for sample ranges (Rmean)
Where A2, D3 and D4 are factors for determining 3 sigma limits for X bar and R control charts (Jacobs & Chase, 2013)
The UCL and LCL lines are placed three standard deviations above and below the center line.
Analysis of Patterns on Control Charts Piplani and Hubele (2001, p. 237) stated, “Control chart analysis is based on the principle that the process variability can be broken down into inherent variability and variability due to assignable causes. Unnatural pattern present in the data may indicate the presence of an assignable cause.” The notion of detecting the presence of unnatural patterns was proposed in the Western Electric Company Handbook (1956). These rules are intended to distinguish sequences of observations on the control charts. Piplani and Hubele (2001, p. 238) stated, “Based on the interpretation of unnatural patterns within the data, an action such as a tool change or re-centering of a process setting is initiated.”
According to the Statistical Quality Control Handbook (Western Electric Company, 1956), the four rules used to test for instability and the existence of a system of non-random causes are: 1. One or more points outside of the control limits (3 sigma limits). * A special cause of variance from a material, equipment, or method. * Mismeasurement of a part or parts. * Miscalculated or misplotted data points. * Miscalculated or misplotted control limits. 2. A run of eight points on one side of the center line. This pattern indicates a shift in the process output from changes in the equipment, methods, or materials or a shift in the measurement system. 3. Two of three consecutive points outside the 2 sigma warning limits but still inside the control limits. This may be the result of a large shift in the process in the equipment, methods, materials, or operator or a shift in the measurement system. 4. Four of five consecutive points beyond the 1 sigma limits.
Al-Ghanim and Jordan (1996, p. 26) stated, “When a process suffers an out of control situation, the process behaviour can be manifested in a variety of unnatural patterns such as trend, sudden shift, cyclic and systematic patterns. Pattern information is vital for process diagnosis and correction as there is a strong cause and effect relationship between pattern shapes and root causes of process deviations.” * Trend – Tool or equipment wear, aging, operator fatigue, gradual change in standards * Sudden shift – new operator, new tool or equipment, new environments * Cycle –rotation of people on the job, seasonal effects * Systematic – presence of a systematic variable in the process
Therefore, detecting pattern behaviour such as trend and cycles can increase the usefulness of control charts and can help guide investigation of the root causes of process deviation (Al-Ghanim & Jordan, 1996, p. 26).
Ethical and Diversity Aspect of methodology
To ensure that the SPC is correctly applied, another pair of eyes in the form of process assurance (PA) should be involved during the SPC. The use of checklists, guidelines and proper training of all impacted operators, checkers, or managers will help ensure that Hot Shot Plastics correctly achieves SPC of high quality plastic keychains.

Results/Discussion Results from 25 Samples Based on the table for 25 sampled curetimes (Jacobs & Chase, 2013, p. 343), the mean of the sample means is 30.40289. The mean for the sample ranges (Rmean) is 5.932155. The mean for the ranges gives the center line for the R control chart. Based on the number of observations in subgroup = 4 from the factor for determining 3 sigma limits for X bar and R control charts (Jacobs & Chase, 2013, p. 329), D3 is 0 and D4 is 2.28. Based on Rmean, D4 and D3, the control limits for the R chart were
LCL = D3 * Rmean= 0
UCL = D4 * Rmean= 13.525314
The R chart was drawn with the 25 sample ranges plotted on the chart. The Control limits and the center line were also drawn. This is shown in the Figure 1 below. All the points are within the control limits; therefore, the process variability is in control.
Figure1
The X bar control chart is constructed below. The center line is the mean of the sample means. The 3 sigma limits by Grant and Leavenworth indicate that A2 is 0.73 when the number of observations in each sample is 4. The control limits calculated are
UCL = mean for sample means + A2 * Rmean = 34.733
LCL = mean for sample means - A2 * Rmean = 26.072
The X bar control chart was drawn in the Figure 2 below with control limits and the center line. Out of control conditions were not observed from Figure 2.

Figure 2 Since both the X bar and the R control charts demonstrate that process variability is in control, the process can be taken to be in control at the stated levels and the control limits.
Results from 12 Additional Samples
Twelve additional samples of curetime data were collected from an actual production run and shown in the table for additional curetimes (Jacobs & Chase, 2013, p. 343). The X bar and the R control charts were drawn with the new additional twelve data with the same control limits established before with 25 original data samples. They are shown below in Figure 3 and Figure 4:

Figure 3

Figure 4

In the R control chart, eight consecutive points are above the center line, and two points are above upper control limit. In the X bar control chart, seven points are on or above upper control limit, and one point is below lower control limit. Both charts show that the process is out of control based on the four rules in the Statistical Quality Control Handbook mentioned previously.

Discussion and Recommendation
Two major trends were observed in the control charts for twelve additional samples with wider process variability. These trends draw attention to the areas of improvement that can be made in order to reduce the process variability. A trend of eight consecutive points above the center line in the R control chart indicates that gradual deterioration or wear in tools or equipments may progress. A trend of cyclical nature of data indicates that there may be temperature or other recurring changes in the environment. Some examples of the recurring changes can be differences between operator techniques, rotation of machines in use, or differences in measuring tools or equipments that are currently used. Furthermore, Freeman (1996) argued, “frequent problems encountered include the incorrect choice of control limits and an inability to generally cope with non random patterns within the data.” In order for Hot Shot Plastics to be successful in statistical control of the curetimes, it is critical to train staff in direct visual analysis of control charts and correct application of the statistical process control as presented in this case study.

References
Al-Ghanim, A., & Jordan, J. (1996). Automated process monitoring using statistical pattern recognition techniques on X-bar control charts. Journal of Quality in Maintenance Engineering, 2, 25–49. doi: 10.1108/13552519610113827
Freeman, J., & Evangeliou, N. (1996). Simulation for training in quality control. Training for Quality, 4, 27-31. doi: 10.1108/09684879610112837
Grant, E. L. & Leavenworth, R.S. (1996). Statistical Quality Control, New York: McGraw-Hill.
Jacobs, F. R.,& Chase, R. B. (2013). Operations and Supply Chain Management (14th ed.) New York, NY: McGraw-Hill/Irwin.
Piplani, R., & Hubele, N. F. (2001). Enhancement and evaluation of pattern recognition in control charts. International Journal of Quality & Reliability Management, 18, 237–253. doi: 10.1108/02656710110383511
Western Electric Company (1956). Statistical Quality Control Handbook, American Telephone and Telegraph Company, Chicago, IL.…...

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Statistical Uses

...Use of Statistical Information HCS/438 August 6, 2012 Use of Statistical Information Statistics is defined as “the science of collecting, organizing, and interpreting data” (Bennett, Briggs, & Triola, 2009). For most patients and their families, the process of healthcare appears simple. People with illnesses are admitted into a hospital facility and a specific course of treatment is identified and the care is carried out by a team of physicians, nurses, and social workers. What is not noticed is a specialized resource team aimed at keeping all patients safe throughout the course of their hospitalization. This paper will identify how statistics are utilized in the infection prevention setting, identify one example of descriptive statistics, identify one example of inferential statistics, explain data at each of the four levels of measurement and describe the advantages of accurate interpretation of statistical information to improve decision making in the workplace. How Are Statistics Used in Your Workplace There are many uses for statistical application in the field of infection prevention and control. The purpose of infection prevention and control is to put into place policies and procedures that minimize the spread of infections, especially in the hospital setting. The primary function of infection prevention and control surveillance is to reduce the occurrence of infections by using risk factors and implementation of risk-risk reduction measures and the...

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