Introduction
Statistical Quality Control is a method by which companies gather and analyze data on the variations which occur during production in order to determine if adjustments are needed (Ebert & Griffin, 2005, p. 214). One of the most common methods used in order to achieve this goal is the quality control chart. The charts are used to provide a visual graphic display of instances when a process is beginning to go out of control. The purpose of the chart is to indicate this trend in order that the system may be brought back into control.
Quality Control Chart
The chart is made up of three indicating lines; the centerline, the upper control limit line, and the lower control limit line. The purpose of the center line is to indicate the mean value for the process while it is in control (NIST Engineering Statistics Handbook, n.d.). The upper control limit line serves as the highest point allowed for the process to remain in control. Naturally, the lower control limit is that point which is the lowest acceptable point allowed for the in control process. The upper and lower control points are also known as random variations. The quality control chart was developed by Walter A. Shewhart of Bell Telephone Labs in 1924, but it wasn't until the 1940's as a result of WWII and military requirements, that statistical quality control were adopted by the military (Schroeder, 2007, p. 159). The following represents the formula that is used to calculate the upper control limit. UCL = p + 3*square root of p(1-p)/n. The lower control limit formula is LCL = p-3*square root of p(1-p)/n. These formulas are used to address part one of the electronic circuit company problem.
Part 1
With a sample size of 100 and an average of 10 defective parts per million, p=.001%, and n=100 the formula for the upper control limit would look like this:
UCL = .001 + 3*square root of .001(1-.001)
100 The upper control limit (UCL) therefore equals .0105%. The LCL formula would look like this:
LCL = .001 – 3*square root of .001(1-.001)
100
The lower control limit (LCL) equals -.0085%. Since the LCL is a negative number, it is rounded up to zero (Schroeder, 2007, p. 166). The center line would equal the average of 10 defective parts per million or .001%.
If the sample size was changed to 10,000 the same formulas are utilized however; the value for n changes from 100 to 10,000.
UCL = .001 – 3*square root of .001(1- .001)
10,000
The UCL is now computed as .001948% or .1948 defective parts in the 10,000 sample lot.
LCL = .001 – 3*square root of .001(1 - .001)
10,000 The LCL is now computed as -.00005179% or .005 defective parts in the 10,000 sample lot. Once again the LCL is rounded up to zero due to it being a negative number. When deciding on whether to use the smaller sample of 100 or the larger sample of 10,000, the choice should be made for the larger sample as the larger sample offers a broader picture of the finished product and is therefore a more accurate indication of quality and the control state of the process.
Part II
Management has decided to use process control by variables instead of by attributes. For variable controls, a circuit voltage will be measured based on a sample of five circuits. The past average for a size five sample has been 3.1 volts, with a range of 1.2 volts.
In order to utilize variable measurement, two charts must be used, one to find the mean, and the other to define the variance. Therefore it is necessary to monitor both the average and range of a process in order to maintain control (Schroeder, 2007, p. 166). In order to compute the control limits for the average chart, x represents average, and R represents range. Then (x) = centerline; A2 is a constant representing three standard deviations in terms of the range (Schroeder, 2007, p. 166) CL = (x) UCL = (x) + A2R LCL = (x) – A2R (x) = grand average of several past x averages.
The control limits for the average chart would then look like this: CL = 3.1 LCL = 3.1 - .577*1.2 UCL = 3.1 + .577*1.2 LCL = 2.4076 UCL = 3.7925 For our range chart we would have a LCL of 2.4076, a centerline of 3.1, and a UCL of 3.7925.
Now it is necessary to figure the control limits for the range chart. The quantities for D3 and D4 are taken from the control chart constants in the Schroeder text (Schroeder, 2007, p. 167). CL = R CL = 1.2 UCL = D4R UCL = 2.115* 1.2 = 2.538 LCL = D3R LCL = 0*1.2 = 0 Therefore the range chart values are LCL 0, centerline 1.2, and UCL 2.538.
The process appears to be out of control with sample 4 on the average chart out of limits, and sample 2 on the range chart out of limits. Whenever a data point falls outside of the control limits, the process is assumed to be out of control and an investigation is warranted to find and eliminate the cause or causes (NIST Handbook, n.d.). It is at this point that a search for an assignable cause begins. An assignable cause may be a change in the operator, the machine, or possibly the material. In any event, the process is halted until the cause is located and corrected. This is the very reason why quality control is in place in many companies. By identifying a point at which a process goes out of control, the company is able to address the issue prior to producing a large number of defective products which would lead to a larger cost issue.
Attribute Chart vs. Variables Chart
Attribute controls are those that are measured on a discrete scale. One of the advantages of the attribute charts is that they allow for quick summaries of the aspects of the products quality. This allows for attribute charts to function without requiring expensive devices and lengthy measurement procedures. Another advantage of the attribute chart is that because of its basic simplicity, it is an easier chart to read and understand. This is a plus for management that may be new to or unfamiliar with quality control procedures.
Variable control charts are more sensitive than attribute control charts. They are better able to alert management to issues or problems that are occurring and in some instances that have yet to occur (Stat Soft Inc., 2003). The major advantage of the variable control chart is that because of its sensitivity and ability to detect problems early, it also an excellent prevention tool for avoiding large amounts of rejected product and therefore is an excellent cost and waste saver.
Even though the variables control chart is more attuned to the quality control process and is capable of giving an earlier indication of trouble or an out of control process, I prefer the attributes control chart for it's simplicity and ease of use. I believe that if the attribute control chart is used properly and the process is monitored often it can be just as effective as the variables control chart.
Conclusion
Control charting is the most technically sophisticated tool of Statistical Quality Control. When the charts are used correctly, they can serve to improve the economic effectiveness of a process. In order for the charts to be effective however, the process must be continuously monitored so as to recognize the possible variations as close to their occurrence as possible (Clemson. edu , n.d.). The control charts serve to illustrate the current operational condition of a process by providing a visual display than clearly indicates whether a process is within limits, out of control, or headed for an out of control condition, offering management time to take corrective action and avoid waste.
Reference
Ebert, R.J., & Griffin, R.W. (2005) Business Essentials (5thEd.). New Jersey: Pearson-Prentice Hall.
Schroeder, R.G. (2007). Operations Management: Contemporary concepts and cases (3rd Ed). New York:McGraw-Hill Irwin.
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