# Research Paper: Statistics Control Chart

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¶ … control chart is. The author is then asked to explain what an "in control" control chart is and what an "out of control" chart is. The author is asked, in general terms, to describe the three different types of control charts. One of those three must be an "in control" chart and another must be an out of control chart. The third of the three can be either and all three must be explained thoroughly. Per the assignment, copies of the charts will be included for visual reference. All of the charts come from scholarly reviewed articles downloaded from an online academic library.

Control Chart Defined

A control chart is used to figure out whether a business process, often manufacturing, is within proper parameters (or control) or not. The charts are often referred to as process-behavior charts or Stewhart charts. The latter's namesake was Walter a. Stewhart. He was an employee for Bell Labs in the early 1900's and his charts were spawned by a need to track and verify the reliability of Bell's equipment. The Stewhart iteration of the control chart was very much based on the Bell curve, which is the curve that shows that there is an equilibrium value for a line of values and most of the values of the plot will either be on or very close to that equilibrium point. A control chart works in pretty much identical fashion (Carey).

The chart is constructed by taking samples of a certain metric or measurement, such as average, proportions or ranges of values and measuring the values for said metric of choice over time. A centering line is plotted through the data set to show the average of the metric being reviewed. At the same time, the standard deviation of the same metric is also calculated. The upper control limit, also known as a UCL, and the lower control limits, also known as the LCL, are based on the above and thus show whether a chart is within control or out of control. In short, an out of control chart is one where data points, one or more, are outside of the upper or lower acceptable ranges for that chart. An "in control" chart is one where all data points are within the upper and lower limits. The upper control limit (UCL) and lower control limit (LCL) are meant to represent a range of values that is "unlikely" to occur during normal conditions. In other words, most to all data points on a control chart would normally be expected to entirely within the range created by the upper control limit and lower control limit (Carey).

Many control charts take the practice of upper control limits and lower control limits a step further and establish different ranges of values in between the upper and lower limits. Points out of those specific other ranges (not the LCL and UCL) would cause a control chart to be out of range but they would help indicate how close to the average, or whatever measure is being used, the data plots on the graph are (Carey).

If points are outside of the upper control limit and/or the lower control limit or even the other interim divisions, it is up to the creator of the chart to figure out why precisely that occurred. It can pertain to an odd or otherwise uncommon situation that led to the spike up or down. However, it can also be due to the parameters and measurements of the graph not being aligned with real-world practice, history or even predictions for the future (Carey).

The measurement of what constitutes above or below the limits of a control chart are often based on one of two measurements. The first is standard deviation, which is generally used to show the variation away from a fixed point for a series of values, as opposed to simple average which can yield the same answer for a wide array of different sets of numbers. Others users of control charts use a blend between standard deviation and ranges of the graph at the same time. Generally speaking, a control chart's eventual values should have at least the vast majority of the values within the desired/expected range. Anything less than 99% of values being in the proper range is cause for concern, either from why the values are out of spec or whether the graph is not calibrated properly (Carey).

There are a good number of different control charts that can be named beyond the above "in control" and "out of control" charts. Examples of these charts include regression control chart, EWMA chart, CUSUM chart, Time Series chart, three-way chart, Stewhart individuals control chart, c-chart, u-chart and p-chart. Regression control charts are used to indicate the quality characteristic measurement for a single subgroup. A CUSUM chart is used to show the cumulative sum of quality characteristic measurement from a single subgroup. A c-chart is used to measure non-conformance over time in a subgroup. A u-chart is used to show the number of non-conforming data plots over a series of time within a single subgroup. (Carey).

Examples of Charts

The author of this response is asked to offer three examples of control charts with at least one being "out of control" and at least one of the other two being "in control."

Source: (Tsung-Tai, and Kuo-Piao, and Fu-Chang, and Chieh-Min, and Ming-Chin)

The above chart is for the risk-adjusted cumulative sum (CUSUM) chart for the EMS system in Taipei County (OHCA) for patients with out-of-hospital cardiac arrest. This chart is clearly out of control at multiple points in the graph with the biggest outlier being at the 1501 patient number mark (Tsung-Tai et al.). As indicated and discsussed above, the amount of plots on this graph that are out of control is quite alarming. Many of the values that are technically within the UCL and LCL are very close to the limit with some values being very far out of the spec, including the aforementioned 1501 area and the 2000 area as well along the x-axis. The creators of this group would have to get to the bottom of why this chart is so off the board in terms of what the defined UCL and LCL is and how many of the values are out of the range. It would be a bad graph construction or there could also be a problem with the activities and processes that are feeding this graph.

Source: (Dekker)

The above chart is also a control chart and it is measuring infections in a quarter on a per 1000 patients unit. It is also "out of control" due to the first spike near the left side of the graph. Were it not for that, the graph would be in control since no other data point is below the upper control limit (which is at 15.50) or below the lower control limit (which is at roughly 8.0) (Dekker). This chart is much more in control than the prior one but it's much, much closer with only one point of spec. The graph could be calibrated and defined incorrectly but it's more likely that the single spike that put the graph out of spec can be defined by extenuating circumstances of some sort. Regardless, the constructors and analyzers of the graph should make sure which it is for future research and analysis to be verifiably proper and accurate.

Source: (Brito)

The third and final chart up for review is in Spanish but it's a perfect example of a "in control" chart. Some of the values towards the right side are very close to the lower control limit, but all of them are above the LCL (Brito). The graph starts out staying very close to the mid-point of the control chart…
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