Statistical Process Control for Data, Essay Example

Control charts are also commonly referred to as Shewhart charts and are modelled in order to reflect particular behaviors of a population. Ultimately, these charts are used to determine if a trend is within a state of statistical control. The process is considered to be in control if 99.7300% of the data points fall within the control limits. If points fall outside of these limits, it indicates that there is a source of variation called special-cause variation. Control charts are created by first selecting a population to study and then identifying the variable that will be examined. The sample will be placed on the x axis and the values will be placed on the y axis. Limits will be chosen based on the expected probability distribution of the population being studied.

Typically, an xbar chart is generated in order to summarize a particular characteristic. A line in the middle of the graph denotes the mean value of the population, and the two dotted lines denote the upper and lower limits. Often on the bottom of the graph, summary statistics are shown that clearly label the number of groups of individuals that were studied, the mean of the trend, the standard deviation. Furthermore, it will specifically label the upper and lower limits in addition to the number beyond limits and the number violating limits, although to some extent this will depend upon the statistical software used in addition to the parameters indicated within in.

In Control Chart

This control chart indicates that the weight of individuals in New York City over a period of time. These results were taken from a phase II research trial, and this was performed to determine whether the weight of each patient would remain constant. This particular test was sorted according to randomized subgroups, so it is not currently possible to determine the weight category of each group. The researchers determined that phase II subgroup number 25 fell into the average measurement. This graph indicates that all elements are in control, which is indicated by the fact that all variable fall within the upper and lower limits that were determined by the researchers. This information tells the researchers that they were successful in ensuring that the weight of their participants would remain constant.

Out of Control Chart

This control chart indicates that the weight of 8 individuals in New York City were determined to indicate their obesity status. This particular test was done for children volunteers and the weight indicated was in kilograms. The researchers determine 18.78 kilograms to be the lower control limit and 22.01 kilograms to be the upper control limit. They found that the average weight of participants was 20.40 kilograms. This graph indicates that there is a single out of control condition, which was a child who weighed approximately 23 kilograms. This information tells the researchers that this child is obese and that they must determine what they can do to help him to ensure that he falls within the project limits, which are indicators of normal weight and therefore health.

Another Type of Control Chart

This control chart differs from those summarized above because it includes two simultaneous charts that summarize both the range and median of weights of study participants. This study organized these individuals into 50 subgroups with a subgroup size of 5. All measurements of the study were in kilograms and utilized young children to determine their obesity status. The first study utilized 20.8 kilograms as the lower control limit and 28.2 kilograms as the upper control limit in order to delineate what normal health was expected to be for the exact patient population studied. The mean median weight for this population was determined to be 24.3 kilograms and the overall trend shown indicated that the system was in control. Therefore, no changes were needed to indicate whether the researchers needed to make any modifications to their population to ensure that they would fit within the predetermined study limits. The mean median range was 5.4 kilograms, indicating that the largest value and the smallest value differed by only a mean weight of 5.4. Therefore, we can assume that a majority of the study participants had approximately the same weight. The predetermined upper control limit for range was 11.5 kilograms and the lower control limit for range was 0 kilograms. Since there were no data point outliers, we can also concluded that this trend was in control, which indicates that every individual in the study had approximately the same weight.

This particular control chart demonstrated that it is useful to show the value of more than one statistical test in a relationship. Although both the median and range were in control in this example, it is possible that these numbers could be in control for one statistical test and not the other. Doing so will help the researchers understand more information pertaining to the degree of control of the trends that they are studying.

Works Cited

Poots A, Woodcock T. Statistical process control for data without inherent order. BMC Medical          Informatics and Decision Making. London, UK: BioMedCentral, 2012.

Shewart, WA. Economic Control of Quality of Manufactured Product. Van Nordstrom, 1931.

Wheeler, Donald J. Understanding Variation. Knoxville, Tennessee: SPC Press, 2000.