· Homework

o Chapter 14: Exercise 14-2 (page 297 of the text)

· Homework

The Run Chart

The run chart is a time series analysis. Its horizontal axis is time and its vertical axis is the data axis. The chart is a data plot; it usually includes a minimum of 12 observations. The data points are connected.

An Example of a Run Chart

The center line of the run chart distinguishes this chart. The center line is the median value of the data. InFigure 14-9the median is 14. The median is used to represent the middle of the data distribution. The mean is not used because a mean can be overly influenced by a small number of very low or high data values.

A run is defined as one or more consecutive data points on the same side of the median. Data points on the center line are ignored. The run chart allows the quality analysts to draw specific conclusions about the data based on the number of runs presented by the data. Once a run chart is prepared, the analyst:

· 1.Counts the number of appropriate data points (ADP). This equals the total number of data observations minus the number of observation on the median line on the run chart. InFigure 14-9, the ADP is 17. Seventeen of the data points are not on the median line.

· 2.Estimates the lower level (LL) and upper level (UL) number of runs using the following formula:

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· Figure 14-9An Example of a Run Chart

· 3.Counts the number of runs (R), defined as the number of one or more consecutive data points on the same side of the median.Figure 14-9demonstrates eight runs.

· 4.If the number of Rs is lower than the LL or greater than the UL, the variation is based upon a change in the process and warrants additional and detailed analysis. If the R is between the UL and LL, the variation is considered natural, and further analysis is not needed.

· 5.The LL forFigure 14-9has been calculated as 5, and UL as 13. If the number of runs is less than 5 or greater than 13, then a fundamental change has occurred that warrants further detailed analysis and potential system change. Because the data inFigure 14-9indicates eight runs, the analyst would conclude the variation in the number of falls is within natural limits and no systematic change is needed.

· 6.Other points to consider signals of process variations that warrant additional analysis include:

o a.If any one run presented by the data has 7 (when ADP is less than 20) or 8 (when ADP is 20 or greater) data points.

o b.If any one run has 14 points that consecutively zigzag the median.

o c.If any run, including the data points on the median, have 6 or more consecutive increasing or decreasing values.

The run chart provides analysts with a systematic approach to assess variation. This assessment of variation is the basis for additional analysis using TQM tools and techniques.

The Control Chart

Run charts and time series analyses can be used to describe the variation in occurrences. More important, control charts can be used to analyze this variation. A control chart tracks variation to determine whether it occurs within predetermined boundaries or limits (natural limits). These charts also provide the ability to draw certain analytic conclusions based upon whether the variation crosses the threshold boundaries used on a control chart. When the variation crosses the control chart’s boundaries, fundamental change in the system’s outcomes has occurred. Variation across or near a boundary is a signal to analyze the underlying system and potentially redesign it.

The concept of control charts is simple. It involves taking a time series analysis and adding appropriate boundaries, called control limits. The control limits represent the band of natural variation inherent in the time series analysis. When these natural variation boundaries are crossed, the analyst should look for fundamental change in the underlying process that creates the occurrencesand (potentially) change the system. Given this approach, the challenge is to find an approach that can be used to establish the appropriate boundaries of the control limits. A control chart is created when these limits are added to a time series analysis.

Control charts provide analysts the ability to assess the variation in occurrences and use the variation as a signal that an intervention is needed. They are based on the fundamental premise that variation is a natural, not abnormal, characteristic examined over a period of time. Control charts accept this natural variation inherent in processes and systems and tell us when we need to act and when the variation being reported is natural and beyond the control of the organization and the manager.

There are many types of control charts based on whether the data are continuous or discrete. The following two provide the analyst with a starting point to use control charts.

· 1.Time series for moving ranges, also known as a range chart and a moving range chart

· 2.Time series for individual values, also known as an X chart

Control Limits for Control Charts

Control limits are the threshold boundaries that are added to a time series analysis to create a control chart. These limits, expressed as an upper limit and lower limit, are intended to provide managers an interpretative context. As stated, when the variation remains within the control limits, the variation is natural. No organizational response is appropriate. The underlying process or system is acting naturally and producing a natural level of variation. Natural variation occurs within the control limits. We always find natural variation. When the variation exceeds control limits and/or presents related characteristics involving these limits and the center line, then the quality analyst must act. The variation is no longer a natural property. It represents a dramatic signal that a fundamental change has occurred in the process or systems underlying the occurrences being examined. Again, notice the use of the term “signal.” The preceding two statements are the fundamental concepts underlying the appropriate generation and use of control charts.

When time series analyses present individual values, not averages or subgroup averages, the average moving range can be calculated and used to establish threshold values. The moving range is calculated by determining the absolute between a preceding and succeeding month (Table 14-4). For example, the number of medically complicated births in January was 19, and in February was 27. The moving range calculation is the difference between January and February, or 8.In March the number of medically complicated births was 20. The moving range, expressed as an absolute number, for February–March is the absolute difference or 7, not -7. A chart can be used to examine the moving ranges, the month-to-month variation that may be occurring.

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o Chapter 14: Exercise 14-2 (page 297 of the text)

• 14-2Using the following data, prepare a run chart, scatter chart, and control chart. A late surgery is defined as any surgical operation that was started more than 30 minutes after its scheduled time (Table 14-4).

Table 14-4Number of Late Surgeries