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To apply this test, look for groups of points above or below the average or centerline. Count consecutive points. Are there groups of seven or more? This is probably the result of a shift in one of the system resources (materials, people, methods, environment, information aids, equipment, and measurement). The following chart, which can be created using SQCpack, shows two groups, one with eight above the centerline and one with seven below.
See also: >> Analyze for special causes of variation >> Any point lying outside the control limits >> 7 or more points in one direction >> Any nonrandom pattern
This is the quickest and easiest test for system stability. Look above the upper control limit and below the lower control limit to see whether any points fall in those regions of the chart. If you are looking at a chart pair (X-bar and R, X-bar and s, or X and MR), look at both charts.
Points falling outside the control limits may be the result of a special cause that was corrected quickly, either intentionally or unintentionally. It may also point to an intermittent problem. The chart below shows two points outside the control limits.
See also: >> Analyze for special causes of variation >> Any point lying outside the control limits >> 7 or more points in a row above or below the center line >> 7 or more points in one direction >> Any nonrandom pattern
The key to chart interpretation is to initially ascertain the type of variation in the system—that is, whether the variation is coming from special or common causes. When the system has only common causes of variation, it is referred to as stable or in control. If, however, the system has special causes of variation, it is referred to as unstable, or out of control.
Look any of the conditions listed below, which indicate that the process is statistically unstable:
When you have determined whether or not there is special cause variation, declare the system stable or unstable.
The t-chart creates a picture of a process over time. Each point on the chart represents an amount of time that has passed since a prior occurrence of a rare event. The time unit might be hours, days, weeks, months, etc. For example, a chart might plot the number of days between infection outbreaks at a hospital. A traditional plot of this data may contain many points at zero and an occasional point at one. A t-chart avoids two types of mistakes: over control and under control that a traditional control chart might generate.
The t-chart helps to identify the two types of variation present in a system, special and common cause, so that appropriate improvement actions can be taken. Specific formulas for t-chart control limits are used with this type of data. T-charts can be created using software programs like SQCpack.
By way of contrast, consider the information that is provided with a chart of lost production due to work time accidents. The chart shows many months where there were no occurrences of lost production. Thus, this chart is not beneficial and provides little insight to know if the process changes resulted in improvement.
Now consider the same data using a t-chart. Instead of plotting the lost production each month, plot the days passed since the last time of lost production. The data is still being collected and charted, but the method used to analyze the information is different. This shows that an improvement is occurring (or has occurred), with the days between lost production increasing.
A g-chart is a chart for attributes data. It is used to count the number of events between rarely-occurring errors or nonconforming incidents.
The g-chart creates a picture of a process over time. Each point represents the number of units between occurrences of a relatively rare event. For example, in a production setting, where cars are produced daily, an unexpected line shutdown may occur. A g-chart might be used to look at the number of units (i.e. cars) produced between line shutdowns. The units produced can be almost anything. For example, you might look at the number of invoices printed, the number of customers served, or the number of patients seen, between occurrences of some event. A traditional plot of data such as this is not conducive to control chart interpretation. The g-chart helps to visualize this data in traditional control chart form. Specific formulas for g-chart control limits are used with this type of data.
The “g” in g-chart stands for geometric, since data relating to events between occurrences represents a geometric distribution. G-charts can be created using software programs like SQCpack.
A rare event chart is used when a traditional control chart is not effective. Consider a rare event chart when one or more of these conditions exist:
Here are some processes in various industries that lend themselves to rare event application.
A rare event chart is a control chart that provides information about the process being studied where the data comes from rarely-occurring incidents. It provides insight into a process when tracking quality measures that occur infrequently enough that tracking them on a traditional control chart tends to be ineffective. Rare event charts were developed in response to the limitations of attributes control charts and individuals charts in rare event scenarios.
In a typical count or attributes control chart, there is a numerator (what is counted) and a denominator (the sample size or items in the pool to count). If many of the periods being counted are zero because no incident has occurred, a chart with many flat lines ensues, where everything is plotted along the x-axis. When an incident occurs, the count of one for this period is plotted, then the counts drop back to zero for the next few periods. This cycle continues, and the resulting control chart looks odd, the control limits are not effective, and the chart fails to provide proof of quality performance.
Two types of rare event charts exist. A t-chart measures the time elapsed since the last event, and a g-chart counts the number of possible opportunities since the last event.
A Pareto diagram is a simple bar chart that ranks related measures in decreasing order of occurrence. The principle was developed by Vilfredo Pareto, an Italian economist and sociologist who conducted a study in Europe in the early 1900s on wealth and poverty. He found that wealth was concentrated in the hands of the few and poverty in the hands of the many. The principle is based on the unequal distribution of things in the universe. It is the law of the “significant few versus the trivial many.” The significant few things will generally make up 80% of the whole, while the trivial many will make up about 20%.
The purpose of a Pareto diagram is to separate the significant aspects of a problem from the trivial ones. By graphically separating the aspects of a problem, a team will know where to direct its improvement efforts. Reducing the largest bars identified in the diagram will do more for overall improvement than reducing the smaller ones.
There are two ways to analyze Pareto data depending on what you want to know:
Counts Pareto: Use this type of Pareto analysis to learn which category occurs most often, you will need to do a counts Pareto diagram. To create a counts Pareto, you will need to know the categories and how often each occurred.
Cost Pareto: Use this type of Pareto analysis if you want to know which category of problem is the most expensive in terms of some cost. A cost Pareto provides more details about the impact of a specific category, than a count Pareto can. For example, suppose you have 50 occurrences of one problem and 3 occurrences of another. Based on a count Pareto, you would be likely to tackle the problem that occurred 50 times first. However, suppose the problem that occurred 50 times costs only $.50 per occurrence ($25 total) and the problem that occurs 3 times costs $50 each time ($150 total). Based on the cost Pareto, you may want to tackle the more expensive problem first. To create a cost Pareto, you will need to know the categories, how often each occurred, and a cost for each category.
An example of a counts Pareto diagram is shown below.
Use a Pareto diagram when you can answer “yes” to both these questions:
Despite its simplicity, Pareto analysis is one of the most powerful of the problem-solving tools for system improvement. Getting the most from Pareto analysis includes making subdivisions, multi-perspective analyses, and repeat analyses.
Subdivisions are useful when data has been first recorded at a very general level, but problem solving needs to occur at a more specific level. A retail chain manager might create a Pareto diagram for all the customer returns of furniture by store in his district. Once he or she has identified the store which contributes most returns to the total, the next step might be to analyze that store’s returns by furniture type. If “chairs” turned up as the biggest category of furniture returns for the store in question, yet another Pareto of chair returns might help to discover whether dining room chairs, occasional chairs, wooden chairs, or upholstered chairs were being returned more frequently. Because the Pareto principle holds for subgroupings of data, such successive analyses can be performed to help teams target small elements of a large problem.
Multi-perspective analyses are useful when data can be stratified or subdivided in several different ways. The retail manager might study customer returns of furniture by number of units and again by cost. A store might discover that chairs have accounted for the majority of items returned over a period of time, but that fine dining sets accounted for the majority of cost. Depending on priority, the problem could be attacked to reduce either the highest frequency or the highest cost item. The district retail manager might study his or her district-wide furniture returns by store, by lot number, by furniture type, by cause for return, by frequency, by cost, by salesperson, by delivery carrier, or by any other set of categories he or she thinks may reveal opportunities for improvement. Multi-perspective Pareto analysis helps assure that a set of data is reviewed from all angles and that many explanations for variability are considered.
Repeat analyses are useful when improvement activity is underway and performance data is changing over time. If the retail manager worked with the store’s delivery staff to reduce the number of fine dining sets being damaged and subsequently returned, it would be useful to repeat an earlier Pareto analysis using more recent data to see if the target category has shrunk. Depending on the cycle of data collection—hourly, daily, weekly, monthly, quarterly, or other—repeated Pareto analyses help to monitor the improvements made to the system producing the data.
Caution is in order for users of Pareto analysis who have not monitored the systems they are studying for stability. A wildly fluctuating system will produce inconsistent Pareto rankings that can lead to misjudgments. If, for example, the retail manager failed to note that customer furniture returns varied greatly from month to month, the ranking of categories may be entirely different in a month with high returns from those of a month in which returns were unusually low. Repeated Pareto analyses can help to confirm rankings, but the most effective protection against being misled is to first use a control chart to tell if the system is stable and predictable.