March 26, 2012
The Tide is High
My last blog, "Who’ll Stop the Rain," explained how collecting too much data creates problems with control charts. Attempting to monitor too many items can be overwhelming and results in the user overlooking the "true" key characteristics of a process. Likewise, collecting only one characteristic, but collecting it too frequently, can create a control chart that isn’t usable. Collecting data too frequently results in incorrect control limits, as well as charts that contain hundreds, or thousands, of unusable data points.
So just how often should we collect our data?
As you should have guessed from the title, I’ll be using the ocean as an example for determining sampling frequency. Our task is to measure the water level at one specific coast location so that we can forecast tide cycles and ocean depth changes. This information will also be evaluated to help predict any unusual conditions, such as storm surge levels.
Planning the Process Study
To help us understand our process – in this case, the ocean tide – we first plan a Process Study. The goal of the study is to gather enough information to determine how to best sample the process. The following steps are taken during the planning stage:
- Define the process conditions.
- Select the operator and measurement process.
- Ensure that the measurement equipment is accurate.
- Standardize the measurement procedure.
- Determine the sampling schedule for the study.
To evaluate the tide cycle, first we need to select a location for measurement. In our example, we need to make sure that our ocean floor location doesn’t change and that we are measuring in the same location at each sampling, so we decide to mount a calibrated scale to a pier support beam. The scale is attached with the base of the scale touching the ocean floor and it is leveled vertically to give an accurate reading. We also realize that the measurement process should be standardized and that readings should only be taken between tides. Measurements taken immediately before, during or immediately after a tidal wave would not be accurate.
Since the tide cycle is an unknown, we must measure the process as frequently as possible to fully understand how the process performs. Since our operators are working at the pier, we have someone available 24 hours a day to take the measurements and record information for us. We decide that taking a reading every fifteen minutes should give enough information about how the process performs. Then the operators are instructed in the measurement process, how to record the data and on how to plot the data on a run chart. The test will run for 7 days so that several tide cycles can be included.
Process Study Results
Analysis of the test results shows that we have a semi-diurnal tide. This means that there are approximately two high tides and two low tides within a 24 hour period, which equals a high to low tide cycle approximately every 6 hours. We also found that the tide has a maximum difference of 2 feet from low to high tide. Based on the process study, we can make the following conclusions:
- There are approximately 6 hours between each high and low tide.
- Sampling every 15 minutes shows a change of 1 inch between subgroups. (There are 2 feet of ocean depth difference from high to low tide. There were 24 samples taken in a 6 hour tide cycle.)
- Standard rule of thumb is to sample 2 or 3 times between process shifts or process cycles. Our study sampled once at high tide, once at low and 22 times during the cycle.
- With a 6 hour long cycle from high to low tide, we could sample every 2 hours and still create a control chart that would effectively monitor the tide cycle.
Setting Your Sampling Frequency
The first step in setting the sampling frequency is to understand the process!
First we plan a controlled Process Study where key characteristics are measured, according to a standard procedure, as often as possible. Once this is set up, we conduct the study for a long enough period of time to understand the process behavior and then plot the data on a run chart and analyze. While analyzing, we look for any "shifts" and /or "cycles" in the process and set your sampling frequency according to the "shifts" and / or "cycles" that are present. Lastly, always plan the sampling frequency to allow for 2 samples between the average shift and / or cycle time.
How Does This Relate to My SPC?
Just as the ocean has a "common" cycle for the tide, our processes have "common cause" variation. SPC control charts allow us to understand this common cause variation and they notify us when something outside of the expected common cause variation occurs. These unusual occurrences, or "assignable cause" issues, can then be evaluated or corrected by the operator. Rational sampling of the process allows for creation of control chart control limits that truly define this common cause variation.
Control charts are only effective when the control limits accurately reflect the process. When the control limits do accurately reflect the process, control charts can be used to not only notify us when assignable causes occur, but they also allow us to make process improvements that reduce the common cause variation. Sometimes we forget that the goal of SPC isn’t to just maintain status quo, it is to improve the processes that we are monitoring!