Statistical Process Control (SPC)

1 Introduction

Statistical Process Control (SPC) is a method that is used to control any process that has a measurable output. Small samples are taken from each batch, measured, and some basic calculations are then made.

2 SPC-Phases

1. Capability Study
   A number of batches is sampled and measured. A fixed sample size, usually five, is taken from each batch, and the average of each batch is calculated. SPC makes use of the Central Limit Theorem, so sample sizes lower than five are discouraged. The number of batches sampled varies, and although twenty is considered to be sufficient, the larger the number is, the better.
   
   Next, the overall average is calculated. This equals the average of the batch averages. The overall standard deviation is also calculated, and this is the standard deviation of the batch averages.
   At this point, customer specifications are checked. These will stipulate a Lower Specification Limit and an Upper Specification Limit. The process is potentially capable if:
   (USL - LSL) is larger than six times the overall process standard deviation
   The reason for this is that the probability of any measurement falling outside plus or minus three standard deviations from the average is only 0.3%.

2. Control Limits
   After the process output has been characterized, it is possible to apply some statistical tests. These are all based on the Normal Distribution, or Gaussian "Bell" Curve. Every Normal Distribution has common features.
   For instance, around 68% of the measurements fall within one standard deviation of the average. About 95% of the measurements fall within two standard deviations, and 99.7% of the measurements fall within three standard deviations.

3. measure or monitor
   To check samples from batches regularly.The SPC chart should show no patterns or trends. For example, if the process is stable and has not shifted , then it is unlikely that 8 points in a row will be above the overall mean. If this happens, it is very likely that the reason is a process shift, rather than just random measurements. This means that the process should be fixed before proceeding.

4. Process Improvement
   When the specification limits dictated by a customer cannot be met, two actions are needed. The first is to deal with parts that are outside customer specification, for example reworking or scrapping the parts. The second, and most important action, is to find out what caused the variation, and then to reduce this variation.

   This is typically the role of the Process Engineer. The engineer will use Six Sigma or other methodologies to improve the process.

3 SPC Rules

When modern companies use Statistical Process Control, rules are applied to the charts to indicate that something has changed. The rules used are usually a sub-set of eight rules that are known as the Western Electric Rules. The eight rules are listed in the following:

• Point Outside Upper or Lower Control Limits
  The Upper and Lower Control Limits are set at three standard deviations from the mean. If a point lies outside either of these limits, there is only a 0.3% chance that this was caused by the normal process.

• Eight Points on the Same Side of the Mean
  There is an equal chance that any given point will fall above or below the mean. The chances that a point falls on the same side of the mean as the one before it is one in two. The odds that the next point will also fall on the same side of the mean is one in four. The probability of getting eight points on the same side of the mean is only around 1%.

• Eight Points Increasing or Decreasing
  The same logic is used here as for "Eight Points on the Same Side of the Mean". Sometimes this rule is changed to seven points rising or falling.

• Two of Three Points Outside Warning Limits
  The Warning Limits are usually set at two standard deviations (i.e. two sigma) from the mean. The probability that any point will fall outside the warning limit is only 5%. The chances that two out of three points in a row fall outside the warning limit is only about 1%.

• Four of Five Points Falling Outside One Sigma
  In normal processing, 68% of points fall within one sigma of the mean, and 32% fall outside it. The probability that 4 of 5 points fall outside of one sigma is only about 3%.

• Fourteen Points Alternating Direction
  This rule treats each pair of adjacent points as one unit. The chances that the second point is always higher than (or always lower than) the preceding point, for all seven pairs is only about 1%.

• Fifteen Points in a Row Within One Sigma
  In normal operation, 68% of points will fall within one sigma of the mean. The probability that 15 points in a row will do so, is less than 1%.

• Eight Points in a Row Outside One Sigma
  Since 68% of points lie within one sigma of the mean, the probability that eight points in a row fall outside of the one-sigma line is less than 1%.

The Western Electric Rules are a set of rules that exist to highlight when something improbable happens in a process. The rationale is that if something happens that is improbable due to normal causes, it has happened due to abnormal causes. The abnormal cause is usually a change, and since change to the product is undesirable, action needs to be taken.

4 SPC Application in Company

We can use SPC technique to manage our project processes or daily works in our company. let me use examples to explain how to use it actually.

1. Manage Project Process
   We can statistic the actual efforts on the different activities (or small tasks) of project processes, such as time. Compare the real time with the planned time, then give out the analysis result using SPC technique and provide a improvement suggestion.

2. Manage Working Hours of Staffs
   Every day all the staffs will email task coaches. We can record the sending time. Also, in our mind we have a average value of the send time, assume that the send time follow a certain distribution. Next, we can use the SPC technique to statistical the working hours of staffs, then indicate that a certain staff need to work hard or keep a rest.