Process Capability with Attribute Data

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About this lesson

Six Sigma projects strive to achieve a process capability that represents Six Sigma quality. The calculation of process capability is quite different depending upon whether the data is variable or attribute. This lesson will present the technique used for determining process capability with attribute data.

Quick reference

Process Capability with Attribute Data

The determination of process capability is quite different depending upon whether the data is variable or attribute.  Attribute data relies on a count of defects in the data set rather than spec limits and descriptive statistics.

When to use

Process capability and process sigma are useful techniques for determining if a process is able to deliver consistently good results.  When using these approaches, if the data is in the form of attribute data, then these techniques must be used rather than those for variable data.

Instructions

Attribute data process capability differs from variable data process capability in several important respects.  There is no measurement scale and numerical value to the data.  Rather the basic unit of measure is a count of defects with respect to a standard.  There is no upper and lower spec limit, instead there are opportunities to either meet the standard or fail the standard.   There is no descriptive statistics of the measure, there is just the count.  Attribute data can be converted to variable data using the central limit theorem or possibly using a transformation such as the binomial distribution.  However, it is much easier to just use counts and the attribute data lookup table.

The attribute data lookup table relies on determining a DPMO (defects per million opportunities) value for the process.  That value is used as the starting point to enter the lookup table and determine a process sigma and process yield.

It is important to understand DPMO, defects and defectives.  These terms are used often in a discussion of Lean Six Sigma and control charting.  The table below shows the definition of these terms and several others that are also relevant to SPC control charting.  Thoroughly learn the definitions of these acronyms and how to calculate them.

The attribute data process capability lookup tables are found in numerous references and online.  If taking the IASSC exam, you will have access to the tables if needed for any of your questions.  To use the table, first calculate the DPMO for the process characteristic.  Using that value, find an entry that is close to that number.  If your DPMO value is between two entries, feel free to interpolate the data in the other two columns.  The other columns are a process sigma, which directly correlates to the process capability value.  Also, the table has a column for expected yield.

Hints & tips

  • It is easy to confuse defects and defectives.  Defects apply to each unique opportunity that is checked against a standard.  Defective always applies to products, processes or systems that normally have many opportunities.
  • DPMO is determined for a particular type of opportunity, so it does correlate to a Cpk for that characteristic.  However, defective units uses measures like PPM (parts per million) and each defective unit could have many different types of defects on it.
  • Generally, when discussing attribute data processes, the process sigma is used instead of converting that sigma to a process capability.
  • While I have talked about the conversion of process sigma to Cpk based upon a simple understanding of the Cpk metric, there is a view that conducts a 1.5 sigma shift when doing the conversion.  The rationale for this is somewhat murky, so I don’t endorse it.  However, you should be aware that your local Lean Six Sigma methodology may include this shift when converting from sigma to process capability.
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  • 00:04 Hello I'm Ray Sheen.
  • 00:06 Well now let's look at how we determine process capability,
  • 00:09 when the process is being measured with attribute data instead of variable data.
  • 00:14 Attribute data is based upon counts of an attribute, process capability discussions
  • 00:19 often focus on variable data that is being measure on a scale.
  • 00:23 But in my experience attribute data is just as prevalent, and
  • 00:27 therefore we need to address it also.
  • 00:29 There will be several SPC charts that are structured for attribute data.
  • 00:33 So this is a type of analysis that is very relevant to our discussion.
  • 00:37 Attribute data at least raw attribute data,
  • 00:40 is not normally formed into a nice normal distribution.
  • 00:44 Therefore, the process capability that's used with variable data will not work.
  • 00:49 When we have a lot of data points, we can apply the central limit theorem and
  • 00:53 create samples or subsets of the data.
  • 00:55 A value can be establish for
  • 00:56 those subsets based upon the number of percentage of attributes in the subset.
  • 01:00 This can eventually create a normal distribution for us, but
  • 01:04 does require a lot of data.
  • 01:06 Another type of transformation that can be use for
  • 01:09 attribute data is to create a binomial function, but
  • 01:12 both of these can require a lot of data and take a long time.
  • 01:16 Well fortunately,
  • 01:17 there is a much simpler way to determine process capability with attribute data.
  • 01:22 We just use the straight up count of defects or occurrences and the units or
  • 01:26 opportunities, let's look at what we mean.
  • 01:29 Attribute data process capability relies on counts of the unit of measure,
  • 01:33 but those counts can be expressed in many different ways.
  • 01:38 So like any good business management system,
  • 01:40 we've figured out how to turn this into acronyms.
  • 01:43 Let me run to each of these because I'll be using these terms throughout
  • 01:47 the rest of this course.
  • 01:49 In particular, when we discuss the attribute data SPC charts.
  • 01:53 So it's important that you understand the definition of each.
  • 01:57 We'll start with the easiest, a defect, that's anything that does not meet
  • 02:00 the standard of acceptable performance, it uses the acronym D.
  • 02:04 We contrast that with defective, defective applies to a product process or system.
  • 02:10 Whenever the product processor system has one or more defects, it is then defective.
  • 02:14 So, if you have a car that has a dead battery,
  • 02:17 a headlight that is not working and a radio that won't turn on.
  • 02:21 You have three defects, but only one defective, DU is the acronym.
  • 02:26 An opportunity is anything that we're checking against the standard, if it meets
  • 02:31 the standard, it passes the opportunity, if it fails the standard, it is a defect.
  • 02:36 If we don't ever look, it's not an opportunity and
  • 02:39 of course the acronym is O.
  • 02:41 A unit is a completed result of a product, process, or system.
  • 02:44 That unit may have many opportunities, depending upon its complexity.
  • 02:49 So we can tie defects to opportunities and
  • 02:52 defectives to units and of course, the acronym is U.
  • 02:55 Now, we can start combining these, first there is DPU, or defects per unit.
  • 03:02 That is the average number defects found on a unit of our data set.
  • 03:07 This can be calculated by adding up all of defects and dividing by number of units.
  • 03:13 Next is DPO or defects per opportunity,
  • 03:16 this is just the pass/fail rate of all the opportunities combined.
  • 03:22 It's calculated by taking the total number of defects found and
  • 03:25 dividing that by all of the opportunities.
  • 03:27 Now, that number can be very small, think about your car.
  • 03:31 There may be hundreds of things that are checked when you bring your car into your
  • 03:35 mechanic.
  • 03:35 So measure that we often use is DPMO which means defects per million opportunities.
  • 03:42 Now don't think you have to actually have a million opportunities before you can do
  • 03:45 this calculation, it's just the DPO calculation multiplied by 1 million.
  • 03:51 That way the values typically number greater than one
  • 03:54 rather than a very tiny decimal.
  • 03:56 But so far, all of this has been dealing with defects.
  • 03:59 Now, we switch gears to work with defectives,
  • 04:02 this is the acronym PPM or parts-per-million.
  • 04:05 It is the percentage of defective units out of all the total units
  • 04:09 multiplied by 1 million.
  • 04:11 This has become a standard industrial measure for small components.
  • 04:15 Let's run through a quick illustration.
  • 04:18 A small sensor used in your car has ten following attributes.
  • 04:21 The company that makes them, ships them to the car manufacturer in batches or
  • 04:26 lots, that have 500 parts in them.
  • 04:28 And one of these batches, there were three components that each had one defect and
  • 04:34 one component with two defects.
  • 04:37 So 500 parts with 10 opportunities means a total of 5,000 opportunities.
  • 04:41 Among those 500 parts there are a total of 5 defects,
  • 04:47 so the defects for opportunity or 5 divided 5000 or .001.
  • 04:53 We convert that to DPMO and we have 1,000 defects per million opportunities.
  • 04:59 Now, there were 500 units and 4 of them were defective with at least 1 defect.
  • 05:03 The PPM is four divided by 500 times 1 million or
  • 05:08 8,000 PPM, I hope this helps.
  • 05:12 Now let's look at how you determined attribute process capability.
  • 05:17 The attribute method we want to work with is DPMO, defect per million opportunities.
  • 05:21 We'll take the DPMO level and use it in a look up table for
  • 05:25 attribute process capability.
  • 05:27 This table converts the DPMO into a process sigma
  • 05:30 which correlates directly with our process capability indices.
  • 05:33 I have a high level version of the table here,
  • 05:36 there're some versions of the table that have more precision in the DPMO column.
  • 05:42 For our purposes feel free to interpolate between the DPMO values.
  • 05:46 So take your process DPMO and
  • 05:48 find the two values that bracket your value in the center DPMO column.
  • 05:53 I normally just do a straight line approximation between these two, or
  • 05:58 if it's very close to one side or the other I'll stick with that.
  • 06:01 Then look to the right of your DPMO value and you will see the Process Sigma.
  • 06:05 The left column is a typical process yield for that level of DPMO.
  • 06:11 Recall that Process Sigma relates to a C PK, a Process Sigma of 3 is a C PK of 1.
  • 06:17 Process Sigma of 6 is a C PK of 2,
  • 06:21 I'm not going to go into the derivation of the values of the table.
  • 06:24 Suffice it to say that those have been validated and
  • 06:26 are acceptable throughout industry.
  • 06:28 If you're worried about the ISSC exam, you have access to this table for
  • 06:33 any questions when they are needed.
  • 06:37 Process capabilities for attribute data can also be established.
  • 06:41 But rather than running through a set of calculations,
  • 06:44 we'll go back to the old school method of going to a look up table.

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