Process Capability - Variable Data

Locked lesson.

Upgrade

About this lesson

Process capability is the statistical analysis conducted to determine if a process performing with only the normal process variation can be expected to meet the customer's expectations at all times. Variable data process capability is tracked with capability indices.

Quick reference

Process Capability - Variable Data

Process capability is the statistical analysis conducted to determine if a process that is performing with only the normal process variation can be expected to meet the customer's expectations at all times. Variable data process capability is tracked with capability indices.

When to use

Process Capability is normally used during the Analyze phase to determine whether an existing process can meet the customer expectations even under the best of conditions.  It is also used during the Control phase to assist the team in determining whether the process operators and managers are maintaining adequate process control.

Instructions

Process capability is an assessment of whether a process is able to consistently deliver results that meet customer expectations.  When working with variable data, it is a ratio of what the customer expects, as expressed in the specification limits for a process parameter, and what the process is able to consistently deliver based upon actual process performance. 

When determining process capability for variable data, direct calculations are performed. These calculations use the upper and lower specification limits for the parameter - which are normally found by adding and subtracting the tolerance limits from the performance target.  The calculations also use the descriptive statistics of mean and standard deviation from the data set for the parameter. 

There are four process capability indices that are a combination of the attributes of short-term versus long-term process performance, and the ideal or best-case performance versus the current state performance.   These are Cp, Cpk, Pp, And Ppk.

 

The Cp and Pp calculations are considered the best case because they use the full width of the allowable specification limits.  The width of the process performance for these indices is represented by the span from minus three standard deviations to plus three standard deviations for a total of six standard deviations. This was based on the initial derivation of control charts developed by Dr. Walter Shewhart.

 

 

The Cpk and Ppk modify the formula so that only a portion of the specification width is used in the numerator and a portion of the process performance is used in the denominator.  The portion used in the numerator is the range from the mean (average) of the process performance data to the closest specification limit.  The portion used in the denominator is one-half of the amount used in the Cp or Pp calculations, that is three standard deviations.

Hints & tips

  • The Cp index is set at the time of the process design.  The specification limits are known and the process standard deviation can be determined. 
  • The Cpk index often changes regularly as the center of the process performance drifts high or low. Over time the Ppk index can drift as it absorbs additional datasets.
  • The Cpk or Ppk can never be better than the Cp or Pp respectively.  When a process is exactly centered, the Cpk and Ppl will equal the Cp and Pp, but as soon as the mean moves away from the center of the specification, the distance to one of the specification limits will shrink and that index will shrink (this is because we are using the “minimum” function which means that we take the smaller of the two ratios)
  • It is impossible to have a negative Cp or Pp, however, it is possible to have a negative Cpk or Ppk if the process performance drifts to the point where the mean value is outside of the specification limits.
Login to download
  • 00:05 Hi, I'm Ray Sheen.
  • 00:06 Now, I've alluded to process capability many times.
  • 00:10 Now, let's dig in and study what process capability means in particular when
  • 00:14 managing a process with variable data.
  • 00:17 >> Process capability is a quantified metric that compares the needs of
  • 00:21 the customer with the process performance.
  • 00:24 Think of it as voice of the customer divided by voice of the process.
  • 00:28 The voice of the customer will be expressed as the specification or
  • 00:32 target value and tolerance limits on that process parameter.
  • 00:36 In particular, we'll need the upper spec limit and the lower spec limit for
  • 00:40 the performance parameter.
  • 00:43 For the voice of the process,
  • 00:44 we'll be using some of our descriptive statistic values.
  • 00:47 In particular, the mean and the standard deviation will be used for variable data.
  • 00:53 And with quantified voice of the customer and
  • 00:56 quantified voice of the process, we can create the process capability metric.
  • 01:01 With quantified voice of the customer and quantified voice of the process,
  • 01:05 we can create the process capability metrics.
  • 01:07 With variable data,
  • 01:09 we'll calculate ratios that serve as our process capability indices.
  • 01:13 These ratios of customer expectation divided by customer performance are Cp and
  • 01:19 Cpk for short-term data, and Pp and Ppk, for long-term or full population dataset.
  • 01:26 All four indices follow the same pattern.
  • 01:29 It's the ratio of the desired performance for
  • 01:32 a process parameter divided by the actual process performance of that parameter.
  • 01:38 That means it's the range allowed on the specification divided by the range of
  • 01:42 the actual process variability.
  • 01:44 So you may be wondering why there are four indices.
  • 01:48 Each of these is a different take on the process performance data.
  • 01:51 The Cp and Pp indices provide a best case perspective.
  • 01:56 These ratios assume that the process is being managed as designed and all is going
  • 02:02 well, while the Cpk and Ppk indices will look at the current performance.
  • 02:07 That means that the Cpk and Ppk are what the customer and
  • 02:10 the process are actually feeling at this time.
  • 02:14 So one immediate insight is that we can never have a better ratio than the Cpp or
  • 02:20 Ppp ratio, they are the best case.
  • 02:23 Now, another perspective in the indices is the Cp and
  • 02:27 Cpk are short-term look at a dataset, a sample dataset ,while Pp and
  • 02:32 Ppk are a longer-term look at the full data population.
  • 02:36 So bottom line, Cpk is what the customer is feeling right now and
  • 02:41 Ppk is what the customer has been feeling for a long time.
  • 02:46 So let's take a look at the calculations.
  • 02:49 I'll talk about Cp and Pp first.
  • 02:51 These are calculated in exactly the same manner.
  • 02:54 The only difference is that the Cp is using the standard
  • 02:57 deviation from the sample of recent experience and
  • 03:01 the Pp is using the standard deviation from the long-term full population.
  • 03:05 This calculation is the allowable range of performance divided by the span of normal
  • 03:09 variation within the process output.
  • 03:12 The allowable range based on customer expectation
  • 03:15 is the span from the upper spec limit to the lower spec limit.
  • 03:19 And the normal performance variation will be from minus 3 standard deviations to
  • 03:23 plus 3 standard deviations, which is a total of six standard deviations.
  • 03:28 And as I said, the only difference between Cp and
  • 03:32 Pp is the size of the dataset that's used in calculating the standard deviation.
  • 03:38 So what does this look like?
  • 03:40 Let's first consider a case where Cp is greater than 1.
  • 03:45 In this case, the span between the spec limits is greater than the span between
  • 03:49 plus and minus 3 sigma.
  • 03:52 As you can see in this diagram, the spec limits are outside the plus or
  • 03:55 minus 3 sigma lines in the normal distribution.
  • 03:59 But when Cp is less than 1, the opposite condition exists.
  • 04:02 The specification is still the same, but
  • 04:05 the variation in the parameter is much larger, so the distribution is much wider.
  • 04:09 Therefore, the span from minus 3 sigma to plus 3 sigma is greater than
  • 04:14 the spec limits, and that means that the ratio is less than 1.
  • 04:18 The implication of this is that if the ratio is less than 1,
  • 04:21 the process will always be generating some out of spec results.
  • 04:25 While if the ratio is greater than 1, the process has the potential to be generating
  • 04:30 good results virtually every time.
  • 04:32 Notice I said, potential.
  • 04:34 We'll use the Cpk and Ppk to look at the reality.
  • 04:38 The reality is that the process is seldom perfectly centered in the middle of
  • 04:42 the specification limits.
  • 04:44 It's either a little high or a little low, so the Cpk and
  • 04:47 Ppk calculations will adjust for that.
  • 04:50 They will essentially split the ratio into two.
  • 04:53 The formula looks like this.
  • 04:54 They will modify the numerator to pick the distance from the mean or
  • 04:58 average value of the data to the closest specification limit, and
  • 05:01 the denominator will then just be threee standard deviations.
  • 05:05 We call it the minimum function because we're taking the smaller of
  • 05:09 the two numerators.
  • 05:10 In our case, that means that we will only use one side of the normal distribution,
  • 05:15 which is just the 3 standard deviations.
  • 05:18 So let's look at the diagram again.
  • 05:20 In this case, the Cpk is less than 1, although the Cp is greater than 1.
  • 05:26 You can see that the distribution of the actual value is shifted
  • 05:30 down to the low side of the allowable range.
  • 05:33 The difference from the lower spec limit to the mean or
  • 05:36 x-bar is significantly less than the width of three standard deviations.
  • 05:41 If the process output had been centered, it would have fit within the spec limits,
  • 05:46 which is why the Cp is greater than 1, even though Cpk is less than 1.
  • 05:51 Let me wrap this up with an illustration.
  • 05:54 Let's say we have a nice little garage or carport,
  • 05:56 and the width of the garage will be my upper spec limit and lower spec limits.
  • 06:01 Now, I can either drive a car or ride a motorbike.
  • 06:04 The width of the car or
  • 06:06 motorbike is analogous to the process width of minus 3 sigma to plus 3 sigma.
  • 06:12 If I park the motorbike in the center of the garage,
  • 06:15 I have lots of room on either side, and both Cp and Cpk are much greater than 1.
  • 06:20 If I parked my car in the center of the garage, it just barely fits.
  • 06:24 In that case, my Cp and Cpk are just barely over 1.
  • 06:29 Now let's say it's late at night, I've been out with friends,
  • 06:32 I'm a little overtired, as I pull my motorbike into the garage,
  • 06:35 I don't quite line it up in the center.
  • 06:37 That's okay.
  • 06:38 Since the Cp is much greater than 1, I can be off to one side and
  • 06:42 still have a Cpk greater than 1.
  • 06:45 But if I'm driving my car and I'm off to one side, I have a problem,
  • 06:49 there will be no allowance for a little bit of drift.
  • 06:53 And while my Cp is still slightly greater than 1,
  • 06:56 because I'm no longer centered, my Cpk is less than 1.
  • 07:00 >> Process capability relates the actual performance of the process to
  • 07:04 the specification limits that are defined by the customer.
  • 07:07 With these ratios, we can quickly determine if we have a design problem or
  • 07:12 a process control problem.

Lesson notes are only available for subscribers.

PMI, PMP, CAPM and PMBOK are registered marks of the Project Management Institute, Inc.

Gift this course