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About this lesson

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 expectations at all time.

Quick reference

Process Capability Principles

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 expectations at all time.

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 maintain adequate process control.

Instructions

Process capability is an assessment of whether a process is able to consistently deliver results that meet customer expectations. 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 attribute data, the process yield is first determined, typically using DPU, DPMO, or PPM. The yield value is then used with a lookup table to determine the process capability indices.

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 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 standard deviations to plus three standard deviations for a total of six standard deviations.

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 width from the mean (average) of the process performance data to the closest specification limit. The portion used in the denominator is the one half of the amount used in the Cp calculation, 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.
  • The Cpk can never be better than the Cp. When a process is exactly centered, the Cpk will equal the Cp, but as soon as it moves away from the center, 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, however it is possible to have a negative Cpk if the process performance drifts to the point where the mean value is outside of the specification limits.
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  • 00:05 Hi, I'm Ray Sheen.
  • 00:06 We've talked about process stability.
  • 00:09 Now, I wanna talk about process capability.
  • 00:12 Process capability is a quantified metric that compares the needs
  • 00:17 of the customer with the process performance.
  • 00:20 Think that is the voice of the customer divided by the voice of the process.
  • 00:24 The voice of the customer will be expressed as a specification target value
  • 00:29 and tolerance limits on that process parameter.
  • 00:32 In particular, we'll need the upper spec limit and the lower spec limit for
  • 00:36 the performance parameter.
  • 00:38 For the voice of the process,
  • 00:39 we'll be using some of the descriptive statistic values.
  • 00:42 The parameter mean and the standard deviation will be used for
  • 00:45 variable data and the yield for attribute data.
  • 00:49 With quantified voice of the customer and
  • 00:51 quantified voice of the process, we can create the process capability metrics.
  • 00:56 With variable data,
  • 00:57 we calculate ratios that serve as the process capabilities indices.
  • 01:01 These ratios of customer expectations divided by process performance are Cp and
  • 01:06 Cpk for short term data and Pp and Ppk for long term data sets.
  • 01:13 Attribute data uses a ratio of success and a look-up table.
  • 01:17 The success ratio is the yield, defects per unit DPU, defects per opportunity DPO,
  • 01:22 defects per million opportunity, DPMO and parts per million, PPM.
  • 01:27 Once the yield has been calculated that value is used with look-up table to
  • 01:31 determine the process capability index.
  • 01:35 Now, all of this assumes the data is normal or at least near normal.
  • 01:39 When the data is not normal, there are special statistical tools and
  • 01:43 techniques that must be used to calculate process capability.
  • 01:46 Frankly, if it's not normal,
  • 01:47 the first thing I try to do is get the process to a condition of normalcy,
  • 01:51 removing any special causes before I even begin to work on process capability.
  • 01:57 So let's dig in to these indices of associated with the variable data.
  • 02:00 The Cp, Cpk, Pp and Ppk, all four indices follow the same pattern.
  • 02:06 There's a ratio of the desired performance for
  • 02:08 a parameter divided by the actual process performance for that parameter.
  • 02:13 The desired performance will be expressed using the specification limits, and
  • 02:17 the actual process performance will be expressed using our descriptive statistics
  • 02:21 of the process parameter.
  • 02:23 So you may be wondering why there are four indices.
  • 02:25 Each of them is a different take on the process performance data.
  • 02:28 The Cp and Pp indices will provide a best case perspective.
  • 02:33 These ratios assume the processes managed as designed and all is going well.
  • 02:38 While the Cpk and Ppk indices will look at the current performance.
  • 02:43 That means that the Cpk and
  • 02:44 Ppk are what the customer and process are actually feeling.
  • 02:48 So one immediate insight we have is that the best case that we'll ever have
  • 02:52 are the Cc and Pp ratios.
  • 02:55 Now, another perspective of the indices is that Cp and Cpk are short term
  • 03:00 looks at the data, while Pp and Ppk are long term looks at the data.
  • 03:05 So bottom line, Cpk is what the customer's feeling right now, and
  • 03:09 Ppk is what the customer's been feeling for some time.
  • 03:12 So let's look at the calculations.
  • 03:14 I will talk about Cp and Pp first.
  • 03:17 These are calculated in exactly the same manner.
  • 03:20 The only difference is that the Cp is using the standard deviation from recent
  • 03:23 experience, and Pp is using the standard deviation from the longer term history.
  • 03:28 This calculation is the allowable range of performance
  • 03:32 divided by the span of normal variation within the process output.
  • 03:36 The allowable range based upon customer expectation
  • 03:38 is the span from the upper spec limit to the lower spec limit.
  • 03:42 And the normal performance variation will be the span for -3 standard deviations to
  • 03:47 +3 standard deviations, which is a total of 6 standard deviations.
  • 03:51 And as I said, the only difference between Cp and
  • 03:54 Pp is the size of the data set used to calculate the standard deviation.
  • 03:58 So, what does this look like?
  • 04:00 Well, let's first consider the case where the Cp is greater than 1.
  • 04:04 In that case, the span between the spec limits is greater than the span
  • 04:08 between the 3 standard deviation lines.
  • 04:11 And you can see in this diagram, the spec limits
  • 04:14 are outside the 3 standard deviation lines of the normal distribution.
  • 04:19 But when Cp is less than 1, the opposite condition exists.
  • 04:23 The spec lines are still the same, but
  • 04:25 the variation in the parameter is much higher, so the distribution is much wider.
  • 04:30 Therefore, the span from -3 standard deviations to +3 standard deviations is
  • 04:35 greater than the spec limits, and that means the ratio is less than 1.
  • 04:40 The implication of this is that if the ratio was less than 1,
  • 04:43 the process is always generating some out of spec results.
  • 04:47 While if the ratio is greater than 1, the process has the potential to be generating
  • 04:51 good results virtually every time.
  • 04:54 Notice I said the potential.
  • 04:56 We'll use the Cpk and Ppk to look at the reality.
  • 04:59 The reality is that the process is seldom perfectly centered
  • 05:03 in the middle of the specification limits.
  • 05:05 It's either a little high or a little low, so a Cpk and
  • 05:08 Ppk calculation will adjust for that.
  • 05:11 They will modify the numerator to pick the distance from the mean or
  • 05:14 average value of the data, to the closest specification limit.
  • 05:19 The formula looks like this.
  • 05:21 The minimum at the beginning of the formula just means that
  • 05:23 you will use the smaller of the two ratios.
  • 05:26 But since you're no longer using the full span,
  • 05:29 from the upper spec limit to the lower spec limit, but
  • 05:31 only a portion, you also need to use only a portion of the denominator.
  • 05:35 In our case, that means we will only use the one side of the normal distribution,
  • 05:39 which is just 3 standard deviations.
  • 05:42 So let's us look at the diagram again.
  • 05:44 In this case, the Cpk is less than 1, although the Cp is greater than 1.
  • 05:49 You can see that the distribution of the actual values is shifted to the left or
  • 05:52 the low side of the allowable range.
  • 05:54 The difference from the lower spec limit to the mean or
  • 05:57 x bar is significantly less than the width of the 3 standard deviations.
  • 06:01 If the process output had been centered,
  • 06:04 all of it could have fit within the spec limits,
  • 06:06 which is why the Cp is greater than 1, even though the Cpk is now less than 1.
  • 06:11 Let me wrap up with an illustration that I hope you can relate to.
  • 06:16 Let's say we have a nice little garage or car port.
  • 06:19 The width of the garage will be my upper spec limits and
  • 06:22 lower spec limits, and I can either drive a car or ride a motorbike.
  • 06:26 The width of the car or motorbike is analogous to my process width of -3
  • 06:30 standard deviations to +3 standard deviations.
  • 06:34 If I park the motorbike in the center of the garage, I have lots of
  • 06:38 room on either side, and both the Cp and Cpk are much greater than 1.
  • 06:43 If I park my car in the garage, it just barely fits.
  • 06:47 In that case, my Cp and Cpk are just barely over 1.
  • 06:51 Now, let's say it's late at night,
  • 06:53 and I've been out with friends and maybe a little overtired.
  • 06:57 As I pull my motorbike into the garage,
  • 07:00 I don't quite line it up to be in the center.
  • 07:02 Well, that's still okay.
  • 07:04 Since the Cp was much greater than 1, I can be off to one side and
  • 07:08 still have a Cpk greater than 1.
  • 07:11 But if I'm driving my car, and I'm off to one side, I have a problem.
  • 07:15 There was no allowance for a little bit of drift.
  • 07:18 And while my Cp is still slightly greater than 1,
  • 07:21 because I'm not centered, my Cpk is less than 1.
  • 07:24 And I've got a problem. Process capability relates the actual performance
  • 07:31 of the process to the specification limits we receive from the customer.
  • 07:36 With these indices, we can quickly see if we have a design problem or
  • 07:41 a process control problem.

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