# Process capability and process performance (Cpk,Cp Pp,Ppk)

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- This topic has 8 replies, 3 voices, and was last updated 8 years, 10 months ago by Loka.

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- January 31, 2011 at 8:45 am #53707
hello experts, i need some guidance regarding my six sigma project as an intern in an car manufacturing company.

The production in the company mainly focus on manufacturing cars (20cars/day) and some might have some defects, therefore the number of cars produce in a day will be less.

Based on the number of good cars produced for the past 6 months, then i calculate the process capability &performance index

I was assigned to design and implement a six sigma method in the company.

And now i am stucked in the measurement phase, where i have to find the process capability(Cpk&Cp) and Process perfomance(Ppk&Pp).

I have found out the mean, std,deviation,USL,LSL of the production. and ended up getting 0.33 Cpk and Cp.Here are the formula i used :

LSL = Mean – Std.dev

USL = Mean + Std.dev

Cp = (USL – LSL) / 6

Cpk(max) = (USL-mean) / 3?

Cpk(min) = (mean-LSL)/ 3?

I have also found out the sigma level of the production, by using the DPMO and refer to the sigma table provided online.

Some people told me that my population number is to small, that’ is why i keep getting bad numbers(0.33)

Hope you guys could help me solved this problem.

Thank you!

0February 1, 2011 at 2:07 am #191186Sorry guys, i forgot to post tha data. Here they are :

**Car type A**OK = 581 cars

TOTAL = 713 cars

DEFECTS = 713 – 581 = 132 cars**Car type B**OK = 453 cars

TOTAL = 658 cars

DEFECTS = 205 cars

Car type COK = 92 cars

TOTAL = 184 cars

DEFECTS = 92 carsNote : the data above is for 6 months period of production.

And the main objective is to find the process performance and capability, So the data i should be using is the number of OK cars, isn’t it?

0February 1, 2011 at 3:06 am #191187

StrayerParticipant@Straydog**Include @Straydog in your post and this person will**

be notified via email.You are getting bad numbers because USL and LSL should not be calculated. They are customer specified. Your capability formulas are correct but since you are incorrectly defining the difference between USL and LSL as 2 standard deviations you will ALWAYS get Cp = .33!

0February 1, 2011 at 6:57 am #191189

BreytenbachParticipant@wynandpb**Include @wynandpb in your post and this person will**

be notified via email.Straydog is correct. Simply replacing what you did, will show that:

Cp = (USL – LSL) / 6

= (Mean + stdev (Mean stdev))/(6 stdev)

= (Mean + stdev Mean + stdev))/(6 stdev)

= (2 stdev)/(6 stdev)

= 2/6

= .333

With**continuous data**, you cannot calculate Cp, …., Ppk unless the specs are given. Any effort to define specs in terms of stdev will lead to a constant ratio between spec width and process capability/performance.

With**discrete data**, you need to understand the difference between defects (an occurred event that does not conform to a specification, such as a dirt spot, film build out of spec, etc.) and defectives (a car with one or more defects).

With defectives, Cp, Cpk, Pp and Ppk cannot be calculated.

With defects, Cp, Cpk and Pp cannot be calculated, only Ppk.

To calculate Process Performance, Ppk, first calculate:

DPMO = 1,000,00*(number of defects)/((Number of opportunities for a defect to occur)(number of cars inspected))

= 1,000,000*(d)/(O*n)

and then calculate as follows, using Excel:

i) z_{LT}(without shift in average) = ABS(NORMSINV (DPMO/1,000,000))

ii) Ppk = 3z_{LT}For example, take Car Type A:

d = number of defects: You used the term defects, but calculated it as Total OK cars, which give number of defectives. You need to count how many defects there are in total.

Use a table such as the following. (Then you can Pareto afterwards and ID priorities as well). Lets say Car 1 had 3 dirt spot (3 defects), the film build on the roof and vendor are out of spec (2 defects), and dip sticks not yet available due to stock shortage (1 defect). The table will then start to look like this (Sorry for strange looking table, but the software used here does not provide for tables. I hope you get the drift).

Spec1:Dirtspots / Spec2:Filmbuild / Spec3:Missingparts / …. / Spec k:???

Car 1: ——-3————-2————-1

Car 2

Car 3

…

Car 581

**Total:—2400———–200——–600——-…-800**

Suppose the totals, as given above, then calculate:

d = Total number of defects

= 2400 + 200 + 600 + …. + 800 = (say) 10000

O = Number of opportunities for a defect to occur

= number of specs

= k = (say) 200

n = Number of cars inspected

= 581

Then: DPMO = 1000000(8000/(200×581))

= 68846

Then z_{LT}(without shift in average) = ABS(NORMSINV (DPMO/1,000,000))

= 1,48

and Ppk = 3z_{LT}

= 4,44.Some advice: On a weekly basis:

1. Create the above table.

2. Plot each type of spec on a c chart.

3. Plot the Ppk on an X and MR control chart to observe significant shift.

4. Pareto the table and identify long and short term priorities.

5. Pick a long term priority for your project. Suggest to management that they should use Kanban or Six Sigma teams to address the other short and long term objectives.Just a last comment: If the past data youve given are true (for car A+B+C: (132+205+92)/(713+658+184) = 27,6%, almost 30% defective), this company is in or will soon be in serious trouble. The hidden cost and waste imbedded in finding the defects and correcting them in almost 30% of all produced car as well as the consequential warranty and other cost are not sustainable and will erode the profitability over the long run. The company need a full fledged SPC and Six Sigma intervention!

Quality greetings

Wynand P B0February 1, 2011 at 8:42 am #191190Thanks for the reply, really appreciated it.

What should i do regarding my USL & LSL? what would be the right definition of them? please explain to me. Thanks a lot!0February 1, 2011 at 6:57 pm #191192

BreytenbachParticipant@wynandpb**Include @wynandpb in your post and this person will**

be notified via email.You can do nothing: You cannot develop a single spec for a whole car and therefore you will not be able to calculate Cp, … Cpk for the whole car with the formulae that you want to use. The only way to do it is as I described.

Each characteristics of the car is specified on its own. You can only use the formulae you want to use with those characteristics (such as film build) that are specificed as**continuous**data. You don’t have continous data (yet).

I cannot really give much advice, since the info you gave is simply not enough.

What I can say is that you need to be clear on what you have to do at the company. You stated that: “I was assigned to design and implement a six sigma method in the company”. This is the job of an experienced BB or MBB. Questions that pop into my mind are: What are your objectives, you plan of action and why are you following DMAIC? Are you doing a project or are you you setting up some metrics by which the impact of future projects can be monitored? What training did you receive? You should only follow DMAIC when doing a project.

If you are doing a project, you must realise that your project cannot improve the whole car. What I generically suggest is that you need to select one or a few areas that will make the biggest impact. Go back to the define phase, start with the VOC/ VOB and CTQ’s and determine, with management and BB/MBB, one CTQ that you must focus on. Looking at the data you gave and the trend of questions you ask, it seems that: “To reduce the % defectives by … much” would be one of them. Call this Y. Since Y = f(X1, X2, … Xk), you need to determine the few significant X’s that determine Y to the extent that you will achieve the project objectives. To do this, analyse the historical data or talk to area managers/supervisors to identify the types of defects that contribute the most to defectives. This could be dirt spots, missing parts, window leaks, logistics, a sub-assembly area, etc. (which bring us back to the table I suggested.) Pick only one. Now determine which process contributes the most to it. Some is easy to identify: dirt spots = paint shop; others not so easy. Stay, for this project, away from any supplier involvement. If it is a large area, such as the paint shop, you need to drill down until you find a specific area/process/charateristic that can be considered the root cause of the problem. Beware of chain reactions: film build consist of clear coat, top coat, first coat and e-coat. You cannot work on top coat before the other coats are in control, since the on build on top of the other. As a general rule, with you first project pick the process in the chain that is the furhest away from the external customer. If this characteristic is**continuous data**, you can then calculate the performance/capability indices you want to use.

This should give you an identifiable process to improve that will contribute to the achievement of the CTQ and VOC/VOB.0February 2, 2011 at 12:48 am #191193Thank you so much for the clear explanation, i will try and let you know.

0February 2, 2011 at 6:11 am #191194**wynandpb wrote:**Straydog is correct. Simply replacing what you did, will show that:

Cp = (USL – LSL) / 6

= (Mean + stdev (Mean stdev))/(6 stdev)

= (Mean + stdev Mean + stdev))/(6 stdev)

= (2 stdev)/(6 stdev)

= 2/6

= .333

With**continuous data**, you cannot calculate Cp, …., Ppk unless the specs are given. Any effort to define specs in terms of stdev will lead to a constant ratio between spec width and process capability/performance.

With**discrete data**, you need to understand the difference between defects (an occurred event that does not conform to a specification, such as a dirt spot, film build out of spec, etc.) and defectives (a car with one or more defects).

With defectives, Cp, Cpk, Pp and Ppk cannot be calculated.

With defects, Cp, Cpk and Pp cannot be calculated, only Ppk.

To calculate Process Performance, Ppk, first calculate:

DPMO = 1,000,00*(number of defects)/((Number of opportunities for a defect to occur)(number of cars inspected))

= 1,000,000*(d)/(O*n)

and then calculate as follows, using Excel:

i) z_{LT}(without shift in average) = ABS(NORMSINV (DPMO/1,000,000))

ii) Ppk = 3z_{LT}For example, take Car Type A:

d = number of defects: You used the term defects, but calculated it as Total OK cars, which give number of defectives. You need to count how many defects there are in total.

Use a table such as the following. (Then you can Pareto afterwards and ID priorities as well). Lets say Car 1 had 3 dirt spot (3 defects), the film build on the roof and vendor are out of spec (2 defects), and dip sticks not yet available due to stock shortage (1 defect). The table will then start to look like this (Sorry for strange looking table, but the software used here does not provide for tables. I hope you get the drift).

Spec1:Dirtspots / Spec2:Filmbuild / Spec3:Missingparts / …. / Spec k:???

Car 1: ——-3————-2————-1

Car 2

Car 3

…

Car 581

**Total:—2400———–200——–600——-…-800**

Suppose the totals, as given above, then calculate:

d = Total number of defects

= 2400 + 200 + 600 + …. + 800 = (say) 10000

O = Number of opportunities for a defect to occur

= number of specs

= k = (say) 200

n = Number of cars inspected

= 581

Then: DPMO = 1000000(8000/(200×581))

= 68846

Then z_{LT}(without shift in average) = ABS(NORMSINV (DPMO/1,000,000))

= 1,48

and Ppk = 3z_{LT}

= 4,44.Some advice: On a weekly basis:

1. Create the above table.

2. Plot each type of spec on a c chart.

3. Plot the Ppk on an X and MR control chart to observe significant shift.

4. Pareto the table and identify long and short term priorities.

5. Pick a long term priority for your project. Suggest to management that they should use Kanban or Six Sigma teams to address the other short and long term objectives.Just a last comment: If the past data youve given are true (for car A+B+C: (132+205+92)/(713+658+184) = 27,6%, almost 30% defective), this company is in or will soon be in serious trouble. The hidden cost and waste imbedded in finding the defects and correcting them in almost 30% of all produced car as well as the consequential warranty and other cost are not sustainable and will erode the profitability over the long run. The company need a full fledged SPC and Six Sigma intervention!

Quality greetings

Wynand P BHello wynand, i was trying to understand the table you’ve described earlier. I have figure out everything, except how do you get the 2400 ?

And regarding the defects and defectives. Does each term has a different calculation process? cos i think, in this case, most of the cars fall under the defects category, as they only have one specific problem. thanks0February 2, 2011 at 7:58 am #191195Sorry for the unclear explanation i gave earlier regarding my background and objective.

I am an intern,assigned to be part of a green-belt six sigma team of a car manufacturing company. Honestly, this is the first six sigma project the company has ever done. We follow the DMAIC steps and so far has done a rough definition on each phase depending on our company’s needs.

But at the moment, we have only reached the measurement process for the real implementation of the six sigma. As the rest of the teams were so busy with their own job, as mostly they are the deputy director, managers,supervisors, and even operators from the different section of the manufacturing processes. So i was the only one that has the time to follow up the methodology. But honestly, i do not have any background on six sigma. Still learning through six sigma books and case studies.First., let me explain to you about our define phase :

We have a measuring technique for the output of our production, which is called “The First run rate” in %. Our daily target is 20 cars per day for Car type A and 12 cars per day for Car type B. For instance, If we reached 20 cars/day for type A , and all of the cars are free of defect, hence our first run rate is 100%.

But unfortunately in the real situation , we have only reached the 86% mark maximum. In some cases , even lower than that.

And the target or the define phase of our six sigma project is to reach the 97% mark, by improving our productivity & quality capabilities.

Through our investigation, we have specify 5 different errors that contributed to the lower first run rate. The 5 factors are :1. Workmanship

2. Parts shortage

3. Part function

4. Production equipment

5. Software problem( ECU programming).These factors are chosen based on the most errors occurred on our production processes

Next is the ‘measurement phase’, the one that i’m dealing with right now. in your opinion, what would be the best way to measure the process capability or performance of this manufacturing process? So far, i’ve calculated the sigma level of each car’s type, through their DPMO

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