Quantitative Capability Assessment

Cp, Cpk, Pp Ppk These are non dimensional constants used to describe capability In 6 Sigma organizations they are more useful than percentage yields Flowserve is Six Sigma capable in only a few processes so we tend not to use these indices. However it is not uncommon for Six Sigma aware customers to ask use to describe our capability using these measures.

Cp Remember a 3 sigma process is 99% good. For many years in high volume manufacturing this was the goal for process capabilities. Once you go beyond 3 sigma process capabilities are measured in fractions of percentages – the numbers are valid but clumsy so the sigma (Cp) scale is used. Cp assumes that you have a normal process centered halfway between the specification limits When you have a 3 sigma process. (i.e. from the mean to the spec limits = 3 sigma) Cp 1, your yield is 99% If your process is more capable, then Cp increases. If you halve the variation in a 3 sigma process it becomes a 6 sigma process & Cp = 2 Cp = 1/3 1 Sigma CP = 1 3 sigma Cp – 2 6 Sigma i.e Cp = Sigma level / 3

Cpk The difference between Cp and Cpk is that Cp assumes the voice of the process is centered half way between the sigma limits and Cpk uses the actual voice of the process mean. The bigger the difference between Cp and Cpk the greater opportunity there is to improve the process capability by centering. For some simple processes this is valuable information as you only need change an offset to increase capability Short -Term Capability Indices Draw a chart of VOP and VOC where VOC was off… see notes. If Cp=Cpk, then the process is centered. The further away VOP the smaller the Cpk value number is. E.g. a process spec limits Lower 0 upper 6 If the voice of the process has standard deviation 2 From the mean to LSL – 1 standard deviation Cpk(USL) = 1/3 From the mean to USL –2 standard deviations Cpk USL = 2/3 CP for the uncentered process = min(1/3, 2/3) = 1/3 If it were centered (I.e. average 3 half way between the LSL (0) and USL (6) the Cpk value would be 3/2 x 3 = 0.5

Cpk(USL) & Cpk(LSL) Short -Term Capability Indices Notice we used Cpk USL and Cpk LSL to identify Cpk These figures should be quoted instead of Cp when you do not have both upper and lower specification limits .

Cpm You are almost never going to use this, but for completeness….. In some processes you will not target the center point. Example cutting impellers you want to cut an impeller diameter between 196 and 200 mm It may be cheaper to bias the target cut towards say 199mm instead of 198mm So in this case if we target 199mm we want to measure the process against the target instead of the center point

Short and Long Term Sigma Remember from modules 1 and 2 over a long period we expect the capability of a process to deteriorate Also we estimate that the difference between the short term capability and long term capability will be 1.5 sigma So if a project team achieves a process that is 99% capable (ST) we expect it to be 80% capable (LT) and to create a process that is 50% good (LT) we aim for 93% (ST)

Short and Long Term Sigma What does short term and long term mean? ‘’It depends!’’ as a guide: Long term is more likely to include special causes Long term is likely to include mixtures of batches, parts and include changing personnel Long term capability does not get worse.

Pk, Ppk, Ppk(usl), Ppk(lsl) The only difference between calculating the C… and P… is that you use the short term sigma level for C.. And the long term sigma level for P…. Remember long term capability = short term capability + 1.5

Normal Capability – Within Cp Between Pp This is another more sophisticated technique for calculating short and long term sigma levels. It relies on your ability to group data. For example you collect the shipments per day. However you know that there is a pattern of shipments during the week so you group the shipments into weeks. You can now calculate the average for each week and the standard deviation for each week. The overall variation is made up of two components – the variation within each week and the variation between each week. Next the assumption that the variation within each week corresponds to short term and the variation between the weeks is long term. By taking these two variations in turn you derive the standard deviation and hence Cp, Pp etc

Normal Capability – Within Cp Between Pp In Minitab you would select these two variations in turn you derive the standard deviation and hence Cp, Pp etc Overall variation = short term variation + long term variation A large difference between the Overall and Within Capability indices may indicate the process is out of control.

PPM parts per million defects The bottom of the capability diagram shows predicted ppm defect rates. The figures are not measured but calculated assuming that the VoP will be normal and using the observed average, standard deviation, sample size and the spec limits. Information is presented as number of ppm exceeding each spec limit. You will probably wish to simplify into percentages -Open File: VOLUMESHIPPED.MTW -Select STAT>QUALITY TOOLS>Capability Analysis(Normal) -Click on Single Column, Click on C3’Y-Shipped’ -Enter in 1 for Subgroup Size -Enter in 0 for Lower Spec , it is a boundary (MUST HAVE AT LEAST 1 LIMIT IN SPECS TO RUN THIS> Upper spec = 5

What to share with Champions and teams? Unless you are confident that your Champion understands CPk, Within variation and parts per million, please edit the graph and delete that information Also please make the title legible It is often best to print the pictures for sharing with non Minitab users rather than asking them to look at your screen

Summary Capability can be shown as a picture For GB start with observed capability In the long term capability gets worse To predict the long term capability You could describe the capability using - % good, parts per million, sigma level, Cp, Pp The one you use will depend on your audience

Exercise Over the telephone you are told that lead time is a problem, customers want lead times less than 25 days and here are the lead times of the last 20 orders 29,15,21,16,30,25,20,28, 21,22,28,30,24,23,45,25, 42,23,27,19 What is the capability? How do you interpret the EDA output? Create a PowerPoint slide which you would use to explain the capability to your champion?

Wrong Answer Title is not easy to read Lots of capability indecies You have not checked for normality upon which the CP… figures rely

Better Answer Shape is not normal Which may mean that we are looking at – Granularity – perhaps there is a reason that there is a gap around orders taking 30-40 days Or perhaps we have two catastrophic failures or perhaps there is a mixture of more than one type of order. Next step is to investigate these two orders with the team. With the two values to the right excluded the remaining data is normal. 75% of orders are shipped in 28 days or less and we can expect an average lead time between 21 and 26 days std deviation 7 days….. continued

Remaining system is stable and shows long term Capability 61%

Even Better Answer Having investigated with the team there is a reason that there is a gap around orders taking 30-40 days as we pull orders into this month if possible. The two orders later than this were delayed by the customer Unless we have more customer delays we can expect around 66% of orders to be within customer expectations To achieve 90% or better we need to make significant process changes to reduce the average lead time by around 5 days

Practice Using data from a project you or your Green Belt are working on create power point slides to describe the Capability

Quantitative Capability Assessment