2 Cp, Cpk, Pp PpkThese are non dimensional constants used to describe capabilityIn 6 Sigma organizations they are more useful than percentage yieldsFlowserve 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.
3 CpRemember 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 limitsWhen 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 = 2Cp = 1/3 1 SigmaCP = sigmaCp – 2 6 Sigmai.e Cp = Sigma level / 3
4 CpkThe 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 capabilityShort -Term Capability IndicesDraw 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 6If the voice of the process has standard deviation 2From the mean to LSL – 1 standard deviationCpk(USL) = 1/3From the mean to USL –2 standard deviationsCpk USL = 2/3CP for the uncentered process = min(1/3, 2/3) = 1/3If 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
5 Cpk(USL) & Cpk(LSL) Short -Term Capability Indices Notice we used Cpk USL and Cpk LSL to identify CpkThese figures should be quoted instead of Cp when you do not have both upper and lower specification limits .
6 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 mmIt may be cheaper to bias the target cut towards say 199mm instead of 198mmSo in this case if we target 199mm we want to measure the process against the target instead of the center point
7 Short and Long Term Sigma Remember from modules 1 and 2 over a long period we expect the capability of a process to deteriorateAlso we estimate that the difference between the short term capability and long term capability will be 1.5 sigmaSo 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)
8 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 causesLong term is likely to include mixtures of batches, parts and include changing personnelLong term capability does not get worse.
9 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
10 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
11 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 etcOverall variation = short term variation + long term variationA large difference between the Overall and Within Capability indices may indicate the process is out of control.
12 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
13 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 informationAlso please make the title legibleIt is often best to print the pictures for sharing with non Minitab users rather than asking them to look at your screen
14 SummaryCapability can be shown as a pictureFor GB start with observed capabilityIn the long term capability gets worseTo predict the long term capability You could describe the capability using - % good, parts per million, sigma level, Cp, PpThe one you use will depend on your audience
15 ExerciseOver 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 orders29,15,21,16,30,25,20,28, 21,22,28,30,24,23,45,25, 42,23,27,19What 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?
16 Wrong Answer Title is not easy to read Lots of capability indecies You have not checked for normality upon which the CP… figures rely
17 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 daysOr perhaps we have two catastrophic failuresor 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
18 Remaining system is stable and shows long term Capability 61%
19 Even Better AnswerHaving investigated with the team there is a reason that there is a gap around orders taking days as we pull orders into this month if possible. The two orders later than this were delayed by the customerUnless we have more customer delays we can expect around 66% of orders to be within customer expectationsTo achieve 90% or better we need to make significant process changes to reduce the average lead time by around 5 days
20 PracticeUsing data from a project you or your Green Belt are working on create power point slides to describe the Capability