Step M2 – Variable Process Capability Capability analysis (Cp, Cpk, Pp, Ppk) indices is a set of statistical calculations used to assess the performance of a system, process, or part compared to its specification limits. Capability analysis has predictive value only if certain priori assumptions are met. Capability Analysis uses specification limits (Spec limits). Spec limits are not the same as control limits. Spec limits are set by the customer, engineering, or management, and control limits are based on the data collected to make a control chart. The capability analysis reveals the percent of product which may lie outside the specification limits and describes how capable the system is. It draws a picture of the distribution to the specifications limits.

Step M2 – Variable Process Capability Priori Assumptions for Calculating Process Capability The process is stable The process is in statistical control The data sample used for the analysis is normally distributed There are enough samples to describe the process – more data results in greater accuracy, greater precision and greater confidence in the results. At least 30 samples but more is better.

Step M2 – Variable Process Capability Process Capability Steps 1 Select output variable for improvement 2. Verify measurement system (MSA) 3. Verify customer requirements 4. Validate Specification Limits 5. Collect sample data 6. Check data for normality 7. Calculate Capability 8. Estimate LT Capability

Step M2 – Variable Process Capability Process Capability Steps 1. Select output variable for improvement. This is your Y (Primary or a secondary metric) of interest and directly linked to your charter business case. 2. Verify measurement system (MSA). Make sure the measurement system is capable GR&R: %Cont <10%, %Study<30%, Dist. Cat. >4 3. Verify customer requirements. Consult customer and/or engineering. Determine if requirements are RUMBA: Reasonable, Understandable, Measurable, Believable, Achievable. 4. Validate specification limits. Check drawings, engineering, SOPs, Control plans, speak with operations.

Step M2 – Variable Process Capability Process Capability Steps 5. Collect sample data. Determine a rational sampling plan and collect short term (ST) or long term data (LT). ST data captures only a small portion of the total variation a process may exhibit. Gather data from more than one shift, one lot, or one operator. LT captures the majority of variation and may include all shifts, many lots, many operators over a longer time than ST data. 6. Check data for normality. Minitab: Stat>Basic Statistics>Normality test. P>0.05 = Normal data. P<0.05 ≠ non-normal data 7. Calculate capability. Calcualte Z-Score, PPM, Yield, or Capability Cp, Cpk. Minitab: Stat>Quality Tools>Capability Analysis 8. Estimate LT capability. As appropriate, estimate LT capability by shifting ST 1.5 sigma, or using Pp and Ppk, LT Z-score, PPM, Yield

Standard Deviation calculated Step M2 – Variable Process Capability Basic Components Lower and upper specification limits supplied by customer or engineering LSL USL Cp Cp is the allowable width versus process spread Sample data from process CPL CPU Cpk is how centered the process is compared to the mean Mean and Standard Deviation calculated This slide represents ±6σ

If the process is centered the Cp and Cpk will be the same Step M2 – Variable Process Capability Two Standard Deviations (s = standard deviation) (plus one and minus one from the mean) is the average distance from the mean for all the sample data. It comprises 68.26% of all the data Four Standard Deviations contains 95.44% of all data Six Standard Deviations captures 99.73% of the process sample data Thus. We use 6s (99.73% of data) to calculate Cp And 3s (1/2 the data) to calculate Cpk upper or Cpk lower depending on which value is smaller 68.26% 95.44% 99.73% If the process is centered the Cp and Cpk will be the same

Step M2 – Variable Process Capability Why we care about Cp and Cpk Cp describes process spread and the % DEFECTS that result Cpk describes process centering and resulting % DEFECTS Both Cp and Cpk are required to describe the process LSL USL Cp CPL CPU This slide represents ±3σ

Step M2 – Variable Process Capability Cp is a ratio between the width of specification limits (allowable width) to the natural variation of a process Cp = USL – LSL 6 * S process spec limits Natural process variation Cp = Upper Spec Limit – Lower Spec limit 6 * Sample Standard deviation Cp = Width between your spec limits Width of your samples

Step M2 – Variable Process Capability Cp is a ratio between the width of the specification limits (allowable spread) versus the actual width of the process Cp = Upper Spec Limit – Lower Spec limit 6 * Sample Standard deviation Which Is Cp = The Width Between Spec Limits Width of your samples 20 50 70 30 Samples Mean of = 50 Std Dev = 5 EXAMPLE Cp = 50 (70 – 20) 6 * 5 (std dev) Cp = 50 30 Cp = 1.67

Step M2 – Variable Process Capability Cpk is a ratio between the distance from the MEAN of your sample and the closest specification limit (LSL or USL) to the width of ½ your process variation 60 LSL 20 USL 70 10 10 3 * 5 30 Samples Mean of = 50 Std Dev = 5 10 15 6 Std Dev Cpk = USL - Mean( ) 3 * Std Dev 50 Cpk = .67 ½ of the data Use USL or LSL - whichever is smaller because that is the direction of our problem

Step M2 – Variable Process Capability If your data set is not a normal distribution there are ways to transform the data in Minitab, otherwise, the calculation is invalid. If you transform the data you have to transform the spec limits as well. Pp and Ppk are the same as Cp and Cpk except Pp and Ppk are predicting long term capability. The long term calculations use overall standard deviation as opposed to calculating the standard deviation of each sub-group. 2 Cpk = 6 σ so be skeptical of capability calculations greater than 2 Short Term (ST) Sigma Level ST Cpk ST Probability ST PPM ST % area under the curve LT Probability LT PPM Ppk 1 .33 .1586553 158655.3 68.26894 .6914625 691462.5 -0.16 2 .67 .0227501 22750.1 95.44998 .3085375 308537.5 0.16 3 1.00 .0013500 1350.0 99.73000 .0668072 66807.2 0.50 4 1.33 .0000317 31.7 99.99366 .0062097 6209.7 0.83 5 1.67 .0000003 .03 99.99994 .0002327 232.7 1.16 6 2.00 .0000000 0.0 99.99999 .0000034 3.4 1.50 This slide represents

Step M2 – Variable Process Capability Determine % defective If one tail is out of spec use the appropriate formula. If both tails are out use both formulas and add the results together (ZUSL + Z LSL). If a Z value is over 4 consider Z equal to zero. _ _ Z USL = USL - X AND/OR Z LSL = X - LSL σ σ Z = Z value USL = Upper Spec Limit LSL = Lower Spec Limit X = Process Sample Mean σ = Sample Standard deviation Using Z table in the Memory Jogger (p. 246) to find each Z value and then multiply that value by 100 to get % outside the spec limit.

Step M2 – Variable Process Capability Calculating Sample Size If Minitab is not available use this rough sample size calculation n = Z2 * S2 h2 n = Minimum sample size (round up) Z = confidence interval (default is 1.96 = 95% confidence) S = Population standard deviation. If unknown use sample standard deviation h = Smallest change you want to detect as measured in the same units as S. If in doubt start by taking total tolerance/10. If still in doubt use 30 or more as a sample size to start.

Step M2 – Variable Process Capability Capability Analysis Using Non-normal Data If the distribution is not normally distributed the capability calculations will not be valid. To use non-normal data use Minitab. STATS > BASIC STATS > NORMALITY TEST P value must be ≥ .05 STATS > QUALITY TOOLS > INDIVIDUAL DISTRIBUTION IDENTIFICATION The output will indicate which distribution most closely fits your data based upon the P value of each distribution. Pick the highest P value. STATS > QUALITY TOOLS > CAPABILITY ANALYSIS > NONNORMAL Choose the distribution indicated from the previous operation. Your output is a graph quoting Pp and Ppk