Process Capability Study (Cpk) Business Excellence DRAFT October 5, 2007 BE-TL3-002-DRAFT-Cpk

2 Table of Contents  Overview & Scope3  Objectives 4  Process Capability Indices 11  Long Term vs Short Term 23 ContentsSlide(s)

3 BE-TL3-002-DRAFT-Cpk Overview & Scope  To define “capability” and complete the notion that quality is customer oriented as defined through the specification limits  What is Quality?  How to perform process capability study  Continuous Data  Normal Distribution  Short-term vs Long-term  Stability vs Capable Process

4 BE-TL3-002-DRAFT-Cpk Objectives  Understand the students level on process capability study on normal distribution  Calculate Process Capability Indices (Cpk, Cpu, Cpl)  Understand long term vs short term process capability

5 BE-TL3-002-DRAFT-Cpk  Fitness for use.  - (Joseph Juran)  The inverse of variability.  - (Douglas Montgomery)  Loss imparted to the society from the time the product/Service is delivered to the customer  - (Genichi Taguchi) What Is Quality?

6 BE-TL3-002-DRAFT-Cpk Capability A process is capable if it is able to produce quality product consistently

7 BE-TL3-002-DRAFT-Cpk Normal Distribution A normal distribution can be described completely by knowing only the:  Mean  Standard deviation

8 BE-TL3-002-DRAFT-Cpk Stat  Basic Statistics  Graphical Summary Variables = Normal Normal Distribution Summary General Guidelines : We can assume that the data is normally distributed if P-value > 0.05 |Skewness| < 1 |Kurtosis| < 1

9 BE-TL3-002-DRAFT-Cpk Capability Which process is the worst? A B C D Mean = 20, Std. Dev = 5 Mean = 15, Std. Dev = 3 Mean = 20, Std. Dev = 3 Mean = 20, Std. Dev = 2 LSL USL LSL USL LSL USL LSL USL

10 BE-TL3-002-DRAFT-Cpk Two Types of Limits Specification Limits (LSL and USL) specify the tolerance for a product’s characteristic Usually created by design engineering To satisfy customer requirements If process has no Specification Limit, Set Spec. Limit = Target mean + 3 Std Dev (Reason : if the project achieve the target, Cpk will be >= 1) Control Limits (LCL and UCL) measures the variation of a sample statistic (mean, variance, proportion, etc)

11 BE-TL3-002-DRAFT-Cpk +  -  68.26% 95.44% 99.74% Process Capability Indices LSL USL µ %Defective = p*100% DPPM = %Defective * 1M

12 BE-TL3-002-DRAFT-Cpk 11 68.26% 95.44% 99.74% Process Capability Indices LSL USL µ %Defective = 1 – 68.26% = 31.74% DPPM = 317,400 11

13 BE-TL3-002-DRAFT-Cpk Process Capability Indices %Defective DPPM LSL=5 USL=15 µ=9.5  =2 Example

14 BE-TL3-002-DRAFT-Cpk Process Capability Indices LSL=5 USL=15 µ=9.5  =2

15 BE-TL3-002-DRAFT-Cpk Process Capability Indices %Defective DPPM +  -  LSL=5 USL=15 µ=9.5  =2 Calc  Probability Distributions  Normal

16 BE-TL3-002-DRAFT-Cpk Process Capability Indices %Defective = ( )*100% = % DPPM = 15,205 +  -  LSL=5 USL=15 µ=9.5  =2 Calc  Probability Distributions  Normal =

17 BE-TL3-002-DRAFT-Cpk Process Capability Indices +  -  LSL=5 USL=15 µ=9.5  =2 %Defective = ( )*100% = % DPPM = 15,205 Z = normsinv( ) = 2.164

18 BE-TL3-002-DRAFT-Cpk Process Capability Indices If data is available, example A sample of 30 components were measured and recorded in Capability Worksheet. Calculate the capability if the USL=15 and LSL=5 Stat  Quality Tools  Capability Analysis  Normal

19 BE-TL3-002-DRAFT-Cpk Process Capability Indices Stat  Quality Tools  Capability Analysis  Normal

20 BE-TL3-002-DRAFT-Cpk Process Capability Indices Not Meaningful if not proper subgrouping

21 BE-TL3-002-DRAFT-Cpk Process Capability Indices Stat  Quality Tools  Capability Analysis  Normal

22 BE-TL3-002-DRAFT-Cpk Process Capability Indices Not Meaningful if not proper subgrouping

23 BE-TL3-002-DRAFT-Cpk Long Term vs Short Term Short TermLong Term CpCp PpPp C pl P pl C pu P pu C pk P pk Z ST Z LT

24 BE-TL3-002-DRAFT-Cpk Long Term vs Short Term  Short Term Capability is the performance of the process without all the assignable causes  Long Term Capability is the performance of the process taking into consideration ALL the assignable causes

25 BE-TL3-002-DRAFT-Cpk Long Term vs Short Term Natural Variation  Variation that are inherent in the process  Cumulative of many unavoidable causes  A process which exhibit only inherent variation is said to be “in statistical control” Assignable Variation  Variation due to some assignable causes, eg. a) improperly adjusted machine b) operator error c) defective raw material  A process operating in the presence of assignable causes of variation is said to be “out-of-control”

26 BE-TL3-002-DRAFT-Cpk Long Term vs Short Term Process Variation is the inevitable differences among individual measurements or units produced by a process. Sources of Variation within unit(positional variation) between units(unit-unit variation) between lots(lot-lot variation) between lines(line-line variation) across time(time-time variation) measurement error(repeatability & reproducibility)

27 BE-TL3-002-DRAFT-Cpk Time Short Term Long Term If no data given, assume 1.5  shift Long Term vs Short Term

28 BE-TL3-002-DRAFT-Cpk Long Term vs Short Term Short TermLong Term (Estimation) C pk P pk = C pk – 0.5 Z ST Z LT = Z ST – 1.5 When long term data is not available, we can estimate the process capability using the following formula

29 BE-TL3-002-DRAFT-Cpk Long Term vs Short Term

30 BE-TL3-002-DRAFT-Cpk Long Term vs Short Term To have good estimation of Short Term and Long Term, collect data in subgroup over time (cover all the foresee- able variations). Example : Worksheet : Subgroup USL : 15 LSL : 4

31 BE-TL3-002-DRAFT-Cpk Long Term vs Short Term Stat  Quality Tools  Capability Analysis  Normal

32 BE-TL3-002-DRAFT-Cpk Long Term vs Short Term Short-term Performance Long-term Performance

33 BE-TL3-002-DRAFT-Cpk Exercise We are interested in knowing the capability of the process of multi-layering bare boards. One of the CTQ is the board thickness (Y) Sigma Multiple (Z) computations are based on Normal distribution properties. 1.Solectron Specifications : LSL = 2.9 mm; USL = 3.1 mm 2.To validate the normality of sample data (Y) 3.Compute the Sigma Multiple of this process from Normal distribution parameters (sample Mean and Sample St. Dev) and specifications Refer Minitab Worksheet: Board_thk_capability.mtw 3 Sample thickness data collected for 25 boards picked at random.