Chapter 7

Process and Measurement System Capability AnalysisIntroduction Variability in the process is a measure of the uniformity of output.Two types of variability:Natural or inherent variability (instantaneous)Variability over timeAssume that a process involves a quality characteristic that follows a normal distribution with mean , and standard deviation, . The upper and lower natural tolerance limits of the process areUNTL = + 3LNTL = - 3

Introduction Process capability analysis is an engineering study to estimate process capability.The ability to meet specifications is the criterion used for measuring the attractiveness of the process.

Introduction The control charts (Previous chapters) talk about variation across samples, but do not have any relation with customer specifications.Process capability represents the performance of a process in a state of statistical control.It is determined by the total variability that exists because of all common causes present in the system. (All special causes have been removed)

Major benefits of process capability analysisUniformity of the outputMaintained or improved qualityProduct and process design may be improvedAssistance in vendor selection and controlReduce total costTechniques used in process capability analysisHistograms or probability plots Control ChartsDesigned ExperimentsProcess Capability Analysis Using a Histogram or a Probability PlotUsing a Histogram (natural tolerance limits)The histogram along with the sample mean and sample standard deviation provides information about process capability.The process capability can be estimated asThe shape of the histogram can be determined (such as if it follows a normal distribution) Histograms provide immediate, visual impression of process performance.Process spread is 3+3 =6 Sigma.

Statistical tolerance limitsDefined by ANSI/ASQC American National Standards Institute/American Society of Quality ControlConfidence level will be given as predefined.Histogram

Process capability indicesCp IndexCpk IndexProcess should first be analyzed to verify that it is in control before its capability is estimated.PCI is an aggregate measure of the goodness of the process performance.

Cp IndexUse and Interpretation of Cp

where LSL and USL are the lower and upper specification limits, respectively. (the difference between the two is specification spread, whereas 6 sigma is process spread)

If is unknown it is

Cp >1, process is quite capable

Cp =1, equal with only 0.26% (0.13 % above USL and 0.13% below USL) of the parts will fall outside the specifications limits. Cp >=1 is desired

If the process is not centered, it is possible that even process with Cp >1, some proportion of the products may be non conforming.

Use and Interpretation of CpOne-Sided Specifications

These indices are used for upper specification and lower specification limits, respectivelyCpu and Cpl are desired to be >=1

Use and Interpretation of CpAssumptionsThe quantities presented here (Cp, Cpu, Cpl) have some very critical assumptions:The quality characteristic has a normal distribution.The process is in statistical controlIn the case of two-sided specifications, the process mean is centered between the lower and upper specification limits.If any of these assumptions are violated, the resulting quantities may be in error.Use and Interpretation of CpThe relative humidity in a greenhouse is expected to be between 65% to 85%. Random samples taken over a span of one week yield the following values. 60, 78, 70, 84, 81, 80, 85, 60, 88, 75.Is the process capable.LSL=65USL=85Mean=76.1SD=9.905Cp is 0.337, indicate the process is not capable of meeting the specifications.

Use and Interpretation of CpCpl Is 0.374 and Cpu is 0.299, indicate the process is not capable of meeting the specifications.If the process variation can not be controlled, the alternative is to increase the process mean, so that it is well within the limit of LSL.Cpk ChartThe location of the parameter also influence the processs ability to produce a conforming product. Cp does not include that, whereas Cpk takes that into consideration. Cpk is min of (Cpu, Cpl)It represents the scaled distance, relative to 3 sigma between the process mean and the closest specification limit. Cpk >=1 is desiredCp represents the process potential, Cpk represents the actual capability of the process.

Process Capability Analysis Using a Control ChartIf a process exhibits statistical control, then the process capability analysis can be conducted. A process can exhibit statistical control, but may not be capable.