F.            Process capability and performance

                                                       1.            Process capability studies
Identify, describe, and apply the elements of designing and conducting process capability studies, including identifying characteristics, identifying specifications and tolerances, developing sampling plans, and verifying stability and normality. (Evaluate)

                                                       2.            Process performance vs. specification
Distinguish between natural process limits and specification limits, and calculate process performance metrics such as percent defective. (Evaluate)

                                                       3.            Process capability indices
Define, select, and calculate C_p and C_pk, and assess process capability. (Evaluate)

                                                       4.            Process performance indices
Define, select, and calculate P_p, P_pk, C_pm, and assess process performance. (Evaluate)

                                                       5.            Short-term vs. long-term capability
Describe the assumptions and conventions that are appropriate when only short-term data are collected and when only attributes data are available. Describe the changes in relationships that occur when long-term data are used, and interpret the relationship between long- and short-term capability as it relates to a 1.5 sigma shift. (Evaluate)

                                                       6.            Process capability for attributes data
Compute the sigma level for a process and describe its relationship to P_pk. (Apply)

Process capability – is a predictable pattern of statistically stable behavior where the chance causes of variation are compared to the engineering specifications. A capable process is a process whose spread on the bell-shaped curve is narrower than the tolerance range. The ability of the process to meet customer requirements.

·          Identifying characteristics – the characteristic should be a key factor in the quality of the product; it should be possible to adjust the value of the characteristic; the operating conditions that affect the measured characteristic should be defined and controlled.

·          Identifying specifications and tolerances – determined by customer requirements, industry standards, or engineering department.

·          Developing sampling plans – the appropriate sampling plan depends upon the purpose and whether there are customers or standards requirements for the study.

·          Verifying stability and normality

o         Chi-square hypothesis test

o         Kolmogorov-Smirnov goodness-of-fit test

o         Anderson-Darling test

Measurement terminology

·          Sensitivity – the ability to detect differences in measurement. A gage should be sensitive enough to detect differences in measurement as slight as one tenth of the total tolerance specification.

·          Reproducibility – the “reliability’ of the gage to reproduce measurements. Customarily checked by comparing the results of different operators at different times.

·          Accuracy – lack of bias. An unbiased true value. Comparison with a standard. Correctness

·          Precision – Repeatability or the ability to repeat the same measurement by the operator at or near the same time. Getting consistent results repeatedly.

·          Bias – difference between the output and the true value. Lack of bias is referred to as accuracy.

·          Linearity – the variation between a known standard or “truth.” It is found by obtaining reference part measurement values throughout the operating range of the instrument and plotting the bias against the reference values.

·          Precision/Tolerance (P/T) ratio – between the estimated measurement error (precision) and the tolerance of the characteristic being measured. Assumptions are:

o         Measurement errors are independent

o         Measurement errors are normally distributed

o         Measurement errors are independent of the magnitude

·          Precision/Total Variation (P/TV) – it is desirable to reduce the P/TV ratio to reduce the effect of measurement variation on assessments of process variation. P/T ratio gives a better picture of the measurement precision relative to specifications while the P/TV ratio is better for internal improvement studies.

·          ANOVA – Analysis of variance – a calculation procedure to allocate the amount of variation in a process and determine if it is significant or is caused by random noise. Allows the interaction between the operator and parts to be determined.

·          Repeatability and Reproducibility (R&R) – used to determine R & R, and process variation. Accuracy and sensitivity about the gages must be assured before an R&R study.

o         Range method – a simple way to quantify the combined R&R of a measurement system.

o         Average and range method – computes total measurement system variability and allows it to be separated into R, R, and part variation. The measurement error should not exceed 10% of the part tolerance.

o         Analysis of variance method – the most accurate and also allows the variability of the interaction between operators and part to be determined.

Process performance vs. specification

Process capability indices

·          Cp – Process Capability index - a measure of the ability of a process to produce consistent results - the ratio between the permissible spread and the actual spread of a process. Potential capability

·          Cpk – taking account of off-centeredness. Actual capability

·          Z value – determines the area outside of specification

Process performance indices

·          Pp – performance index – potential performance

·          Ppk – long-term capability of a process – actual performance.

·          Cpm

Short-term vs. long-term capability – using variable data is preferred over attribute data.

·          Short-term – control limits are narrower; smaller amount of data has less variation.

·          Long-term –

·          Machine capability – a measure of the inherent best short-term capability of a machine or process.

Process capability for attributes data – capability is defined as the average proportion or rate of nonconforming product using stable control charts for attribute data.