IES 331 Quality Control

1. IES 331 Quality Control Chapter 7 Process and Measurement System Capability Analysis Week 10 August 9–11, 2005

2. Process Capability • Uniformity of the process • A uniformity of output • Process Capability Analysis: Quantifying variability relative to product requirements or specifications Natural tolerance limits are defined as follows:

3. Process Capability Analysis • Process Capability Analysis: • In the form of probability distribution having… • a specified shape, • center (mean), and • spread (standard deviation) • A percentage outside of specifications • However, specifications are not necessary to process capability analysis

4. Major Uses of Process Capability Analysis • Predicting how well the process will hold the tolerances • Assisting product developers/designers in selecting or modifying a process • Assisting in establishing an interval between sampling process • Specifying performance requirements for new equipment • Selecting suppliers • Planning the sequence of production processes • Reducing the variability in a manufacturing process

5. Process may have good potential capability Reasons for Poor Process Capability

6. Process Capability Analysis using a Histogram or a Probability Plot • If use Histogram, there should be at least 100 or more observations • Data collection Steps • Choose machines or machines. Try to isolate the head-to-head variability in multiple machines • Select the process operating conditions • Select representative operator • Monitor data collection process

7. Exercise 7-11: page 377 The weightsof nominal 1-kg containers of a concentrated chemical ingredient are shown here. Prepare a normal probability plot of the data and estimate process capability

8. Exercise 7-11: page 377(cont)

9. Process Capability Ratios • Process capability ratio (PCR Cp)introduced in Chapter 5 • Percentage of the specification band used up by the process Exercise 7-7: A Process is in statistical control with CL(x-bar) = 39.7 and R-bar = 2.5. The control chart uses sample size of 2. Specification are at 40+/-5. The quality characteristic is normally distributed. Find Cpand P

10. One-Sided PCR Exercise 7-7: A Process is in statistical control with CL(x-bar) = 39.7 and R-bar = 2.5. The control chart uses sample size of 2. Specification are at 40+/-5. The quality characteristic is normally distributed. Find C puand Cpl

11. Interpretation of the PCR

12. Assumptions for Interpretation of Numbers in Table 7-2 • The quality characteristic has a normal distribution • The process is in statistical control • In the case of two-sided specifications, the process mean is centered between the lower and upper specification Violation of these assumptions can lead to big trouble in using the data in Table 7-2.

14. Cp does not take process centering into account • It is a measure of potential capability, not actual capability

15. A Measure of Actual Capability Cpk = minimum (Cpu, Cpl) • Measure the one-sided PCR for the specification limit nearest to the process average. • If Cp = Cpk, the process is centered at the midpoint of the specifications, • If Cpk < Cp , the process is off-center • Cpmeasures potential capability, • Cpk measures actual capability

16. Normality and Process Capability Ratios • The assumption of normality is critical to the usual interpretation of these ratios (such as Table 7-2) • For non-normal data, options are • Transform non-normal data to normal • Extend the usual definitions of PCRs to handle non-normal data • Modify the definitions of PCRs for general families of distributions

17. Confidence Interval and Tests of Process Capability Ratios Confidence intervals are an important way to express the information in a PCR • Exercise 7-20: Suppose that a quality characteristic has a normal distribution with specification limits at USL = 100 and LSL = 90. A random sample of 30 parts results in average of 97 and standard deviation of 1.6 • Calculate a point estimate of Cpk • Find a 95% confidence interval on Cpk • How can we decrease the width of confidence interval on Cpk?

18. Process Capability Analysis Using a Control Chart • Process must be in an in-control state to produce a reliable estimates of process capability • When process is out of control, we must find and eliminate the assignable causes to bring the process into an in-control state

19. Gauge and Measurement System Capability Studies • Determining the capability of the measurement system • Variability are from (1) the items being measured, and (2) the measurement system • We need to: • Determine how much of the total observed variability is due to the gauge or instrument • Isolate the components of variability in the instrument system • Assess whether the instrument of gauge is capable

20. Example 7-7

21. Setting Specification Limits on Discrete Components • For components that interact with other components to form the final product • To prevent tolerance stack-up where there are many interacting dimensions and to ensure that final product meets specifications • In many cases, the dimension of an item is a linear combination of the dimensions of the component parts

22. Exercise 7-30 • Three parts are assembled in series so that their critical dimensions x1, x2, and x3 add. The dimensions of each part are normally distributed with the following parameters: • µ1 = 100; std dev1 = 4 • µ2 = 75; std dev2 = 4 • µ3 = 75; std dev3 = 2 • What is the probability that an assembly chosen at random will have a combined dimension in excess of 262