Session XI. Process Capability

Transcription

1 Session XI Process Capability

2 Central Limit Theorem If the population from which samples are taken is not normal, the distribution of sample averages will tend toward normality provided that the sample size, n, is at least 4. This tendency gets better and better as the sample size gets larger. The standardized normal can be used for the distribution averages with the modification. Z X X X n

3 Central Limit Theorem Illustration of central limit theorem

4 Central Limit Theorem Dice illustration of central limit theorem

5 Control Limits & Specifications Relationship of limits, specifications, and distributions

6 Control Limits & Specifications The control limits are established as a function of the average Specifications are the permissible variation in the size of the part and are, therefore, for individual values The specifications or tolerance limits are established by design engineers to meet a particular function

7 Process Capability & Tolerance The process spread will be referred to as the process capability and is equal to 6σ The difference between specifications is called the tolerance When the tolerance is established by the design engineer without regard to the spread of the process, undesirable situations can result

8 Process Capability & Tolerance Three situations are possible: Case I: When the process capability is less than the tolerance 6σ<USL-LSL Case II: When the process capability is equal to the tolerance 6σ=USL-LSL Case III: When the process capability is greater than the tolerance 6σ >USL-LSL

9 Process Capability & Tolerance Case I: When the process capability is less than the tolerance 6σ<USL-LSL Case I: 6σ < USL-LSL

10 Process Capability & Tolerance Case II: When the process capability is equal to the tolerance 6σ=USL-LSL Case II: 6σ = USL-LSL

11 Process Capability & Tolerance Case III: When the process capability is greater than the tolerance 6σ>USL-LSL Case III: 6σ > USL-LSL

12 Process Capability The range over which the natural variation of a process occurs as determined by the system of common or random causes Measured by the proportion of output that can be produced within design specifications

13 Process Capability This following method of calculating the process capability assumes that the process is stable or in statistical control: Take 25 (g) subgroups of size 4 for a total of 100 measurements Calculate the range, R, for each subgroup Calculate the average range, R bar= ΣR/g Calculate the estimate of the population standard deviation µ R 0 Process capability will equal 6σ d2 0

14 Process Capability The process capability can also be obtained by using the standard deviation: Take 25 (g) subgroups of size 4 for a total of 100 measurements Calculate the sample standard deviation, s, for each subgroup Calculate the average sample standard deviation, s bar = Σs/g Calculate the estimate of the population standard deviation Process capability will equal 6σo µ s 0 c 4

15 Capability Index Process capability and tolerance are combined to form the capability index. C p where C 6 0 USL LSL 6 p 0 capabilityindex USL LSL tolerance process capability

16 Capability Index The capability index does not measure process performance in terms of the nominal or target value. This measure is accomplished by C pk. C pk where C Min{( USL X ) or ( X LSL) 3 p capabilityindex USL LSL tolerance 6 0 process capability

17 Capability Index C p = USL - LSL 6 ơo The Capability Index does not measure process performance in terms of the nominal or target C pk = min{ (USL- X), ( X-LSL)}

18 Capability Index 1. The Cp value does not change as the process center changes 2. Cp=Cpk when the process is centered 3. Cpk is always equal to or less than Cp 4. A Cpk = 1 indicates that the process is producing product that conforms to specifications 5. A Cpk < 1 indicates that the process is producing product that does not conform to specifications

19 Capability Index 6. A Cp < 1 indicates that the process is not capable 7. A Cpk=0 indicates the average is equal to one of the specification limits 8. A negative Cpk value indicates that the average is outside the specifications

20 C pk Measures C pk = negative number C pk = zero C pk = between 0 and 1 C pk = 1 C pk > 1