借鉴他人：诺机亚培训教材(编辑修改稿)

借鉴他人：诺机亚培训教材(编辑修改稿)内容摘要：

cess. What Measurements Can Be Used to Describe Process variation? 21 169。 NOKIA 2001 • sST often notated as or sigma, is another measure of dispersion or variability and stands for “shortterm standard deviation”, which measures the variability of a process or system using “rational” subgrouping. s R N d R dST jjN  12 2* *where is the range of subgroup j, N the number of subgroups, and d2* depends on the number N of subgroups and the size n of a subgroup (see next slide) R X Xj j j m a x m i nWhat Measurements Can Be Used to Describe Process variation? 22 169。 NOKIA 2001 d2* values for SST Where: N = no. of subgroups, n = no. of samples in each subgroup d2* d2 Typical: N=20 amp。 n=5 23 169。 NOKIA 2001 • • • • • • • x3 • x2 • x1 • x10 x _ t 1)(...)()( 222212Nxxxxxxss NLTLT15)()()()()( 22222LTsExample: What Measurements Can Be Used to Describe Process variation? 24 169。 NOKIA 2001 The Difference Between SST and sLT !! mean Time Dimension Short term Standard Deviation Long term Standard Deviation Subgroup size n = 5 Number of subgroups N = 7 Subgroup No. 1 25 169。 NOKIA 2001 The difference between the standard deviations sLT and sST gives an indication of how much better one can do when using appropriate production control, like Statistical Process Control (SPC). s x x x x x xNLTN      ( ) ( ) . . . ( )1 2 2 2 21s R N d R dST jjN  12 2* *Shortterm standard deviation : Longterm standard deviation : The difference between sST and sLT 26 169。 NOKIA 2001 The difference between sST and sLT •The difference between sLT and sST is only in the way that the standard deviation is calculated •sLT is always the same or larger than sST •If sLT equals sST, then the process control over the longer term is the same as the shortterm, and the process would not benefit from SPC •If sLT is larger than sST, then the process has lost control over the longer term, and the process would benefit from SPC •The reliability of sLT is improved if the data is taken over a longer period of time. Alternatively sLT can be calculated on several occasions separated by time and the results pared to see whether sLT is stable 27 169。 NOKIA 2001 Exercise 1: Sample Distributions 1. In Excel file Data exercise you find 100 measurements being the result of a capability study. The specification for the dimension is 15,16,01 2. How well does the sample population fit the specification, . should we expect any parts outside spec? 3. Mention possible consequences of having a part outside spec . 4. Mention possible causes of variation for parts. 5. Calculate the sample mean and sample standard deviation for the 100 measurements. Use the average and stdev functions Excel. 28 169。 NOKIA 2001 Section 3. Cp and Cpk Concept 29 169。 NOKIA 2001 Defining Cp and Pp Sample mean Process variation 6*s stp sL SLU SLC*6 USLLSL LSL USL Nominal dim ltp sL SLU SLP*6The tolerance area divided by the total process variation, irrespective of process centring. 30 169。 NOKIA 2001 Defining Cpk and Ppk ststpk sm e anU SLsL SLm e anC*3,*3m i nSample mean Process variation 3s Process variation 3s Mean LSL USLMean LSL USL Nominal dim ltltpk sm e anU SLsL SLm e anP*3,*3m i nCpk and Ppk Indexes account also for process centring. 31 169。 NOKIA 2001 What is the Difference Between Cp and Cpk? • The Cp index only accounts for process variability • The Cpk Index accounts for process variability and centering of the process mean to the design nominal • Therefore, Cp  Cpk • NOTE: Same applies also for Pp and Ppk Cp = Cpk (both low) LSL USL Mean = Nominal Reject parts Reject parts Cp hi。