【正文】 2023年 3月 19日星期日 4時(shí) 46分 38秒 04:46:3819 March 2023 ? 1一個(gè)人即使已登上頂峰，也仍要自強(qiáng)不息。 2023年 3月 19日星期日 上午 4時(shí) 46分 38秒 04:46: ? 1最具挑戰(zhàn)性的挑戰(zhàn)莫過于提升自我。勝人者有力，自勝者強(qiáng)。 :46:3804:46Mar2319Mar23 ? 1越是無能的人，越喜歡挑剔別人的錯(cuò)兒。 , March 19, 2023 ? 閱讀一切好書如同和過去最杰出的人談話。 2023年 3月 19日星期日 4時(shí) 46分 38秒 04:46:3819 March 2023 ? 1空山新雨后，天氣晚來秋。 。 :46:3804:46:38March 19, 2023 ? 1意志堅(jiān)強(qiáng)的人能把世界放在手中像泥塊一樣任意揉捏。 :46:3804:46Mar2319Mar23 ? 1世間成事，不求其絕對圓滿，留一份不足，可得無限完美。 , March 19, 2023 ? 很多事情努力了未必有結(jié)果，但是不努力卻什么改變也沒有。 2023年 3月 19日星期日 4時(shí) 46分 38秒 04:46:3819 March 2023 ? 1做前，能夠環(huán)視四周；做時(shí)，你只能或者最好沿著以腳為起點(diǎn)的射線向前。 。 :46:3804:46:38March 19, 2023 ? 1他鄉(xiāng)生白發(fā)，舊國見青山。 :46:3804:46Mar2319Mar23 ? 1故人江海別，幾度隔山川。 , March 19, 2023 ? 雨中黃葉樹，燈下白頭人。 ?=1, ?) ???xExponential (x。 6? away from the process mean ?, . Cp ? 2, ? and the process shifts by less than ?, . Cpk ? , ? then the process will yield less than dppm rejects. 6? 6? Shift ? ? What’s Six Sigma Quality — Now Mikel J Harry claims that the process mean between lots will vary, with an average process shift of ?. k? = z? + ? k? = z? + ? Shift ? z? Note: Sigma Capability = ?(dpmo) ? ?(dppm) Process Capability for NonNormal Data Not every measured characteristic is normally distributed. Characteristic Distribution Cycle Time Exponential Reject Rate Binomial Defect Rate Poisson Process Capability for Cycle Time The Weibull Distribution is a general family of distribution with where scale parameter ? is the value at which CDF=%, and shape parameter ? determines the shape of the PDF. ? ? ??????? ??? ??????? x1 ex,。3USLMinC pk ??????? ????????? ???? ???Process Capability For a normally distributed characteristic, the defective rate F(x) may be estimated via the following: For characteristics with only one specification limit: a) LSL only b) USL only ? ? ? ? ? ?USLxPrLSLxPrxF ???? ?????? ?????? ? ??????????? ? ???? USL1LSL? ? ? ?? ?USLLSL Z1Z ?????LSL USL ? ? ? ? ? ?LSLZLSLxPrxF ????? ? ? ? ? ?USLZ1USLxPrx ?????Example 2 Specification Limits : 4 to 16 g Machine Mean Std Dev (a) 10 4 (b) 10 2 (c) 7 2 (d) 13 1 Determine the defective rate for each machine. Example 2 Mean Std Dev ZLSL ZUSL F(xLSL) F(xUSL) F(x) 10 4 66,807 66,807 133,614 10 2 1,350 1,350 2,700 7 2 66,807 3 66,811 13 1 0 1,350 1,350 Lower Spec Limit = 4 g Upper Spec Limit = 16 g Process Potential vs Process Performance (a) Poor Process Potential (b) Poor Process Performance LSL USL LSL USL Experimental Design ? to reduce variation Experimental Design ? to center mean ? to reduce variation Process Potential vs Process Performance Process Potential Index (Cp) Cpk 2, 1, 1, 1, 1, 1, Defective Rate (measured in dppm) is dependent on the actual bination of Cp and Cpk.. Process Potential vs Process Performance a) Cp = 2 Cpk = 2 b) Cp = 2 Cpk = 1 c) Cp = 2 Cpk 1 Cp – Cpk ? Missed Opportunity Alternative Process Performance Index ? ? 2ppmT1CC ?????? ?????Process capability statistics measure process variation relative to specification limits. The Cp statistic pares the engineering tolerance against the process’s natural variation. The Cpk statistic takes into account the location of the process relative to the midpoint between specifications. If the process target is not centered between specifications, the Cpm statistic is preferred. Process Stability A process is stable if the distribution of measurements made on the given feature is consistent over time. Time Stable Process Time Unstable Process ucl lcl ucl lcl Within vs Overall Capability Within Capability (previously called shortterm capability) shows the inherent variability of a machine/process operating within a brief period of time. Overall Capability (previously called longterm capability) shows the variability of a machine/process operating over a period of time. It includes sources of variation in addition to the shortterm variability. Within vs Overall Capability Within Overall Sample Size 30 – 50 units ? 100 units Number of Lots single lot several lots Period of Time hours or days weeks or months Number of Operators single operator different operators Process Potential Cp Pp Process Performance Cpk Ppk Within vs Overall Capability Wi thi np 6LSLUSLC???Wi thi npl 3LSL????Wi thi npu 3USL????Wit hinpk 3NSLC???Overal l6LSLUSLP??Overal lplOveral lpuP?Over allpk??? Within Capability Overall Capability The key difference between the two sets of indices lies in the estimates for ?Within and ?Overall . Estimating ?Within and ?Overall Consider the following observations