【文章內(nèi)容簡介】 mple size of nk unitsFSGS M00 Rev B 35p Chart? Following Shewhart’s principle, the Center Line and Control Limits of a p chart are根據(jù)休哈特原理，中心線和控制線分別是 :FSGS M00 Rev B 36? The p chart also assumes a symmetrical bellshape distribution, with symmetrical control limits on each side of the center line/P圖呈對稱鈴型分布，控制線對稱地分布在中心線的兩側(cè) .? This implies that the binomial distribution is approximately close to the shape of the normal distribution, which can happen under certain conditions of p and n這說名在 p n 一定的條件下，二項分布接近正態(tài)分布 :216。 p ? 1/2 and n 10 implying np 5216。 For other values of p, the general guideline is to have np 10 to get a satisfactory approximation of the normal to the P不等于 1/2，通則是使 np10,這樣就可以使二項分布得到滿意的正態(tài)型p ChartFSGS M00 Rev B 37? If the sample size is not constant, then the Control Limits of a p chart may be puted by either method如果樣本大小不為常數(shù)，控制線可以用以下任意一放法得到 :a) Variable Control Limits變量控制線where ni is the actual sample size of each sampling i這里 n是每次抽樣的實(shí)際數(shù)b) Control Limits Based on Average Sample Size控制線基于平均樣本數(shù)where n is the average (or typical) sample size of all the samples這里 n是所有樣本數(shù)的平均值p ChartFSGS M00 Rev B 38When to Use Control Limits Based on Average Sample Size instead of Variable Control Limits當(dāng)使用基于樣本平均大小的控制線時4 Smallest subgroup size, nmin, is at least 30% of the largest subgroup size, 30%4 Future sample sizes will not differ greatly from those previously When using Control Limits Based on Average Sample Size, the exact control limits of a point should be determined and examined relative to that value if當(dāng)使用基于樣本平均大小的控制線時，每一點(diǎn)的控制線由于那一點(diǎn)的值來決定如果 :4 There is an unusually large variation in the size of a particular sample某一特別的樣本的大小有明顯的變化4 There is a point which is near the control p Chart Average Sample SizeFSGS M00 Rev B 39np Chart? If the sample size is constant, it is possible to base a control chart on the number nonconforming (np), rather than the fraction nonconforming (p).如果樣本大小是常數(shù)，可以基于控制圖的不合格品數(shù)，而非部分不合格品數(shù)? The Center Line and Control Limits of an np chart are:FSGS M00 Rev B 40Sample Size for p and np ChartsSample Size is determined based on the 2 criteria樣本大小基于 2個標(biāo)準(zhǔn)來決定 :1. Assumption to approximate Binomial Distribution to a Normal Distribution假定二項分布近似正態(tài)分布1. To ensure that the LCL is greater than 制線大于 0For p ? For p = other valuesFSGS M00 Rev B 41c ChartDefects per Unit (DPU)單位缺陷Error Rate / Defect Rate缺陷率Defects per Opportunity2023020100Sample NumberSample Countc ChartC===FSGS M00 Rev B 42c ChartIf the number of nonconformities (defects) per inspection unit is denoted by c, then如果每個檢查單元的缺陷數(shù)為 c,則 :The Center Line and Control Limits of a c chart are:FSGS M00 Rev B 43u Chart? In cases where the number of inspection units is not constant, the u chart may be used instead, with如果檢查單元的數(shù)量不為常數(shù)，則用 u圖 :? If the average number of defects per inspection unit is denoted by u, then如果每個檢查單元的平均缺陷數(shù)用 u表示，則Where ci is the count of the number of defects in number of inspection units, ai這里 ci 是數(shù)量為 ai的檢查單元的缺陷數(shù)FSGS M00 Rev B 44u ChartThe Center Line and Control Limits of a u chart are:FSGS M00 Rev B 45Sampling Plans for X Chart 均值圖抽樣計劃Sampling frequency?抽樣頻率Sample size?樣本大小Width of control limits?控制線寬度FSGS M00 Rev B 46Sampling Frequency抽樣頻率? The most desirable situation with regards to detecting shifts would be to take large samples very frequently探測變化最理想的做法是頻繁地抽取大的樣本 . ? But this is usually not economically feasible, and the problem is one of resource 題，這在經(jīng)濟(jì)上不可行? Should we take smaller samples at short intervals? Or larger samples at longer intervals?可以在較短時間內(nèi)抽取小樣本嗎， 或在較長時間間隔內(nèi)抽取較大樣本嗎? Current industry practice tends to favour smaller, more frequent samples目前業(yè)界的共識是頻繁地抽去小樣本Designing an XR Chart FSGS M00 Rev B 47Sampling Frequency ARL抽樣頻率 平均運(yùn)轉(zhuǎn)周期? A good way is to start evaluating sampling frequency is to determine the required sampling frequency statistically一個好的方法是評估抽樣頻率，統(tǒng)計地決定需要的抽樣頻率 We use the Average Run Length (ARL) to do this我們使用 平均運(yùn)轉(zhuǎn)周期來決定? Then finally weigh the puted results with sound practical judgement最后根據(jù)計算結(jié)果和慣例來決定Designing an XR Chart FSGS M00 Rev B 48Control Charts – Sampling Risks?If there is no change in the process, there is still a chance of getting a point out of the 3? control limits. What is the implication?如果制程沒有改變，但有一點(diǎn)在 3?控制線外，它表示什么呢3 ?3 ?%Lower Control LimitCenter LineUpper Control LimitWhat does each area of % mean?每一個這樣的區(qū)域代表什么？%%FSGS M00 Rev B 49Control Charts – Sampling RisksType I Error一類錯誤?Concluding that the process is out of control when it is really in control制程受控，但卻認(rèn)為已經(jīng)失控?? = probability of making Type I error范此類錯誤的可能性 = monly known as the producer’s risk制造商的風(fēng)險 = total of % for control limits of +/ 3?對于 +/ 3?控制線， 范此類錯誤的可能性為 %Lower Control LimitUpper Control LimitCenter LineSample Number or Time%%Is process really out of control? Or is the point outside due to random variation?FSGS M00 Rev B 50Control Charts – Sampling RisksType I Error and Tampering一類錯誤及 干預(yù)? If the process is really in control, and process adjustment is made because of Type I error, it is called tampering with the 受控但由于范 一類錯誤 而調(diào)整 制程，這叫干預(yù)制程? Tampering has been shown to actually increase the variability of the process!干預(yù)制程實(shí)際是給制程增加變異FSGS M00 Rev B 51Control Charts – Sampling RisksType II Error二類錯誤Concluding that the process is in control when it is really out of control制程不受控但卻認(rèn)為它受控? = probability of making Type II error范此類錯誤的可能性