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Chapter 6 Control charts for Attributes

Chapter 6 Control charts for Attributes. 組別：第三組 成員：鍾弘智 9421710 張耀升 9421721 柯宗祐 9421722 林郁勝 9421740 吳立文 9421745. Agenda. Introduction The control chart for fraction nonconforming The control chart for fraction nonconforming (defects)

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Chapter 6 Control charts for Attributes

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  1. Chapter 6 Control charts for Attributes 組別：第三組 成員：鍾弘智9421710 張耀升9421721 柯宗祐9421722 林郁勝9421740 吳立文9421745

  2. Agenda • Introduction • The control chart for fraction nonconforming • The control chart for fraction nonconforming (defects) • Choice between attributes and variable control charts • Guidelines for implementing control charts

  3. 6-1 Introduction • Attributes chart are generally not as informative as variable chart because there is typically more information in a numerical measurement that in merely classifying a unit as conforming or nonconforming.

  4. 服務業品質特性

  5. 6-2 The control chart for fraction nonconforming • Definition of fraction nonconforming : The ratio of the number of nonconforming items in a population to the total number of item in that population. • The statistical principle : Based on binomial distribution. x=0,1,2….,n

  6. Definition of sample fraction nonconforming : The ratio of the number of nonconforming units in the sample D to the sample size n. The distribution of the random variable can be obtained from binomial.

  7. 6-2.1 Development and Operation of control chart • By the Shewhart control chart : if w is a statistic that measures a quality characteristic, and mean is and variance is .

  8. Standard Given • If a standard value of p is given, then the control limits for the fraction nonconforming are

  9. No Standard Given • If no standard value of p is given, then the control limits for the fraction nonconforming are where

  10. Trial Control Limits • Control limits that are based on a preliminary set of data can often be referred to as trial control limits. • The quality characteristic is plotted against the trial limits, if any points plot out of control, assignable causes should be investigated and points removed. • With removal of the points, the limits are then recalculated.

  11. EX.6-1 Inspection frozen orange juice cardboard cans.To establish the control chart, 30 sample of n=50

  12. We can find the mean p • calculate the upper and lower control limits • therefore

  13. ＜資料初步不合格率管制圖＞

  14. Design of the Fraction Nonconforming Control Chart • The parameters : the sample size, frequency of sampling, and the width of the control limits. • The sample size can be determined so that a shift of some specified amount,  can be detected with a stated level of probability (50% chance of detection). If  is the magnitude of a process shift, then n must satisfy:

  15. Interpretation of Points on the Control Chart for Fraction Nonconforming • Care must be exercised in interpreting points that plot below the lower control limit. • They often do not indicate a real improvement in process quality. • They are frequently caused by errors in the inspection process or improperly calibrated test and inspection equipment.

  16. The np control chart • The actual number of nonconforming can also be charted. Let n = sample size, p = proportion of nonconforming. The control limits are:

  17. 6-2.2 Variable Sample Size • Since different numbers of units could be produced in each period, the control chart will have a variable sample size. And we can constructing and operating the chart with three approaches： 1.Variable sample size 2.Control limits based on average sample size 3.The standardized Control Chart

  18. Variable sample size • The approach is determine for each individual sample that are based on specific sample size.

  19. ＜變動樣本大小之不合格率管制圖的資料＞

  20. 變動樣本大小之不合格管制圖 使用Minitab之管制圖

  21. Control Limits Based on an Average Sample Size • Control charts based on the average sample size results in an approximate set of control limits. • The average sample size is given by • The upper and lower control limits are

  22. ＜根據平均樣本大小的管制圖＞

  23. The Standardized Control Chart • The points plotted in standard deviation units. Center line at zero, and upper and lower control limits of +3 and -3 . The variable plotted on chart is：

  24. ＜標準化的管制圖＞

  25. ＜使用Minitab的標準化管制圖＞

  26. 6-2.3 Nonmanufacturing Application • In the nonmanufacturing environment, many quality characteristics can be observed on a conforming or nonconforming basis.

  27. 6-2.4 The Operating-Characteristic Function and Average Run Length Calculations • The operating-characteristic(OC) function of the fraction nonconforming control chart is a graphical display of the probability of incorrectly accepting the hypothesis of statistical control(type II) againt the process fraction nonconforming.

  28. Example • For this example, n = 50, p = 0.30, UCL = 0.3697, and LCL = 0.0303. Therefore, from the binomial distribution,

  29. OC curve for the fraction nonconforming control chart with p = 0.2, LCL = 0.0303 and UCL = 0.3697.

  30. Average Run Lengths (ARLs) • The average run lengths for fraction nonconforming control charts can be found as before: • The in-control ARL is • The out-of-control ARL is

  31. Example • For this example, the chart parameters n=50 UCL=0.3697, LCL=0.0303 and CL=0.2. From the Table6-6,the probability of a point plotted in control is 0.9973 the value of ARL is

  32. 6-3.1 固定樣本大小時的程序

  33. 標準未知

  34. 樣本6與樣本20出現異常排除這兩個樣本然後修正 樣本6與樣本20出現異常排除這兩個樣本然後修正

  35. 缺點數進一步分析

  36. 樣本大小的選擇：u圖 u=x/n

  37. 6-3.2 變動樣本大小時的程序

  38. 標準化管制圖

  39. 6-3.4 操作特性函數（1） C圖的OC曲線 例題6-3代入 因為C屬於整數

  40. 6-3.4 操作特性函數（2） u圖的OC曲線 <nLCL>：代表大於或等於nLCL的最小整數 [nUCL] ：代表小於或等於nUCL的最大整數

  41. 6-3.5 低不良水準的處理（1） 情 形：當不良水準非常低時產生不合格品的時間 會很長，使用u圖和C圖會非常沒有效率 的時候。 改善方式：利用兩個連續缺點數出現的間隔時間來作 為新的管制圖，時間間格管制圖對於低不 良水準的製程很有效率。

  42. 6-3.5 低不良水準的處理（2） • 假設缺點或事件發生的機率為卜氏分配，事件發 生間隔機率就是指數分配。 • 指數分配管制圖太過於偏斜，管制圖會非常不對 稱。 改善方法：Nelson（1994）建議將指數隨機變數轉 換成韋伯隨機變數（分配趨近於常態）。 假設x為常態分配，建立x的管制圖。

  43. 6-3.5 低不良水準的處理（3）

  44. 6-3.5 低不良水準的處理（4） 錯誤的間隔時間的常態機率圖 資料經轉換之後的常態機率圖

  45. 6-3.5 低不良水準的處理（5） • 偵測小變動方法：1.累積和 2. 指數加權平均（EWMA） ※Kittlitz研究管制圖的指數轉換，建議使用x=

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