TAILIEUCHUNG - Product and Process Comparisons_6

Tham khảo tài liệu 'product and process comparisons_6', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Approximate intervals that contain most of the population values SEMMECH MOME rTOOLS IM SEARCH BACK NEXT http div898 handbook prc section2 2 of 2 5 1 2006 10 38 45 AM . Percentiles ENGINEERING STATISTICS HANDBOOK hW tools raids lỉEÂtCH BACK Nixf 7. Product and Process Comparisons . Comparisons based on data from one process . What intervals contain a fixed percentage of the population values . Percentiles Definitions of order statistics and ranks Definition of percentiles Estimation of percentiles For a series of measurements Y1 . Yn denote the data ordered in increasing order of magnitude by Y 1 . Y N . These ordered data are called order statistics. If Y j is the order statistic that corresponds to the measurement Yi then the rank for Yi is j . yD yj -j Order statistics provide a way of estimating proportions of the data that should fall above and below a given value called a percentile. The pth percentile is a value Y p such that at most 100p of the measurements are less than this value and at most 100 1- p are greater. The 50th percentile is called the median. Percentiles split a set of ordered data into hundredths. Deciles split ordered data into tenths . For example 70 of the data should fall below the 70th percentile. Percentiles can be estimated from N measurements as follows for the pth percentile set p N 1 equal to k d for k an integer and d a fraction greater than or equal to 0 and less than 1. 1. For 0 k N 2. For k 0 Y p Y 1 3. For k N Y p Y N http div898 handbook prc section2 1 of 2 5 1 2006 10 38 45 AM . Percentiles Example and interpretation Note that there are other ways of calculating percentiles in common use Definition of Tolerance Interval For the purpose of illustration twelve measurements from a gage study are shown below. The measurements are resistivities of silicon wafers measured in . i Measurements Order stats Ranks 1 9 2

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