5_Variable Control Charts

# 5_Variable Control Charts - Lecture Notes OR 182 282...

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Lecture Notes - OR 182, 282, Professor Jim Harris, Variable Control Charts - 1 SINGLE VARIABLE CONTROL CHARTS PRELIMINARIES Benefits • Good Record Keeping • Awareness of Quality Importance • Awareness of Management Support When, Where, How to use Control Charts • Where trouble is likely to occur and can affect the process • First use tied to substantial cost reduction (to show to management) • # is dependent on facilities for manual vs. computer implementation > Manual 1. more training 2. more computational burden 3. not in real time > Computer 1. available storage 2. variable displays 3 more advanced trechniques

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Lecture Notes - OR 182, 282, Professor Jim Harris, Variable Control Charts - 2 K-SIGMA CHARTS Basic Chart Design • For statistic Y is +k .5 Y Y • But and are rarely known thus Y Y > Phase I Charts 1. use data to estimate and via and ^ ^ YY 2. Data must be recent enough to be relevant and be constructed with rational subgruops 3. plot data used to estimate and on the chart for Y Y Y if all data within control limits process in control and ÊÊ estimates hold if any data not within control limit investigate to see if assignable cause present and remove data ONLY if assignable cause found > Phase II Charts 1. Plot new data against estimated control limits and investigate for assignable cause when indication is given 2. Periodically revise estimate for and Y Y
Lecture Notes - OR 182, 282, Professor Jim Harris, Variable Control Charts - 3 • Remeber not every point beyond the control limits means the process is "out of control", only that we should check and see if it is. >we are visually testing several hypothesis if p Pr{a single point outside the CL} (=.0027 for k 3) Ê´ œ and if and m points are plotted Pr{at least one out of m points outside the control limits} Ê 1 Pr{none outside} 1– (1–p) (binomial distribution) œ œ m 1 – ( p) (binomial expansion) ± Š‹ x0 m m x x œ 1 – [1–mp + p – ] mp (if m is moderate m<50) œâ ¸ m 2 2 do not be surprised to find a few outside CLs when process is "in control". Ê • Limits may also be adjusted for example if we want the probability of m points inside the limits to be .0027 then mp = .0027 p = .0027/m set k Z ( 3) (m=20 Z =3.81) Êœ   p 0027/20 Þ

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Lecture Notes - OR 182, 282, Professor Jim Harris, Variable Control Charts - 4 Variable Control Charts Considered X for central tendancy S (and S ) for variability (good properties, best for larger values of n) 2 R for variability (esierr and good approximation for smaller n) Notation • m 20 or more subgroups sample size n 4, 5 or 6, œœ • Data Setup GROUP (j) X X X S R 1 m XS R " jn j j j j â ã œ •X is the ith observation, in the jth subgroup, i=1, . .., n, j=1, . .., m ij •X is the ith smallest observation, in the jth subgroup, i=1, .
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5_Variable Control Charts - Lecture Notes OR 182 282...

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