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Variation and Control Charts A Leadership Perspective Please give credit to www.spcforexcel.com when using this presentation.www.spcforexcel.com

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How Do We Look at Data? Sales (000) in Jan-10: $11,229 Budget for Jan-10: $10,000 Sales in Jan-09: $7,997 A number by itself has little meaning. So, we naturally want to compare it to something. But to what? Typical comparisons include: This month’s result to last year’s result This month’s result to budget YTD result to last year’s YTD YTD result to budget

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Financial Reports 1Q 2010BudgetVariance2Q 209Variance Sales $30,14830,00014823,8236,325 2Q 2010BudgetVariance2Q 2009Variance Sales $ 27,46030,000(2,540)33,545(6,085) First Quarter Sales: Second Quarter Sales: 2010 YTDBudgetVariance2009 YTDVariance Sales $ 57,60860,000(2,392)57,368240 YTD Sales:

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Variation in Metrics Sales in Jan-10: $11,229 Sales in Feb-10 $10,016 Are these two numbers the same? The measurements we take reflect the variation in the process. The problem with measurement systems that compare one time frame to another (like the financial report) is that the actual performance (variation) of the process is hidden – we don’t know if there are special causes or just common causes.

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Measurements and the Underlying Process Let’s return to the financial report from before – things did not look too good – especially in the second quarter. Let’s explore another method of examining the data that reveals the “voice of the process” – the true performance. 2010 YTDBudgetVariance2009 YTDVariance Sales $ 57,60860,000(2,392)57,368240

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Measurements and the Underlying Process The table below shows the monthly data used to make the earlier tables. What does this data tell you? Often, it is difficult to understand the process by looking at a table of numbers. MonthSalesMonthSalesMonthSales Jan-097997Jul-098133Jan-1011229 Feb-099132Aug-097215Feb-1010016 Mar-096694Sep-098278Mar-108903 Apr-0910005Oct-0911117Apr-109617 May-0912055Nov-096481May-108190 Jun-0911485Dec-096897Jun-109653

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It is often better to examine the data as a time series chart. –No major change in monthly sales - some months better than others –Financial report indicated a problem (2Q 2010) –Time series tells a different story –There is a problem though – sales aren’t increasing

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Adding the average line helps with interpreting the process behavior –Nine points above, nine points below –Monthly sales fairly predictable –Range from about $600,000 to about $1,200,000 –Can provide an early warning of problems

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Control Limits The time series charts can be further enhanced by adding natural process (control) limits These limits define the boundaries for common causes of variation With common cause of variation: –The upper control limit (UCL) is the largest value you can expect –The lower control limit (LCL) is the smallest value you can expect As long as the all the points are within the limits and there are no patterns, only common cause of variation is present The process is said to be “in control” –To improve it, you must fundamentally change the process

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Sales chart with natural process limits –Process is “in control” –Can predict what will happen in the future –It is not the limits, but the story that the chart tells –Provides feedback on whether the process is changing or staying the same

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Interpreting Time Series Charts Points beyond the limits UPNL Avg LPNL Special cause

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Zones Test The zone tests are valuable tests for enhancing the ability of control charts to detect small shifts quickly. –The first step in using these tests is to divide the control chart into zones. The chart is divided into six equal zones: three above the average and three below the average. UCL LCL Avg A B C C B A

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Test for Zone A X = Out of Control Point UCL LCL Avg A B C C B A X X A special cause of variation exists if there are two out of three consecutive points in zone A or beyond (on one side of the average).

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Test for Zone B X = Out of Control Point UCL LCL Avg A B C C B A X X A special cause of variation exists if there are four out of five consecutive points in zone B or beyond (on one side of the average).

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Test for Zone C X = Out of Control Point UCL LCL Avg A B C C B A X A special cause of variation exists if there are seven or more consecutive points in zone C or beyond (on one side of the average).

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Rule of Seven Tests UCL Avg LCL UCL Avg LCL UCL Avg LCL UCL Avg LCL Seven Points in a Row Above the Average Seven Points in a Row Below the Average Seven Points in a Row Trending DownSeven Points in a Row Trending Up

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In Control or Out of Control?

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Summary

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CD-ROM Chap 17-1 A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. A Course In Business Statistics 4 th Edition CD-ROM Chapter 17 Introduction.

CD-ROM Chap 17-1 A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. A Course In Business Statistics 4 th Edition CD-ROM Chapter 17 Introduction.

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