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1. WB YAHYAand A ADENIYI SUPER QC PACK SQC SOFTWARE Version 1 0 0 Software for Analyzing Quality Control Data Developed by W B Yahya and I A Adeniyi Department of Statistics University of Ilorin P M B 1515 Ilorin Nigeria e mail woyahya unilorin edu ng zicoy6k3 gmail com USER S MANUAL PREAM BLE This manual presents how to use Super QC pack version 1 0 0 to analyse various forms of quality control data and construct the necessary control charts SYSTEM REQUIRMENTS AND INSTALLATION The SQC version 1 0 0 can be installed and run on any 32 or 64 bits Windows XP Windows VISTA Windows 7 and Windows server 2003 2008 operating systems A minimum of 256MB of RAM with at least 17M B hard disc space is required for optimal performance To install SQC version 1 0 0 simply double click on QC pack set up a windows installer would pop up click next to proceed select users Just Me or Everyone and choose installation folder click next to finalize your installation After the installation the Shortcut to Super QC Pack icon will be deposited on the desktop and in the user s program menu Click on this icon to launch the SQC software The Super QC pack set up can be downloaded directly from the following web address www unilorin edu ng sqcpack yahya adeniyi webpage htm CITATION INFORMATION It is required that any user of the Super QC Pack for research purposes should reference the2. software this way Yahya W B and Adeniyi I A 2012 Super QC Pack A novel software for analyzing Quality Control data Department of Statistics University of Ilorin www unilorin edu ng sqcpack yahya_adeniyi webpage htm Table of Contents A HOW TO CONSTRUCT VARIOUS CONTROL CHARTS WITH SQC SOFTWARE 4 1 TheP Chart r r ee ee ss eee Ok 4 2 TheC Chart r a a Siti a ER wn 6 3 Theu Chart 0 0 ccc cee eee ee Sees 6 4 TheR Chart f h A ee 7 5 TheS Chart eee eee rM 9 6 TheX BarChart 4 BAY eee 10 B PROCESS CAPABILITY INDICES aaa aaa 12 References A HOW TO CONSTRUCT VARIOUS CONTROL CHARTS WITH SQC SOFTWARE 1 The P Chart The P chart is a type of attribute control charts that is most applicable to situations where the occurrence of defectives is not rare To use this chart the percentage of defectives may be expected to be more than 5 of the total number of units produced In this chart the percentage of defectives per batch over time is plotted However the control limits are based on the binomial distribution of proportions The center line CL upper control limit UCL and lower control limit LCL are estimated by the following CL p _ 24 gt n j l where dj is the number of defectives in group batch j and nj is the corresponding sample size in group b
3. Launch the program and select S chart from the type of chart options and click the OK button ii All other steps are the same as in the R chart except that the standard deviations are to be specified or supplied here instead of the ranges where necessary 6 The X BAR Chart X Bar chart is a type of control chart used to monitor changes in the mean of a process Montgomery 2005 The center line CL is the grand mean of all the groups batches given by u which if it is unknown a priori from a stable process can be estimated from the data by x 5xX ma where X isthe mean of samples in group batch j j 1 2 m The upper control limit UCL of the process is determined by O T aa while its lower control limit LCL is determined by X Z ds i Jn where o is the standard deviation of the process under stable condition n is the number of Sample in each group and Z IS the quantile of the standard normal distribution at significance level a Like the center line u the value of o is not usually known and can only be estimated from the Samples collected from the process The following two statistics are available to estimate o Q gt lI S gt l Q gt Or ola 10 where Ris the average of all the m groups ranges and S is the average of all the m groups standard deviations as earlier defined for R and S charts respectively For unequal group sample sizes nj the centre line CL is computed by
4. column for equal sample sizes across the groups or with group ranges and sample sizes in the first and second columns of the csv file respectively for unequal Sample sizes if the sample ranges are to be used vii If the actual raw observations are to be used the csv file loaded must contain observed values for each batch in different columns starting with the first column Also the column labels must be the first row of the data in all cases as earlier remarked viil After entering or loading the correct data successfully click the continue button to view the chart and all the control limits The chart can be exported following step 1 vi above The S Chart Like R chart the S chart is a type of control chart used to monitor process variation using the standard deviations of the subsamples To construct the S chart the following statistics are required CL s s We l ci UCL S Z r Cy l ci K esi z 3 Ci where S is the standard deviation of samples in group j given by and S l n while constant c4 is as defined in Montgomery 2000 and Champ and Woodall For varying group sample sizes nj the above estimators become 1 m CL S S gt n j 2 UCL S Z 9 1 cy 2 lg DS respectively where o is estimated by andc n is as earlier stated but evaluated at m cn each group sample sizes nj Analysis using SQC software
5. is Your Capability Index Applied Statistics 39 331 340 Champ C W and Woodall W H 1987 Exact Results for Shewhart Control Charts with Supplementary Runs Rules Technometrics 29 393 399 Grant E L and R S Leavenworth 1980 Statistical quality control 5 ed New York M cGraw Hill Montgomery D C 2000 Introduction to Statistical Quality Control 4th ed John Wiley amp Sons New York NY USA Montgomery DC 2005 Introduction to Statistical Quality Control 5th edition John Wiley amp Sons New York NY USA Wetherill G B and Brown D W 1991 Statistical Process Control New York Chapman amp Hall Zhang S and Wardrop 1990 Interval Estimation of the Process Capability Index Communications in Statistics Theory and M ethods 19 21 4455 4470 N F Zhang G A Stenback D M Wardrop Interval Estimation of the Process Capability Index Communications in Statistics Theory and Methods 19 21 4455 4470 1990 15
6. n m j gt n j l lt M X Xij II II Here Individual UCL and LCL are computed for each group ki by UCL X Z Ea 24 7 O fe 241 LCL X Z The estimate of o above is determined by rao or D depending on whether d n i ow the range or standard deviation of samples in each group is used LS ebsively Analysis using SQC software Vi Vil Launch the program and select X Bar chart from the type of chart options and click the OK button to continue In the options window select the form of the data to be used means S D or Ranges for summary statistics of samples or Actual values for actual observations of units in each group Select Click to type in data option to type in data or click Open a csv file option to load or open a csv file If Click to type in data and Actual values options are selected together then the number of samples batches must be specified in the Enter number of Samples below space irrespective of whether the Equal Sample sizes option or Unequal sample sizes option is selected Select Unequal sample sizes option if sample sizes in all batches are not equal if otherwise select Equal Sample sizes and enter the sample size in the text box labeled Enter sample size If the Unequal sample sizes option is selected the sample size text box will be deactivated and the user will hav
7. SQC software Vi 4 Launch the program and select U chart from the type of chart options and click the OK button In the options window select whether the sample sizes are equal or not across the group batches If the sample sizes are equal then user should supply sample size in the text box labeled Enter size of samples if the unequal sample size option is selected then the sample size text box will be deactivated and the user will have to supply the size of each sample in the data entry window Click on Click to type in data button to type in data or on Open a csv file button to load open an excel csv file Choose the number of sigma of interest and click on the continue button to proceed If Click to type in data option is selected a data entry window will be displayed If the Sample size is equal only one column will be displayed to type in number of defectives or proportion of defectives But if unequal sample sizes option is selected then two columns with labels No of defects per subgroup and Sizes will be displayed If Open a csv file option is selected then click on Browse to load a csv file with number of defects in the first column for equal sample sizes across the groups or with the number of defects and sample sizes in the first and second columns of the csv file respectively for unequal sample sizes Also the column labels must be the first row of the da
8. atch j The control limits are zA Y UCL p Z o n N l p n S LO pb Z gt For varying sample sizes nj the centre line is computed as above The control limits for sample j are given as k j gt UCL p Z 2 2 nm g gt LCL p Z TY W where pj d nj is the proportion of defectives in batch j Analysis using SQC software The following steps enumerate how to use SQC package to develop a P chart Launch the program and select P chart from the type of chart options and click the OK button li In the options window select the form of the data that will be supplied for the chart number of defectives or proportion defectives Note that if the data is in proportion of defectives per sample then select the proportion defectives option If the data is in number of defectives per sample then select the number of defectives option The default is number of defectives Vi Vil Vill 2 Select whether the sample sizes are equal or not If the sample sizes are equal then user should supply sample size in the text box labeled Enter size of samples if the unequal sample size option is selected then the sample size text box will be deactivated and user will have to supply the size of each sample in the data entry window Also the number of sigma width of the confidence interval to be used should be supplied The defa
9. defectives all values should be integers Also the values of the sample sizes to be specified for unequal sample sizes must be integer values No value should be negative After entering and loading the correct data successfully click the continue button to view the control limits and the chart If all previous steps had been done correctly and successfully then the chart and control limits window would be displayed The chart could be exported to external file or clip board copying for pasting This is done by right clicking on the chart and selecting the export dialog option select export format e g JPG j peg format BM P Bitmap format etc and select export destination clipboard for pasting file or printer Finally select the export size to have the plotted control chart The C Chart The C charts are used to monitor the number of defects per unit The statistics involve in the construction of the C chart are as follow 1 CL c De aps i where cj is the number of defects in unit batch j and m is the number of units inspected The control limits are UCL c Z ve 2 LCL c Z ve 2 Analysis using SQC software The following steps enumerate how to use SQC package to develop a C chart l Launch the program and select C chart from the type of chart options and click the OK button li In the options window select the Click to type in data option to type data or Open a csv file option to ope
10. e sample means the first column and the sample range second column and the respective sample size the third column can be entered The fourth column is optional where the sample standard deviation may be entered if the sample size is more than 25 However the SQC can accommodate range values for sample size up to n 2025 If Click to type in data and Actual values options are selected together irrespective the sample size a data entry window with m columns will be displayed where actual observations for each of the m groups will be provided The number of groups samples m must be specified in the Enter number of sample below space before continue If Open a csv file and means S D or Ranges options are selected together with equal sample size enter the sample size for each group in the box with Enter sample size n in the box below Continue to load a csv data file with the first and second columns containing the samples groups means and ranges standard deviations respectively Use sample standard deviations if the sample size in each group is more than 25 If Open a csv file and Actual values options are selected together irrespective the Sample size click on browse tab to load a csv data file with m columns of the actual observations After entering or loading the correct data successfully click the continue button to view the chart and all the control limits The chart can be ex
11. e to supply sizes of each sample in the data entry window Select Use sample ranges Use sample STD DEV or Use a Known process STD DEV option if the range of samples in each batch the standard deviation of samples in each batch or a Known process standard deviation is to be used to compute the UCL and LCL Choose the number of sigma of interest and click on the continue button to proceed If Click to type in data means S D or Ranges together with Use sample ranges or Use sample STD DEV options are selected with equal sample size a data entry window 11 Vill XI xii xiii with two columns will be displayed where the sample means the first column and sample range or standard deviation second column can be entered The sample size for each group must be entered into the box with Enter sample size n in the box below If Click to type in data means S D or Ranges together with Use sample STD DEV options are selected with unequal sample sizes a data entry window with three columns will be displayed where the sample means the first column and the sample standard deviation second column and the respective sample size the third column can be entered If Click to type in data means S D or Ranges together with Use sample Ranges options are selected with unequal sample sizes a data entry window with four columns will be displayed where th
12. n an excel csv Comma Separated Values file Choose the number of sigma of interest and click on the continue button to proceed ili If Click to type in data option is selected a data entry window will be displayed with a column where number of defects per units would be entered If Open a csv file option is selected the number of defects must be entered into the first column of the csv file with column name label specified Note that no value should be negative and all values should be integers iv After entering or loading the correct data successfully click the continue button to view the control limits and the chart The chart can be exported following step 1 vi above 3 The U Chart U chart is a type of control chart used to monitor number of defects count type data where the sample size is greater than one typically the average number of defects per unit The centre line for a u chart is computed by age oa II J nN Mes J where djis the number of defects in batch j and nj is the sample size in batch j j 1 m The control limits are II STET UCL u Z 2 arm LCL u Z 2 For varying sample sizes the centre line is computed as above However the control limits for Sample batch j are given as UCL u Z p 2 LCL u Z 2 Note that la the proportion of defects in batch j will be plotted against the batch number j rn J Analysis using
13. pe in data and either the means and Ranges or means and Standard Deviation are selected a data entry window with two columns will be displayed where the sample means the first column and the sample range or standard deviation second column could be entered only for equal sample sizes across the groups For unequal sample sizes the third column would be added where the respective sample sizes would be entered If Click to type in data and Actual values options are selected together irrespective of the sample size a data entry window with m columns will be displayed where actual observations for each of the m groups will be provided If Open a csv file and either the means and Ranges or means and Standard Deviation are selected together with equal sample size click on browse tab to load a csv data file with first and second columns containing the samples groups means and ranges standard deviations respectively For unequal sample sizes additional third column should be added where the sample sizes would be provided If Open a csv file and Actual values options are selected together irrespective of the Sample size click on browse tab to load a csv data file with m columns of the actual observations After entering or loading the correct data successfully click the continue button to view the process capability indices REFERENCES Bissell A F 1990 How Reliable
14. ported following step 1 vi above THE PROCESS CAPABILITY INDICES A process capability index uses both the process variability and the process specifications to determine whether the process is capable of meeting the preset specifications Zhang et al 1990 More details can be found elsewhere Grant and Leavenworth 1980 Wetherill and Brown 1991 The SQC software computes the Cp Cpr Com indices of a given manufacturing or service process using the following statistics C USL LSL eo ies xt C min CO CO USL LSL e e s eq o X t where USL is the upper specification limit LSL is the lower specification limit t is the target value and X is the mean of the process performance obtained from the sample A value of e is usually 6 in the computations of Cp and Cpm while e is taken to be 3 for C computations Bissell 1990 Also o is the standard deviation of the process computed using the group ranges as m R a IS N or the standard deviation as ano or the pooled variance given as M j d n M j c n S z where both d n and c n are as earlier defined and S al Sh 1 S j l n m mM C m i gt n m j l nm lI Analysis using SQC software The following steps enumerate how to use the application to compute the various process Capability indices Launch the program and select process capability from the type of chart options and click the OK bu
15. ta as earlier remarked All values should be positive integers After entering or loading the correct data successfully click the continue button to view the chart and all the control limits The chart can be exported following step 1 vi above The R Chart R chart is a type of control chart used to monitor process variation using the ranges of the subgroups The construction of R chart requires the computations of centre line CL and the upper and lower control limits given by u R17 I d d z Mg R17 I a ES d where Ris defined by R L 3 R and the values of d gt and ds are as defined in Montgomery ma 2000 and Champ and Woodall 1987 For varying group sample sizes the following estimators for the construction of R chart apply ders YR m j l gt i nN The upper and lower control limits for samples in group are given by UCL R Z 0d n 2 LCL R Z 0d n a where o is estimated by Ly 7 while ds is as earlier stated but only evaluated at each m jal 42 group sample sizes nj j 1 m Analysis using SQC software l Launch the program and select R chart from the type of chart options and click the OK button li In the options window select the form of the data to be used ranges already obtained or the actual observations of units in each group Select the Ranges option if the ranges are to be used or the Actual values option if the actual raw values are
16. to be used ili Select Click to type in data option to type in data or click Open a csv file option to load or open a csv file If Click to type in data and Actual values options are selected together then the number of samples batches must be specified in the Enter number of Samples below space irrespective of whether the Equal Sample sizes option or Unequal sample sizes option is selected iv Select Unequal sample sizes option if sample sizes in all batches are not equal if otherwise select Equal Sample sizes and enter the sample size in the text box labeled Enter sample size If the Unequal sample sizes option is selected the sample size text box will be deactivated and the user will have to supply sizes of each sample in the data entry window Choose the number of sigma of interest and click on the continue button to proceed v If Click to type in data option is selected a data entry window with one column for the range of each batch for equal sample sizes or a data entry window with two columns the first column for ranges and the second for sample sizes for unequal sample sizes will be oF displayed If actual raw observations are to be used a data grid with m columns indicating the number of groups batches desired would be displayed vi If Open a csv file option is selected then click on Browse to load a csv file with group ranges in the first
17. tton to continue li In the options window select the form of the data to be used from means and Ranges means and Standard Deviation or Actual values options lil If Actual values options is selected then select method of estimating capability sigma o from use average Range Use average Standard Dev or Use within subgroup variation option as the case may be Provide the number of sample only if Type in data option is selected iv If any of the options means and Ranges or means and Standard Deviation is selected then select whether the sample sizes are equal or not Specify the sample size n in the text box labeled Enter sample size for equal samples if otherwise select unequal Sample size option and the sample size text box will be deactivated and the user will have to supply sizes of each sample in the data entry window v Select the Click to type in data option to type data or Open a csv file option to load a csv data file 13 Vi vil viii XI xii Select the type of specification limit s used by the process Double specification Upper and lower Upper or Lower Also it may be necessary to specify the target value of the process If this is not supplied SQC would use the average of both the USL and LSL Choose the number of sigma of interest and click on the continue button to proceed If Click to ty
18. ult is 3 sigma which sets 99 74 confidence limit for upper control limit UCL and lower control limit LCL Click on the continue button to provide data Click the Click to type in data button to type in data on the interface or Open a csv file button to load open an excel csv Comma Separated Values file If Click to type in data option is selected a data entry window will be displayed If Sample size is equal only one column will be displayed to type in number of defectives or proportion of defectives But if unequal sample sizes option is selected then two columns with labels No of defectives per sample and sample sizes will be displayed If Open a csv file option is selected the number of defectives or proportion of defectives as the case may be must be entered into the first column of the csv file for equal sample sizes across the groups batches For unequal sample sizes the number of defectives or proportion defective as the case may be and the sample sizes should be entered in the first and second columns of the csv file respectively The column labels must be the first row of the data If column name s is are not specified the values in the first row will be taken as the column names labels which will automatically reduce the number of groups batches by one Note that if the form of data is proportion defective no value should be greater than 1 and if the form of data is number of
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