{"text_format":"5","workbook":"xls","n_sheets":6,"sheets":["QC","p-chart","c-chart","Xbar & R chart","Process Capability","Acceptance Sampling"],"props":{"title":"P-Chart","subject":"POM 2nd Edition","creator":"Authorized Gateway Customer","last_modified_by":"SAT-User"},"defined_names":["accept_no","accept_no","Acceptance_no.__c","act_alpha","act_alpha","act_beta","act_beta","alpha","alpha","aql","aql","aql_ltpd","aql_ltpd","aql_ltpd","beta","beta","chart_data","chart_data","Defective","Defective","LCL","LCL","ltpd","ltpd","LTPD_AQL","n_x_aql","n_x_aql","n_x_aql","opt_accept_no","opt_accept_no","opt_samp_size","opt_samp_size","p_accept","p_accept","pct_defective","pct_defective","pData","pData","PropData","PropData","sample_size","sample_size","Sample_size__n","Sample_size__n","table_data","table_data","table_data","UCL","UCL"],"not_rendered":{"charts":6,"images":9,"macros":1,"external_links":5,"defined_names":53,"comments":2},"notes":{"written":2,"chars":96},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"QC","index":0,"n_rows":79,"n_cols":2,"rows_kept":79,"merged":[[2,1,2,2],[15,1,15,2],[29,1,29,10],[44,1,44,3],[60,1,60,3]],"flags":["formulas_cached_only"]}
["Quality Control"]
[]
[null,"p-chart"]
[null,"The p-chart is used to control the proportion of defective items in a sample. "]
[null,"User inputs the no. of samples, sample size, sigma limits, and no. of defectives in each sample. "]
[null,"Sigma limits refer to the number of standard deviations used to establish the control limits. "]
[null,"   Control limits are normally set at 1, 2, or 3 standard deviations from the mean. "]
[null,"   Sigma limits are the Z value in the p-chart formulas. "]
[null,"The number of samples can range from 2 to 30. The sample size is unlimited."]
[]
[null,"Excel calculates the proportion defective, p-bar, and the upper and lower control limits for the control chart. "]
[null,"The control limits and mean are graphed, along with the proportion defectives. "]
[null,"The decision maker determines whether or not the process is in control. "]
[null,"A process is in control if all points lie between the control limits and if no patterns are evident. "]
[]
[null,"c-chart"]
[null,"The c-chart is used to control the number of defects in an item."]
[null,"User inputs the no. of samples, the no. of defects in each sample, and the sigma limits. "]
[null,"Sigma limits refer to the number of standard deviations used to establish the control limits. "]
[null,"   Control limits are normally set at 1, 2, or 3 standard deviations from the mean. "]
[null,"   Sigma limits are the Z value in the c-chart formulas. "]
[null,"The number of samples can range from 2 to 30. "]
[]
[null,"Excel calculates c-bar, and the upper and lower control limits for the control chart. "]
[null,"The control limits and mean are graphed, along with the no. of defects. "]
[null,"The decision maker determines whether or not the process is in control. "]
[null,"A process is in control if all points lie between the control limits and if no patterns are evident. "]
[]
[null,"Xbar & R chart"]
[null,"X-bar and R charts are used to control the central tendency and dispersion of a process. "]
[null,"User inputs no. of samples and sample size, along with data from several observations in each sample."]
[null,"Multiple observations are needed to ensure the process follows a normal distribution."]
[]
[null,"Excel calculates the average of each sample, X-bar, and the range of each sample, R. "]
[null,"The average of the averages, X-bar-bar is also calculated and used in the control limit formulas. "]
[null,"The control limit formulas are shown on the worksheet. The A and D variables refer to the Control Chart Factors Table."]
[null,"   (Scroll down the worksheet to find it). The correct table values are associated with the problem's sample size."]
[null,"    The appropriate entries have been copied from the Control Chart Factors Table and appear at the top of the worksheet."]
[]
[null,"Both an X-bar and an R-chart are graphed for each problem. They include the control limits, the mean, and X-bar or R values. "]
[null,"The decision maker determines whether or not the process is in control. "]
[null,"Both the X-bar and R charts have to be in control for the process to be in control. "]
[null,"A process is in control if all points lie between the control limits and if no patterns are evident. "]
[]
[null,"Process capability"]
[null,"Process capability determines whether a process is capable of meeting product specifications. "]
[null,"User inputs design target, design tolerance, process mean and process standard deviation."]
[null,"The design tolerance is a +/- value expressed as a positive number. "]
[]
[null,"Excel calculates the upper and lower spec limits, the process capability ratio, Cp, and the process capability index, Cpk."]
[null,"Cp compares the design tolerance range with the process range in a ratio format."]
[null,"If Cp =1, the process is just capable. If Cp< 1, the process is incapable. If Cp is >1, the process is capable."]
[null,"A Cp value of 1 is 3 sigma quality. A Cp value of 2 is 6 sigma quality."]
[]
[null,"Cpk determines whether the mean of the process is centered between the specification limits. "]
[null,"The mean is centered when Cp and Cpk are equal."]
[null,"If Cpk <1, the mean is off-center and defects will occur. "]
[null,"If Cpk >1, the mean may be off-center but it is still capable of meeting product specs."]
[null,"A process that is in control is not necessarily capable."]
[]
[null,"Acceptance sampling"]
[null,"Acceptance sampling is used to decide whether or not to accept a lot of goods based on sample results."]
[null,"User inputs AQL and LTPD. Excel calculates the sample size and acceptance number."]
[]
[null,"AQL = acceptance quality level; an acceptable % defective; expressed as a decimal no. "]
[null,"LTPD = lot tolerance percent defective; the maximum % defective tolerated by the consumer; expressed as a decimal no."]
[null,"Sample size = the number of items to be tested"]
[null,"Acceptance no. = the maximum no. of defective items in the sample that are allowed for the lot to be accepted"]
[]
[null,"The best sampling plan model assumes an alpha of .05 and a beta of .10. "]
[null,"Alpha = producer's risk; the probability that a good lot is rejected"]
[null,"Beta = consumer's risk; the probability that a bad lot is accepted"]
[]
[null,"To graph a sampling plan, enter a sample size and acceptance no. into the trial sampling plan."]
[null,"The graph, called an Operating Characteristic (OC) Curve, shows the probability of accepting a lot given different levels of quality."]
[null,"The actual Alpha and Beta from the graph are shown."]
[]
[null,"To construct an OC curve for the best sampling plan, input the sample size and acceptance no. calculated earlier into the trial sampling plan."]
[null,"The actual Alpha and Beta should be close to .05 and .10 but may not match exactly."]

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["p-Chart"]
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["Input:",null,null,"Output:"]
["No. of samples",100,null,"p =",0.23]
["Sample size ",2,null,"UCL =",{"v":1.1227205609819906,"d":"1.12"}]
["Sigma limits",3,null,"LCL =",{"v":0,"d":"0.00"}]
[]
[null,null,"Calculations"]
[null,"Number of","Proportion"]
["Sample","Defectives","Defective","p","UCL","LCL"]
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[4,5,{"v":2.5,"d":"2.500"},0.23,{"v":1.1227205609819906,"d":"1.1227"},{"v":0,"d":"0.0000"}]
[5,5,{"v":2.5,"d":"2.500"},0.23,{"v":1.1227205609819906,"d":"1.1227"},{"v":0,"d":"0.0000"}]
[6,5,{"v":2.5,"d":"2.500"},0.23,{"v":1.1227205609819906,"d":"1.1227"},{"v":0,"d":"0.0000"}]
[7,5,{"v":2.5,"d":"2.500"},0.23,{"v":1.1227205609819906,"d":"1.1227"},{"v":0,"d":"0.0000"}]
[8,5,{"v":2.5,"d":"2.500"},0.23,{"v":1.1227205609819906,"d":"1.1227"},{"v":0,"d":"0.0000"}]
[9,5,{"v":2.5,"d":"2.500"},0.23,{"v":1.1227205609819906,"d":"1.1227"},{"v":0,"d":"0.0000"}]
[10,5,{"v":2.5,"d":"2.500"},0.23,{"v":1.1227205609819906,"d":"1.1227"},{"v":0,"d":"0.0000"}]
["Total",46]

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["c-Chart"]
[{"$nulls":9},"c-Chart Formulas"]
["Input:",{"$nulls":3},"Output:"]
["No. of samples",10,null,null,"c-bar",{"v":2.5,"d":"2.50"}]
["Sigma limits",2,null,null,"UCL",{"v":5.66227766016838,"d":"5.66"}]
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[null,null,"Calculations"]
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[4,3,{"v":2.5,"d":"2.50"},{"v":5.66227766016838,"d":"5.66"},{"v":0,"d":"0.00"}]
[5,2,{"v":2.5,"d":"2.50"},{"v":5.66227766016838,"d":"5.66"},{"v":0,"d":"0.00"}]
[6,2,{"v":2.5,"d":"2.50"},{"v":5.66227766016838,"d":"5.66"},{"v":0,"d":"0.00"}]
[7,4,{"v":2.5,"d":"2.50"},{"v":5.66227766016838,"d":"5.66"},{"v":0,"d":"0.00"}]
[8,4,{"v":2.5,"d":"2.50"},{"v":5.66227766016838,"d":"5.66"},{"v":0,"d":"0.00"}]
[9,2,{"v":2.5,"d":"2.50"},{"v":5.66227766016838,"d":"5.66"},{"v":0,"d":"0.00"}]
[10,2,{"v":2.5,"d":"2.50"},{"v":5.66227766016838,"d":"5.66"},{"v":0,"d":"0.00"}]
["Total",25]

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["Xbar and R Charts"]
[]
["Input:",{"$nulls":3},"Output:",{"$nulls":3},"Table Values"]
["No. of samples",{"$nulls":4},"X-Bar","Range",null,"N",0]
["Sample size",{"$nulls":3},"UCL",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},null,"A2",{"$error":"#N/A"}]
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[null,"Observations",{"$nulls":4},"Calculations",null,"Xbar Chart",null,"R-chart"]
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[8,{"$nulls":5},{"$error":"#DIV/0!"},{"v":0,"d":"0.00"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
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[10,{"$nulls":5},{"$error":"#DIV/0!"},{"v":0,"d":"0.00"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
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{"$rows_empty":20}
["Control Chart Factors for Xbar and R Charts"]
["Sample size, n","Mean Factor, A2","Upper Range, D4","Lower Range, D3"]
[2,1.88,3.268,0]
[3,1.023,2.574,0]
[4,0.729,2.282,0]
[5,0.577,2.115,0]
[6,0.483,2.004,0]
[7,0.419,1.924,0.076]
[8,0.373,1.864,0.136]
[9,0.337,1.816,0.184]
[10,0.308,1.777,0.223]
[11,0.285,1.744,0.256]
[12,0.266,1.716,0.284]
[13,0.249,1.692,0.308]
[14,0.235,1.671,0.329]
[15,0.223,1.652,0.348]
[16,0.212,1.636,0.364]
[17,0.203,1.621,0.379]
[18,0.194,1.608,0.392]
[19,0.187,1.596,0.404]
[20,0.18,1.586,0.414]
[21,0.173,1.575,0.425]
[22,0.167,1.566,0.434]
[23,0.162,1.557,0.443]
[24,0.157,1.548,0.452]
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["Input:","Design target ="]
[null,"Design tolerance (+/-) ="]
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[null,"Process mean ="]
[null,"Process standard deviation ="]
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[null,"Lower spec limit =",null,{"v":0,"d":"0.00"}]
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