set ou e
vers 2.1
set di p 23
set mo 1
#d ;

di _n(5) in w
"                 PROCESS CAPABILITY ANALYSIS USING STATA" _n
"                 ---------------------------------------" _n(2);

di in g
"In this tutorial, we show how to use Stata to perform a process capability" _n
"analysis of a subset of some data in DeVor, Chang & Sutherland (1992). It" _n
"consists of (coded) measurements of the inside diameter of machined cylinder" _n
"bores obtained in 31 samples, each of size 5. The (coded) lower and upper" _n
"specification limits are" in y " 195" in g " and" in y " 203"
in g ", respectively." _n(2)

"We begin the analysis by using Stata's" in w " xchart" in g " and"
in w " rchart" in g " commands to determine" _n
"whether  the process is in control. If so, we then estimate the following" _n
"summary measures:" _n
"                   - process mean and standard deviation" _n
"                   - process capability indices" _n
"                   - fraction nonconforming" _n
"                   - percent yield" _n(2)

"We also plot a histogram of the measurements and perform a Shapiro-Wilk test" _n
"for normality." _n;


di in w ". infile x1-x5 using cylinder.dat";
n inf x1-x5 using cylinder.dat;

set mo 0; mor; set mo 1;


di _n in w _dup(75) "-" _n
in g "First, we " in w "describe" in g " and " in w "list"
in g " a portion of our data:" _n
in w _dup(75) "-" _n(2)
". describe";
n d;


di _n in w ". list in 1/3";
n l in 1/3;

set mo 0; mor; set mo 1;



di _n(4)
in w _dup(79) "-" _n
in g "Next, we use Stata's '"
in w "rchart"
in g "' command to plot an R-chart." _n(2)

"Check to see if points fall outside the control limits and whether the plotted" _n
"points exhibit a systematic pattern. If so, there is evidence that the process" _n
"variation is out of control." _n
in w _dup(79) "-" _n(15);

di in w ". rchart x1-x5, connect(l)";
set mo 0; mor;
cap n rchart x1-x5, connect(l);
set mo 1;



di _n(5)
in w _dup(79) "-" _n
in g "Since the R-chart exhibits process control, we next use Stata's '"
in w "xchart" in g "'" _n
in g "command to plot an Xbar-chart." _n(2)

"Check to see if points fall outside the control limits and whether the plotted" _n
"points exhibit a systematic pattern. If so, there is evidence that the process" _n
"mean is out of control." _n
in w _dup(79) "-" _n(15);

di in w ". xchart x1-x5, connect(l)";
set mo 0; mor;
cap n xchart x1-x5, connect(l);
set mo 1;


di _n(4)
in w _dup(79) "-" _n
in g
"Both the R-chart and Xbar-chart indicate that the process is in statistical" _n
"control. Therefore, we can now estimate the various relevant process" _n
"capability summary measures. We have to read in the data again as a single" _n
"sample (rather than 31 separate samples)." _n
in w _dup(79) "-" _n(12);

di in w ". drop _all" _n(2)
". infile x using cylinder.dat";
drop _all;
n inf x using cylinder.dat;

set mo 0; mor; set mo 1;


di _n(5)
in w _dup(79) "-" _n
in g
"We can have a visual assessment of process capability by obtaining a histogram" _n
"with lines representing the specification limits inserted. We use Stata's " _n
in w "graph" in g " command to obtain the required graphic." _n
in w _dup(79) "-" _n(16);

di in w ". gr x, bin(8) ylab xlab(192.5,196.5,200.5,204.5,208.5) normal xline(195,203)" _n(2);
set mo 0; mor;
cap n gr x, bin(8) ylab xlab(192.5,196.5,200.5,204.5,208.5) normal xline(195,203);
set mo 1;


di _n(5)
in w _dup(79) "-" _n
in g
"From the previous figure, we note that a fairly significant portion of the " _n
"histogram extends beyond the specification limits. This is an indication of " _n
"poor capability. We can quantify this by computing appropriate process " _n
"capabilty indices and other summary statistics but before we do so, we use " _n
"Stata's '" in w "swilk" in g "' command to check whether the sample data
supports the " _n
"hypothesis of a normal probability model for the measurements." _n
in w _dup(79) "-" _n(7);

di in w ". swilk x" _n(2);
n swilk x;

set mo 0; mor; set mo 1;


di _n(5)
in w _dup(79) "-" _n
in g
"The hypothesis of a normal probability model for the sample measurements" _n
"cannot be rejected at the 5 % level of significance." _n(2)

"We next use our '"
in w "pciest.ado" in g "' program to compute relevant process capability " _n
"indices and other summary statistics like fraction nonconforming and percent" _n
"yield. This program requires estimates of process mean and standard deviation." _n
in w _dup(79) "-" _n(3);

di in w " . sum x" _n(2);
n sum;

di _n(3) in w ". pciest 199.95 2.90, f(195) s(203)" ;

set mo 0; mor; set mo 1;

n pciest 199.95 2.90, f(195) s(203);

di _n(2)
in w _dup(79) "-" _n
in g
"The estimated process mean is close to the mid-point of the specification" _n
"range. However, the natural tolerance of the process is greater than the" _n
"allowable spread. This implies poor capability and this is reflected in" _n
"the values of the estimated capability indices and also in the percent" _n
"yield of the process." _n
in w _dup(79) "-";

set mo 0; mor; set mo 1;

drop _all;