Practical Control Charts Case Study

Prévia do material em texto

<p>Practical	Control	Charts</p><p>Control	Charts	Made	Easy</p><p>By</p><p>Colin	Hardwick</p><p>Copyright	©	Colin	Hardwick</p><p>Smashwords	Edition</p><p>Portions	of	information	contained	in	this	publication/book	are	printed	with</p><p>permission	of	Minitab	Inc.	All	such	material	remains	the	exclusive	property	and</p><p>copyright	of	Minitab	Inc.</p><p>All	rights	reserved.</p><p>Contents</p><p>Introduction</p><p>What	are	Control	Charts?</p><p>When	Should	They	Be	Used?</p><p>Main	steps	in	constructing	control	charts</p><p>Summary</p><p>Introduction</p><p>This	guide	has	been	produced	specifically	for	engineers	to	implement	control</p><p>charts	and	gain	maximum	understanding	of	a	process	to	improve	it.	It	will	allow</p><p>you	to	solve	real	world	problems.	It	does	not	discuss	the	history	or	mathematics</p><p>of	the	technique	except	where	absolutely	necessary	to	illustrate	an	important</p><p>point.</p><p>Control	Charts	are	an	incredibly	powerful	tool	in	the	right	hands	and	will	allow</p><p>proper	understanding	of	process	performance.	This	will,	in	turn,	allow	that</p><p>process	to	be	improved	and	eliminate	wasted	activity	based	on	assumed</p><p>knowledge	of	a	process	rather	than	actual	data.</p><p>In	this	guide,	a	software	package	called	Minitab®	Statistical	Software	is	used	to</p><p>construct	control	charts	and	analyse	process	performance.	You	can	download	a</p><p>free	30-day	trial	at	www.minitab.com</p><p>Minitab	is	just	one	software	package	that	will	do	this	but	it	is	my	preferred</p><p>package	simply	because	I	believe	it	to	be	the	best	available	–	both	for	ease	of	use</p><p>and	accuracy	of	analysis.	I	have	included	several	screenshots	taken	from	Minitab</p><p>where	such	screenshots	aid	explanation.</p><p>Traditional	teaching	of	Control	Charts	is	generally	poor	in	my	opinion.	This	is</p><p>for	two	principal	reasons;</p><p>The	teaching	is	carried	out	by	a	mathematician	or	statistician,	who	blinds	the</p><p>student	with	complex	formulae	and	makes	the	subject	seem	far	more	complex</p><p>than	necessary.	Result;	students	who	will	forever	decry	the	technique	as	too</p><p>complex	or	too	time	consuming	to	be	of	any	practical	use	in	the	real	engineering</p><p>world.</p><p>The	teaching	is	carried	out	by	a	real-world	engineer,	who	does	not	have</p><p>sufficient	grasp	of	the	subject	matter	to	convey	it	succinctly	and	simply.	Result;</p><p>students	who	don’t	believe	that	the	technique	works	and	therefore	steer	clear	of</p><p>it	in	preference	of	what	they	know	best	–	changing	one	factor	at	a	time	and</p><p>testing	the	result.	I	will	show	later	that	in	the	clear	majority	of	cases	this	is	quite</p><p>simply	the	wrong	approach.</p><p>So,	work	through	the	text,	don’t	worry	it’s	short,	and	use	Minitab	to	try	out	the</p><p>various	examples.	You	will	quickly	see	just	how	powerful	this	tool	is	in	practice</p><p>and	how	easy	it	is	to	use.</p><p>What	are	Control	Charts?</p><p>Control	charts	are	a	simple	and	effective	way	to	monitor	process	performance.</p><p>They	will	show	you	when	a	process	is	out	of	control.	This	means	that	a	process</p><p>is	not	stable	and	some	form	of	corrective	action	is	required.</p><p>Control	charts	are	a	method	of	graphing	process	data	in	time	order.	Major</p><p>features	include	a	centre	line	and	control	limits,	one	upper	limit	and	one	lower</p><p>limit.	The	centre	line	is	the	performance	mean	and	the	limits	show	process</p><p>variation.	The	most	common	limits	are	based	on	3	standard	deviations	of	the</p><p>process	data.	The	upper	limit	is	the	process	mean	+	(3	standard	deviations)	and</p><p>the	lower	limit	is	process	mean	–	(3	standard	deviations).</p><p>It	is	extremely	important	not	to	confuse	control	limits	with	tolerance	limits.</p><p>The	process	itself	cannot	read	a	drawing	and	understand	tolerances	–	it</p><p>produces	output	with	variation,	irrespective	of	where	the	tolerance	limits</p><p>are	set!</p><p>A	good	process	has	variation	within	the	control	limits	and	the	specification	limits</p><p>are	outside	the	control	limits.	This	means	that	the	process	is	in	control	and	will</p><p>produce	output	that	is	consistently	within	tolerance.</p><p>When	Should	They	Be	Used?</p><p>In	engineering	and	science,	the	most	common	reasons	for	using	control	charts</p><p>are;</p><p>To	monitor	the	performance	of	a	process.</p><p>To	tell	you	when	a	process	is	drifting	or	is	out	of	control.</p><p>To	identify	reasons	for	changes	in	variation.</p><p>To	allow	changes	to	be	made	to	the	process	and	assess	the	effect	on	process</p><p>performance.</p><p>There	are	several	other	reasons	but	let’s	keep	it	simple	for	now	and	consider	only</p><p>the	above	reasons	which	will	account	for	most	of	the	problems	you	decide	to</p><p>solve.</p><p>Main	steps	in	constructing	control	charts</p><p>Step	1:	Choose	the	appropriate	control	chart	for	your</p><p>data</p><p>The	first	question	to	ask	is	“is	your	data	continuous	or	attribute	data?”</p><p>Continuous	data	usually	involves	decimals	or	fractions.	Examples	are	diameter,</p><p>height,	weight,	time	etc.</p><p>Attribute	data	is	usually	pass/fail	data	rather	than	variable	data.	Examples</p><p>include	the	number	of	defective	items	in	a	group	or	the	number	of	defects	in	a</p><p>unit.</p><p>The	second	question	to	ask	is	“will	you	collect	data	individually	or	will	you</p><p>collect	it	in	sub-groups?”</p><p>Collecting	individual	data	means	just	that.	There	is	no	grouping	at	all	and	each</p><p>data	point	is	considered	independent	of	another.</p><p>Collecting	sub-group	data	means	that	a	group	of	units	have	been	created	under</p><p>the	same	set	of	conditions.	As	an	example,	suppose	you	are	operating	a	process</p><p>which	produces	200	units	per	hour.	Simply	collecting	individual	data	would</p><p>mean	that	you	have	a	high	number	of	results	in	a	short	space	of	time	and</p><p>therefore	might	miss	longer	term	trends	and	effects.	A	way	around	this	is	to	take</p><p>a	random	sample	of,	say,	10	units	each	hour	for	24	hours.	Each	sample	of	10</p><p>units	is	called	a	sub-group.</p><p>The	sub-group	size	should	not	be	too	large.	Typical	sizes	are	5-10	units	collected</p><p>every	hour	or	so	are	common.	The	idea	is	to	collect	data	(in	this	case	sub-</p><p>groups)	for	long	enough	to	make	sure	that	major	sources	of	variation	have	the</p><p>opportunity	to	occur.	If	you	take	small	frequent	samples	then	a	shift	in	process</p><p>performance	will	be	seen	sooner	rather	than	later	and	you	will	have	less</p><p>potentially	defective	product	with	which	to	deal.</p><p>Having	considered	the	above	two	questions,	we	can	select	the	appropriate</p><p>control	chart.</p><p>Let’s	turn	our	attention	to	the	different	types	of	charts	that	are	available	in</p><p>Minitab.</p><p>If	you	click	on	Stat/Control	Charts	you	will	see	the	seven	types	of	charts	that	are</p><p>available	in	addition	to	something	called	“Box	Cox	Transformation”.	This	is	a</p><p>technique	which	allows	normally	distributed	data	to	be	transformed	to	a	more</p><p>normal	distribution.	Control	Charts	assume	data	which	is	normally	distributed	so</p><p>if	your	data	is	not	then	Box	Cox	can	be	used	to	allow	the	use	of	Control	Charts.</p><p>Most	people	find	it	difficult	to	understand	if	data	is	normal	enough	to	use</p><p>Control	Charts	–	my	experience	is	that	most	engineering	and	scientific	data	is</p><p>normal	enough	to	make	use	of	the	power	of	control	charts.	Minitab	does	have</p><p>several	tools	available	with	which	to	test	normality	and	I’ll	cover	these	in	some</p><p>of	the	later	examples.</p><p>The	seven	types	of	charts	that	you	will	see	listed	are	shown	in	the	following</p><p>screenshot:</p><p>Let’s	go	through	each	of	these	in	turn.</p><p>Types	of	control	charts</p><p>Variables	Charts	for	Subgroups</p><p>If	you	click	on	this	option	you’ll	see	this:</p><p>There	are	clearly	seven	options,	which	we’ll	deal	with	in	turn.</p><p>Xbar-R	Chart</p><p>This	type	of	chart	is	generally	used	when	you	have	continuous	data	and	sub-</p><p>group	sizes	of	8	or	less.	They	will	show	you	the	stability	of	a	process	over	time,</p><p>enabling	the	identification	and	correction	of	process	instabilities.	As	an	example,</p><p>let’s	take	a	typical	data	set	with	and	plot	it	using	Minitab.</p><p>Click	on	the	Xbar-R	option	as	shown	in	the	screenshot	above	and	you’ll	see	this:</p><p>I’ve	entered	the	data	into	the	first	column	of	Minitab,	which	is	C1.	In	this	case,</p><p>all	the	data	is	in	one	column	so	the	first	option	shown	by	the	arrow	can	remain</p><p>without	change.	The	other	option	is	“Observations	for	a	sub-group	are	in	one</p><p>row	of	columns”.	This	is	used	when	you	have	sub	group	data	and	Minitab	will</p><p>assume	that	the	data	is	entered	into	the	worksheet	in	time	order.	So,	for	each	sub</p><p>group	the	data	is	entered	into	adjacent	rows.	Here’s	an	example	of	data	entry:</p><p>This	shows	three	sub	groups,</p><p>each	with	three	data	points.</p><p>So,	let’s	return	to	our	previous	example.</p><p>You	will	notice	that	the	box	on	the	left	is	empty.	This	is	where	we	would	expect</p><p>to	see	C1,	the	column	identity	containing	our	data.	To	see	this,	simply	click	in</p><p>the	empty	box	directly	underneath	the	option	“All	observations	for	a	chart	are	in</p><p>one	column”	and	C1	will	appear	in	the	left-hand	selection	box.	It	will	look	like</p><p>this:</p><p>Now	click	on	C1	and	then	the	“Select”	button	underneath	it.	You’ll	then	see	this:</p><p>Since	this	type	of	chart	is	variable	with	sub-groups,	the	next	step	is	to	enter	the</p><p>sub-group	size	which	must	be	between	2	and	100.	We’ll	enter	5	as	the	size	as	an</p><p>example.</p><p>Below	the	sub-group	size	box,	you’ll	see	five	option	boxes;	Scale,	Labels,</p><p>Multiple	Graphs,	Data	Options,	Xbar-R	Options.	Let’s	go	through	them	in	turn:</p><p>Scale:	This	option	provides	several	sub-options.	If	you	click	on	the	scale</p><p>button	you’ll	see	this:</p><p>You	can	select	either	‘Index”	or	“Stamp”	using	the	two	radio	buttons	provided.</p><p>The	“Stamp”	option	will	add	labels	that	show	values	such	as	dates	and	times</p><p>from	columns	that	you	specify.	The	“Index”	option	will	add	labels	that	show	the</p><p>order	of	the	data.	My	advice?	–	can	be	useful	but	I’d	simply	leave	the	option	set</p><p>as	is	and	don’t	worry	about	making	the	job	more	complex	than	necessary.</p><p>Axis	and	Ticks:	Simply	provides	an	option	to	show	(or	not)	axes	and	tick	lines</p><p>for	both	axes	of	the	control	chart.	Again	–	just	leave	set	to	default	is	my	advice.</p><p>Gridlines:	Allows	the	option	to	display	gridlines	for	ticks.</p><p>Reference	Lines:	allows	the	option	to	add	reference	lines	to	the	control	chart	–</p><p>you	can	guess	my	advice!</p><p>Labels:	as	you	might	expect,	this	provides	an	option	to	add	titles,	sub-titles</p><p>and	footnotes	to	control	charts.	Very	useful	if	you	have	several	similar</p><p>looking	control	charts	since	it	prevents	confusion	about	which	one	you	are</p><p>looking	at.</p><p>Multiple	Graphs:	This	is	actually	a	very	useful	option	which	I	generally</p><p>recommend	you	use.	When	you	enter	more	than	one	column	of	data</p><p>Minitab	will	create	separate	charts	for	each	column.	When	you	have	several</p><p>control	charts	it’s	very	useful	to	use	the	same	y-scale	for	each	chart	–	which</p><p>allows	easier	understanding	of	the	variability	of	each	data	set	for	each</p><p>control	chart.</p><p>Data	options:	This	allows	you	to	include	or	exclude	specific	rows	of	data.</p><p>The	default	is	to	include	all	data	points	–	If	you	have	specific	data	which	has</p><p>a	good	reason	to	be	excluded	then	this	is	a	good	way	of	achieving	it.	When	I</p><p>say,	“good	reason”	I	don’t	mean	excluding	data	points	outside	control</p><p>limits.	This	is	simply	cherry	picking	the	data	to	show	what	you	want.</p><p>Xbar-R	Options:	This	provides	several	options	as	shown	in	the	following</p><p>screenshot:</p><p>I	don’t	tend	to	use	these	options	much	but	I’ll	talk	you	through	them:</p><p>Parameters:	allows	you	to	set	a	mean	and	standard	deviation	rather	than</p><p>Minitab	estimating	it	from	the	data.	Rarely	a	requirement	so	I	tend	to	leave</p><p>Minitab	to	do	its	estimating.</p><p>Estimate:	allows	you	to	exclude	specific	sub-groups	when	estimating	process</p><p>parameters.	Also	provides	two	options	for	estimating	standard	deviation.</p><p>The	default	is	R-bar	which	is	simply	the	average	of	all	the	sub-group</p><p>ranges.	This	is	perfectly	adequate	for	sub-group	sizes	of	between	2	and	8.</p><p>This	will	certainly	cover	the	vast	majority	of	control	charts	that	you</p><p>produce.</p><p>Limits:	allows	you	to	draw	additional	control	limits	on	charts	and	allows	an</p><p>option	to	calculate	control	limits	when	the	sub-group	sizes	are	not	the	same.</p><p>This	is	quite	rare	and	therefore	the	option	will	rarely	be	used.</p><p>Tests:	allows	various	options	to	change	the	specific	tests	for	identifying</p><p>special	cause	variation	(see	glossary)	In	most	cases	the	default	settings	are</p><p>perfectly	adequate.</p><p>Stages:	this	allows	you	to	create	a	historical	control	chart	demonstrating</p><p>how	a	process	changes	over	specific	periods	of	time.	This	is	most	useful</p><p>when	making	changes	to	a	process	because	of	a	control	chart.	You	can	then</p><p>see	the	process	before	the	change	and	the	process	after	the	change	to	see	the</p><p>difference	on	the	same	chart.</p><p>Box-Cox:	allows	the	data	to	be	subject	to	Box	Cox	transformation,	which</p><p>I’ve	explained	previously.</p><p>Display:	allows	various	display	options	to	be	changed,	such	as	which	sub-</p><p>groups	to	display.</p><p>Storage:	allows	the	saving	of	various	parameters	such	as	points	plotted	and</p><p>control	limit	values.</p><p>The	other	types	of	charts	for	sub-groups	are:</p><p>Xbar-S	Chart</p><p>This	type	of	chart	is	generally	used	when	you	have	continuous	data	and	sub-</p><p>group	sizes	of	9	or	more.	Like	the	X-bar-R	chart	it	enables	you	to	monitor	the</p><p>stability	of	a	process	over	time,	enabling	the	identification	and	correction	of</p><p>process	instabilities.	The	basic	options	are	identical	to	the	Xbar-R	chart	options.</p><p>I-MR-R/S	(Between/Within)	Chart</p><p>This	type	of	chart	is	used	when	each	sub-group	is	a	different	part	or	batch.	It</p><p>allows	you	to	monitor	the	mean	and	the	variation	within	sub-groups.	Like	the</p><p>previous	charts,	you	can	view	process	stability	over	time	and	identify	and	correct</p><p>process	instabilities.</p><p>Xbar	Chart</p><p>This	type	of	chart	is	very	like	the	Xbar-S	chart	and	as	the	name	suggests,	it	looks</p><p>at	the	mean	of	a	process	with	continuous	data	in	sub-groups.</p><p>R	Chart</p><p>This	type	of	chart	is	very	like	the	Xbar-R	chart	and	as	the	name	suggests,	it	looks</p><p>at	the	variation	of	a	process	when	you	have	continuous	data	and	sub-group	sizes</p><p>of	no	more	than	8.</p><p>S	Chart</p><p>This	type	of	chart	is	very	like	Xbar-S	chart	and	it	looks	at	the	variation	(standard</p><p>deviation)	of	a	process	when	you	have	continuous	data	and	sub-group	sizes	of	9</p><p>or	more.</p><p>Zone	Chart</p><p>This	is	a	slightly	different	type	of	chart.	It	is	used	in	specific	circumstances	when</p><p>you	want	to	monitor	the	mean	of	a	process	with	a	control	chart	that	uses	sigma</p><p>intervals	(these	are	termed	zones)	and	a	type	of	cumulative	scoring	system	to</p><p>identify	special	causes.	I	don’t	find	it	very	useful	and	rarely	use	it.</p><p>Variables	Charts	for	Individuals</p><p>These	charts,	as	the	name	suggests,	are	used	when	you	have	continuous	data</p><p>which	is	not	in	sub-groups.	Let’s	look	at	the	various	types:</p><p>I-MR</p><p>Use	this	to	monitor	both	mean	and	variation	of	a	process	where	the	data	is</p><p>continuous	and	not	in	sub-groups.</p><p>Z-MR</p><p>Use	this	to	monitor	both	mean	and	variation	of	a	process	which	has	different</p><p>parts	when	there	are	not	many	parts	produced.	These	are	generally	known	as</p><p>short-run	processes	and	because	they	are	short	run	with	relatively	low	numbers</p><p>of	parts	they	often	don’t	produce	enough	data	to	allow	good	estimates	of	the</p><p>process	parameters.	This	type	gets	you	round	that	problem	by	pooling	and</p><p>standardizing	the	data.</p><p>Individuals</p><p>Use	this	to	monitor	the	mean	of	a	process	where	the	data	is	continuous	and	not	in</p><p>sub-groups.	You’ll	see	that	this	is	like	the	I-MR	chart	described	above.</p><p>Moving	Range</p><p>Use	this	to	monitor	the	variation	of	a	process	where	the	data	is	continuous	and</p><p>not	in	sub-groups.	You’ll	see	that	this	is	like	the	I-MR	chart	described	above.</p><p>Attributes	Charts</p><p>Let’s	now	turn	our	attention	to	attribute	charts.	If	you	select	Attribute	Charts</p><p>you’ll	see	this:</p><p>Let’s	go	through	the	eight	different	types	of	attribute	charts:</p><p>P	Chart	Diagnostic</p><p>I	don’t	use	this	type	of	chart	vary	often	but	it	can	be	very	useful	in	the	right</p><p>circumstances.</p><p>It	checks	for	something	called	overdispersion	or	underdispersion	in	the	data.</p><p>What	this	means	is	that	it	looks	at	expected	variation	versus	the	observed</p><p>variation	in	the	data.	If	there	is	a	significant	difference	then	the	solution	is	a</p><p>Laney	P	chart	–	since	this	adjusts	for	these	types	of	conditions.	At	its	simplest	–</p><p>if	you	don’t	test	then	you	could	make	incorrect	decisions	from	the	control	chart</p><p>output.</p><p>If	you	click	on	the	P	Chart	Diagnostic	option	you’ll	see	this:</p><p>We	select	the	column	containing	the	data	as	described	previously	and	set	the	sub</p><p>group	size.	There	is	then	an	option	to	omit	or	include	specific	sub-groups	when</p><p>estimating	parameters.	Include	all	of	them	unless	you	have	good	reasons	to	omit</p><p>them.	Good	reasons	might	be	known	problems	due	to</p><p>data	collection	mistakes	or</p><p>even	obvious	non-stable	conditions	in	the	data	such	as	the	producing	machine</p><p>running	through	a	warm	up	cycle	before	achieving	steady	state	conditions.</p><p>P</p><p>This	type	of	chart	is	used	to	monitor	the	proportion	of	defective	items,	where</p><p>each	item	can	be	easily	categorised	as	either	a	pass	or	a	fail.	There	are	the	same</p><p>options	as	described	in	the	Xbar-R	chart	previously.</p><p>Laney	P</p><p>As	described	in	the	P	Chart	diagnostic	section	previously,	this	is	used	when	the	p</p><p>chart	shows	excessive	over	or	under	dispersion.</p><p>NP</p><p>This	type	of	chart	is	used	to	monitor	the	number	of	defective	items,	where	each</p><p>item	can	be	easily	categorised	as	either	a	pass	or	a	fail.	There	are	the	same</p><p>options	as	described	in	the	Xbar-R	chart	previously.</p><p>U	Chart	Diagnostic</p><p>Like	the	P	charts	described	previously,	the	U	Chart	diagnostic	is	used	to	test	for</p><p>over	or	under	dispersion,	more	specifically	in	defect	data.</p><p>U</p><p>This	type	of	chart	is	used	to	monitor	the	number	of	defects	per	unit	and	each</p><p>item	can	have	multiple	defects.	It	has	the	same	options	as	the	Xbar-R	chart</p><p>described	previously.</p><p>Laney	U</p><p>Like	the	Laney	P,	this	type	of	chart	is	used	when	the	U	Chart	shows	excessive</p><p>over	or	under	dispersion.</p><p>C</p><p>This	chart	is	used	to	monitor	the	number	of	defects	where	each	item	can	have</p><p>multiple	defects.	Don’t	use	it	when	using	sub-groups	of	unequal	sizes,	since	its</p><p>designed	for	equal	sub-group	sizes.</p><p>Time	Weighted	Charts</p><p>These	types	of	charts	are	meant	to	supplement	normal	control	charts.	They	are</p><p>specifically	used	when	you	want	to	detect	small	shifts	in	process	performance</p><p>such	as	those	less	than	3	standard	deviations.	The	charts	described	previously	are</p><p>typically	used	to	detect	instability	in	processes	through	special	cause	variation.</p><p>Once	a	process	is	stable	and	in	control	a	time	weighted	chart	can	be	used	to</p><p>detect	small	but	significant	movements	in	process	performance.</p><p>There	are	three	types	of	time	weighted	charts	from	which	to	choose.	These	are:</p><p>Moving	Average	charts</p><p>Use	this	type	of	chart	when	you	want	to	detect	small	shifts	in	process	mean.	It</p><p>can	be	used	with	individual	or	sub-grouped	data.</p><p>Exponentially	Weighted	Moving	Average	(EWMA)	charts</p><p>These	are	used	to	detect	small	shifts	in	the	process	mean	with	little	influence</p><p>from	low	or	high	readings.	You	can	use	this	type	of	chart	for	both	individual	data</p><p>and	sub-grouped	data.</p><p>Cumulative	Sum	(CUSUM)	charts</p><p>Use	this	type	of	chart	to	detect	small	shifts	in	process.	It	plots	cumulative	sums</p><p>of	the	deviations	of	each	value	from	the	target	value.	Since	it	is	a	cumulative</p><p>plot,	small	shifts	in	the	process	mean	will	show	as	steadily	increasing	or</p><p>decreasing	trends.	You	can	use	it	for	both	individual	and	sub-grouped	data.</p><p>Multivariate	Charts</p><p>There	are	four	types	of	multivariate	charts	available	in	Minitab.	These	are:</p><p>T²	-	Generalized	Variance</p><p>T²</p><p>Generalized	Variance</p><p>Multivariate	EWMA</p><p>Let’s	look	at	each	of	these:</p><p>T²	-	Generalized	Variance</p><p>This	type	of	chart	is	very	like	the	X-bar,	Xbar-S	and	I-MR	charts	but	it	uses</p><p>multiple	variables	rather	than	just	one.	It	is	used	to	monitor	process	location	and</p><p>variability	of	two	or	more	variables	(which	are	related)	and	check	that	they	are	in</p><p>control.</p><p>If	you	click	on	the	T²	-	Generalized	Variance	option	you	will	see	this:</p><p>You	already	know	how	to	select	the	variables	and	enter	sub-group	size.	There	are</p><p>then	4	option	buttons,	three	of	which	I’ve	described	before	but	the	T2	–GV</p><p>Options	button	is	new	and	specific	to	this	type	of	chart.	Click	on	the	option	and</p><p>you’ll	see	this:</p><p>On	the	Parameter	tab,	you’ll	see	that	you	need	to	enter	the	mean	and	something</p><p>called	the	“Covariance	Matrix”.	You	can	see	the	instruction	about	entering</p><p>values	and	the	fact	that	Minitab	will	use	them	instead	of	estimating	them	from</p><p>the	data.	You	can	enter	a	mean	for	each	variable.	If	the	means	are	in	columns,</p><p>enter	one	column	per	variable.</p><p>Now	you	need	to	enter	the	covariance	matrix!	Covariance	is	simply	a	measure	of</p><p>the	extent	to	which	corresponding	elements	from	two	sets	of	ordered	data	move</p><p>in	the	same	direction.	The	two	sets	of	data	are	arranged	in	matrix	which	is	a	set</p><p>of	rows	and	columns.</p><p>The	other	options	are	very	like	the	ones	I	described	before	in	the	Xbar-R	chart</p><p>section.	My	advice	is	that	if	you	wish	to	use	this	type	of	chart	then	enlist	the	help</p><p>of	your	friendly	local	Black	Belt	or	Master	Black	Belt.</p><p>T²	Chart</p><p>This	type	of	chart	is	very	like	the	X-bar	and	individuals	charts	but	it	uses</p><p>multiple	variables	rather	than	just	one.	It	is	used	to	monitor	process	locations	of</p><p>two	or	more	variables	(which	are	related)	and	check	that	they	are	in	control.</p><p>Generalized	Variance</p><p>This	type	of	chart	is	used	to	monitor	the	process	variability	of	two	or	more</p><p>variables	(which	are	related)	and	check	that	they	are	in	control.	It	is	like	the	R,	S</p><p>and	Moving	Range	charts.	A	simple	example	is	a	process	which	uses	both</p><p>temperature	and	pressure.	These	two	are	clearly	related	and	you	may	want	to</p><p>understand	how	these	affect	an	output	variable	such	as	material	strength	by</p><p>monitoring	both	at	the	same	time.</p><p>(Top	Tip	–	Design	of	Experiments	is	a	superb	way	of	estimating	the	effect	of</p><p>each	variable	separately	and	the	combined	effect	called	an	interaction)</p><p>Multivariate	EWMA</p><p>This	type	of	chart	is	used	to	monitor	the	process	variability	of	two	or	more</p><p>variables	(which	are	related)	and	check	that	they	are	in	control	by	using	an</p><p>exponentially	weighted	control	chart.	Each	plotted	point	is	weighted	from</p><p>previous	data,	giving	more	weight	to	more	recent	data.	This	allows	you	to	detect</p><p>small	process	shifts	quickly.	It	is	like	the	EWMA	chart	but	uses	more	than	one</p><p>variable.</p><p>Rare	Event	Charts</p><p>There	are	two	types	of	Rare	Event	charts,	the	G	type	and	the	T	type.</p><p>G	type</p><p>This	is	used	when	you	are	interested	in	the	time	between	rare	events	or	the</p><p>number	of	opportunities	for	a	rare	event.	Traditional	charts	are	not	good	for	very</p><p>infrequent	events	since	they	require	large	amounts	of	data	to	calculate	accurate</p><p>control	limits.	This	would	take	very	large	amounts	of	time.	This	type	of	chart</p><p>resolves	that	issue.</p><p>T	type</p><p>These	are	used	to	monitor	the	time	between	rare	events.	You	may	wish	to	know</p><p>if	the	rate	is	increasing	or	decreasing	to	allow	early	management	action	–	this	is</p><p>the	chart	to	use	for	that	scenario.</p><p>Ok,	so	we’ve	looked	at	all	the	various	control	charts	available	in	Minitab.	The</p><p>choice	may	seem	overwhelming	but	the	PC	version	of	Minitab	includes	a	simple</p><p>flow	chart	to	make	control	chart	selection	easy	and	quick	(it’s	not	yet	available</p><p>in	the	Mac	version).	It	is	reproduced	below:</p><p>Figure	1:	Control	Chart	Selection	Flow	Chart</p><p>You	can	see	that	this	allows	simple	selection.	You	can	also	click	on	the	charts	at</p><p>the	bottom	and	you’ll	be	taken	to	the	correct	area	in	Minitab	to	create	the</p><p>selected	chart.</p><p>Step	2:	Choose	the	time-period	for	collection	of	data.</p><p>Once	you	have	selected	your	chart	you	need	to	select	an	appropriate	time-period.</p><p>In	practice	this	is	simple.	Select	a	time-period	that	is	highly	likely	to	show</p><p>variations	in	the	process	output.	As	an	example,	let’s	say	you	are	running	a</p><p>manufacturing	process	over	3	shifts	–	then	make	sure	you	cover	all	three	shifts	in</p><p>selecting	a	time-period	for	either	individual	data	or	sub-group	data.	Another</p><p>example	is	when	you	have	a	machine	with	multiple	stations,	say,	20	different</p><p>ones,	each	producing	a	single	part.	In	this	case	ensure	that	output	from	all	20</p><p>stations	is	included	in	your	sample	time-period.</p><p>Step	3:	Collect	the	data,	construct	the	control	chart</p><p>and	analyse	the	data.</p><p>As	data	is	produced,	log	it	and	when	you	have	all	the	data	it’s	time	to	use</p><p>Minitab’s	extensive	capability	to	select,	construct	and	analyse	the	data.	I’ve</p><p>covered	the	various	choices	of	control	chart	and	the	flow	chart	provides</p><p>guidance	on	which	one	to	select.	Later	I’ll	cover	some	worked	examples	step	by</p><p>step	to	show	you	how	to	construct	and	analyse	the	data.</p><p>Step	4:	Look	for	signals	on	the	control	chart.</p><p>This	is	where	it	starts	to	get	interesting.	The	first	thing	we	are	interested	in	is	the</p><p>identification</p><p>of	common	cause	and	special	cause	variation.	Common	cause</p><p>variation	is	contained	within	the	control	limits	on	a	control	chart	and	it’s	often</p><p>referred	to	as	the	usual	quantifiable	variability	from	a	process.	Special	cause,	on</p><p>the	other	hand,	is	unusual,	not	normally	observed	and	initially	non-quantified</p><p>variation.	As	the	name	suggests	this	is	variation.</p><p>The	basic	idea	is	to	eliminate	the	special	cause	variation	since	this	is	not</p><p>predictable	and	makes	the	process	unstable.	Once	we	have	done	that	we	can	set</p><p>about	reducing	the	common	cause	variation	if	required.	If	the	control	limits	lie</p><p>outside	the	tolerance	limits	then	you	will	be	producing	unacceptable	defects.	We</p><p>need	the	variation	in	process	output	to	be	such	that	the	tolerance	limits	are</p><p>outside	the	control	limits.	This	means	that	the	variation	in	process	output	is</p><p>predictable	and	a	large	proportion	will	be	acceptable	against	the	tolerances.</p><p>Most	control	charts	use	+/-	3	sigma	as	the	calculated	control	limits	and	if	all</p><p>process	output	is	within	these	limits	AND	the	tolerances	are	outside	these	limits</p><p>then	you	have	at	least	99.7%	of	output	meeting	the	tolerance.	Assuming	no</p><p>special	cause	variation	is	seen	then	you	have	a	process	which	is	both	stable	and</p><p>capable	(of	meeting	the	required	tolerances).</p><p>So	how	do	we	identify	special	cause	variation?	Special	cause	is	defined	when</p><p>certain	signals	are	observed.	Minitab	uses	eight	such	signals	and	you	can	see</p><p>them	(and	modify	them	if	required)	by	clicking	on	the	“Tests”	tab	shown	below</p><p>as	an	example	(this	is	for	an	I-MR	chart	but	the	same	tests	are	available	for	other</p><p>control	charts).</p><p>You	can	see	that	there	are	eight	tests	listed	with	K	being	the	test	values.	You	can</p><p>change	these	but	I’d	leave	them	as	default	if	I	were	you.	The	tests	are	self-</p><p>explanatory	and	Minitab	will	test	against	all	of	them	and	report	its	findings.</p><p>Step	5:	Take	appropriate	action	based	on	the	signals</p><p>The	type	of	action	taken	will	really	depend	on	the	type	of	test	failure	and</p><p>knowledge	of	the	process.	My	advice	is	to	gather	all	the	relevant	experts	together</p><p>and	discuss	the	results.	This	includes	the	quality	engineer	responsible	for	the</p><p>process	and	the	operatives	running	the	process.	The	test	results	should	be</p><p>discussed	and	reasons	for	test	failures	debated.</p><p>This	frequently	starts	to	highlight	issues	and	potential	reasons	for	the	failures.</p><p>Sometimes	people	ask,	“what	happens	if	we	can’t	identify	the	reasons	for	test</p><p>failures”	The	answer	is	to	debate	and	agree	potential	causes	and	act	by	changing</p><p>an	appropriate	machine	parameter.</p><p>Repeat	the	trial	and	create	a	new	control	chart.	Has	the	output	changed?	If	it	has</p><p>then	you	have	the	potential	to	affect	process	output.	If	it	has	not	then	you	can</p><p>cross	that	potential	root	cause	off	the	list	as	affecting	process	output.</p><p>Step	6:	Continue	to	monitor	the	process,	acting	as</p><p>appropriate.</p><p>If	the	process	is	stable	and	in	control	then	continue	to	monitor	the	process</p><p>(ideally	by	using	the	operatives	to	complete	the	control	charts)	to	ensure	it	stays</p><p>that	way.	In	this	way	process	drift	will	be	identified	quickly	and	very	often</p><p>before	any	significant	non-conformance	has	been	produced.</p><p>If	the	process	shows	special	cause	variation	is	present	by	exhibiting	failures	of</p><p>one	or	more	of	the	tests	described	earlier	then	go	back	to	step	5	and	take	further</p><p>action	before	repeating	the	process	run.</p><p>We’ve	now	looked	at	the	basic	step	by	step	approach	to	selecting	and	applying</p><p>control	charts	to	improve	a	process	but	it’s	easier	to	understand	with	some</p><p>worked	examples,	so	let’s	get	to	it.</p><p>Worked	Examples</p><p>Example	1	–	I-MR	Chart</p><p>We	have	been	asked	to	look	at	a	specific	problem	with	a	chemical	process.	There</p><p>are	specific	limits	that	are	required	to	be	met	for	the	output	chemical,	known	as</p><p>Minitabazene	(see	what	I	did	there?)	from	the	process.	The	product	needs	to</p><p>have	pH	within	specified	limits	of	2	and	6.	The	machines	manufacture	batches	of</p><p>the	chemical	and	one	sample	is	taken	from	each	batch.	The	data	is	not	sub-</p><p>grouped.</p><p>If	we	examine	the	control	chart	flowchart	we’ll	see	that	this	requires	an	I-MR</p><p>chart.</p><p>Let’s	measure	acidity	for	100	consecutive	batches.	We	get	the	operatives	to</p><p>sample	each	batch	and	collate	the	data	into	Minitab	by	placing	the	data	in	a</p><p>single	column.	It	looks	like	this.</p><p>There	is	an	assumption	that	data	is	normally	distributed	in	control	charts	so	let’s</p><p>check	that.</p><p>An	easy	way	is	to	examine	the	plotted	histogram	and	see	if	it	looks	something</p><p>like	a	normal	distribution	or	bell	curve.	To	do	this	we	click	on:</p><p>Stat/Quality	Tools/Capability	Analysis/Normal.	It	looks	like	this.</p><p>We	then	see	this:</p><p>We	click	on	C1	and	then	“Select”.	We	don’t	have	sub-groups	so	we	can	simply</p><p>enter	1	in	the	sub-group	size	and	then	the	lower	and	upper	specification	limits.</p><p>All	the	other	options	are	left	as	default	and	clicking	“OK”	produces	the</p><p>histogram	shown	below:</p><p>This	look	something	like	a	lumpy	bell	curve.	We	can	then	carry	out	further	tests</p><p>such	as	an	Anderson-Darling	Test	(yes	that’s	its	real	name!)	but	I’d	be	happy	to</p><p>assume	normality	at	this	point.	Let’s	take	a	quick	look	at	something	called	a</p><p>probability	plot.	To	produce	this,	we	click	on:</p><p>Stat/Basic	Statistics/Normality	Test…………..as	shown	below.</p><p>Click	“OK”	and	the	probability	plot	appears	like	this:</p><p>The	basic	idea	here	is	that	the	better	the	data	fits	the	straight	line	the	more	you</p><p>can	assume	that	the	data	is	normally	distributed.	At	this	point	I’m	more	than</p><p>happy	to	proceed	on	that	basis.</p><p>We	can	now	get	on	and	produce	the	I-MR	chart.	To	do	this	choose:</p><p>Stat/Control	Charts>Variables	Charts	for	Individuals>I-MR	and	select	pH	as	the</p><p>variable.	We	click	on	the	“Labels”	tab	to	add	a	title	and	click	on	“OK”.</p><p>This	Produces	the	I-MR	chart	as	follows:</p><p>Minitab	tests	the	data	against	each	of	the	8	key	tests	identified	earlier	and	reports</p><p>any	failures.	In	this	case,	we	see	this	report:</p><p>We	can	see	that	for	the	individual	data,	we	have	a	failure	of	Test	5	(we	have	2</p><p>out	of	3	points	more	than	2	standard	deviations	from	center	line),	test	failed	at</p><p>points	34,	38	and	39.</p><p>We	can	also	see	that	the	moving	range	chart	shows	a	failure	of	Test	1	(one	point</p><p>more	than	3	standard	deviations	from	the	mean)	but	there	are	two	points	listed,	6</p><p>and	78.</p><p>Failed	points	indicate	non-random	patterns	in	the	data,	which	can	be</p><p>considered	as	special	cause	variation	-	these	need	to	be	investigated.</p><p>The	other	aspect	to	note	are	the	actual	values	for	the	control	limits,	with	the</p><p>Lower	Control	Limit	(LCL)	at	0.799	and	the	Upper	Control	Limit	(UCL)	at</p><p>7.675.	Remember	that	the	tolerance	limits	are	2	and	6	respectively.	The	tolerance</p><p>limits	are	inside	the	confidence	limits,	which	means	that	the	process	is	currently</p><p>incapable	of	meeting	the	specification.</p><p>We	therefore	need	to	reduce	the	common	cause	variation	or	increase	the</p><p>tolerance	to	ensure	capability	of	the	process.</p><p>Example	2	–	Xbar-R	Chart</p><p>The	next	problem	with	which	we	are	presented	is	the	perceived	poor	quality	of</p><p>cylinders	being	produced	by	three	production	machines.	The	cylinders	have	a</p><p>critical	dimension,	which	is	the	diameter	of	each	cylinder.</p><p>Each	machine	runs	for	three	shifts	and	there	is	already	a	sampling	regime	in</p><p>place,	taking	five	cylinders	from	each	machine	on	each	shift.</p><p>Referring	to	the	flowchart,	we	have	continuous	data,	being	collected	in	sub-</p><p>groups	of	less	than	eight.	This	directs	us	to	the	use	of	a	Xbar-R	Chart.</p><p>We	have	already	determined	that	the	data	can	be	considered	normally</p><p>distributed,	so	we	can	go	ahead	with	construction	of	the	control	chart.	We	are</p><p>going	to	create	an	Xbar-R	chart	for	each	machine.</p><p>We	click	on:	Stat/Control	Charts>Variable	Charts	for	Subgroups>Xbar-R</p><p>We	can	then	click	on	the	drop-down	list	and	select	the	option	to	All	observations</p><p>for	a	chart	are	in	one	column	and	enter	Machine	1	Machine	2	Machine	3.	In	the</p><p>box	marked	Subgroup	sizes,	enter	Subgroup	ID.	The	data	input	should	look	like</p><p>this:</p><p>The	settings	should	look	like	this:</p><p>Now	click	on	the	Xbar-R	options	button	and	select	the	“Tests”	tab.	We	are	going</p><p>to	select</p><p>which	tests	we	want	Minitab	to	apply	to	the	data.	In	this	case,	we</p><p>choose	Test1	(1point	>	K	standard	deviations	from	center	line),	Test	2	(K	points</p><p>in	a	row	on	same	side	of	center	line)	and	Test	7	(K	points	in	a	row	within	1</p><p>standard	deviation	of	center	line	(either	side))</p><p>Many	people	get	confused	about	which	tests	to	apply.	My	advice	is	to	use	the	3</p><p>tests	described	above	to	establish	the	control	limits	for	the	process	under</p><p>examination.	After	the	initial	control	limits	have	been	calculated	then	you	can</p><p>use	the	values	of	these	limits	and	omit	Test	7.</p><p>Now	click	on	“OK”.</p><p>Minitab	will	now	produce	the	control	charts,	one	for	each	machine	and	apply	the</p><p>selected	tests.	They	will	look	like	this:</p><p>Underneath	the	charts	will	be	the	test	output	in	the	same	way	as	I	described	in</p><p>the	I-MR	chart	section	above.	It	will	look	like	this:</p><p>It	is	evident	that	machine	2	is	in	control	but	machines	1	and	3	are	not	because</p><p>they	have	test	failures	as	detailed	above.</p><p>We	now	must	take	some	action	to	understand	why	machines	1	and	3	are	not	in</p><p>control.	As	I	described	earlier,	get	the	interested	parties	together	and	discuss	the</p><p>results	using	the	control	charts	as	a	guide.	You	are	looking	to	identify	reasons	for</p><p>the	test	failures.	Once	changes	have	been	made	further	samples	can	be	taken	and</p><p>new	control	charts	produced	to	see	what	effect	the	changes	have	had.</p><p>Example	3	–	Xbar-S	Chart</p><p>Production	of	the	Xbar-S	chart	is	the	same	as	the	Xbar-R	chart,	except	of	course,</p><p>you	have	sub-groups	of	9	or	more.</p><p>Example	4	–	P	Chart</p><p>We	now	enter	the	world	of	attribute	charts,	which	have	specific	uses.	Let’s	take</p><p>an	example	where	we	are	running	a	train	company	and	there	are	several</p><p>customer	complaints	concerning	trains	running	late	to	the	timetable	(sound</p><p>familiar?)	We	therefore	want	to	collect	the	data	and	gain	specific	information	to</p><p>assess	what	proportion	of	trains	are	late	each	day	over	a	3-month	period.	A</p><p>defective	is	a	late	train.</p><p>We	start	by	entering	the	data,	one	column	containing	the	total	number	of	trains</p><p>that	ran	each	day	and	the	other	containing	the	number	of	late	trains.	It	will	look</p><p>like	this:</p><p>Next,	we	set	up	the	control	chart.	We	choose	Late	trains	as	the	variable	and	the</p><p>sub-group	size	is	total	trains	(note	that	in	this	example	we	have	unequal	sub-</p><p>group	sizes).</p><p>It	will	look	like	this:</p><p>Next,	we	choose	the	tests	we	want	Minitab	to	perform	by	clicking	on	the	P	Chart</p><p>Options	button	and	choosing	the	“Tests”	tab.	We	see	this:</p><p>In	this	example,	we	choose	both	Test	1	and	Test	2.	You	can	select	whatever	tests</p><p>you	want	from	the	four	available	but	I’ve	found	the	first	two	are	the	most	useful.</p><p>Finally	we	click	“OK”</p><p>Minitab	produces	the	P	Chart,	it	will	look	like	this:</p><p>We	can	see	that	three	points	are	out	of	control	and	the	failure	report	shows	this:</p><p>Interestingly,	the	failure	points	appear	to	be	at	regular	intervals	and	this	might	be</p><p>a	clue	as	to	the	reasons	for	late	running.	For	example,	are	they	always	on	the</p><p>same	day?	Are	they	always	the	same	driver?	These	are	the	types	of	questions	to</p><p>ask	to	identify	the	special	causes	of	the	late	running	trains.</p><p>Example	5	–	U	Chart</p><p>The	U	Chart	works	in	a	similar	way	to	the	P	Chart,	except	that	it	is	used	to</p><p>monitor	the	number	of	defects	per	unit,	say,	in	a	complex	product	such	as	a	TV</p><p>or	computer.	Producing	the	chart	is	done	in	the	same	way	as	the	P	chart.</p><p>To	summarise	the	choice	of	control	charts	there	are	several	points	to	remember:</p><p>If	you	don’t	have	sub-groups	then	use	the	I-MR	Chart.</p><p>If	you	have	sub-groups	sizes	of	2-8	then	use	the	Xbar	R	Chart.</p><p>If	you	have	sub-groups	sizes	of	more	than	8	then	use	the	Xbar	S	Chart.</p><p>If	your	data	is	attribute	(such	as	number	or	proportion	of	defectives)	then	use</p><p>attribute	charts	like	the	P	Chart	or	the	U	Chart.</p><p>Summary</p><p>Ok,	that’s	it.	I’ve	tried	to	keep	things	as	simple	and	easy	as	possible	and	to</p><p>present	a	practical	guide	to	control	charts.</p><p>Some	of	the	methods	I	have	described	may	upset	the	purist	statisticians	and</p><p>mathematicians	out	there	but	I’ve	used	these	methods	over	more	than	thirty</p><p>years	to	find	solutions	to	seemingly	insolvable	problems	resulting	in	savings	of</p><p>tens	of	millions	of	pounds.	To	me	that’s	proof	enough	that	I’m	doing	something</p><p>right!</p><p>In	the	right	hands	control	charts	are	a	powerful	tool	in	assessing	process</p><p>performance	and	making	effective	improvements.	They	are	the	preferred	option</p><p>to	opinions	and	dogma	since	they	are	based	on	evidence	and	data.	Try	the</p><p>techniques	described	in	this	guide	and	you’ll	see	what	I	mean.</p><p>Cover Page</p><p>Practical Control Charts: Control Charts Made Easy!</p><p>Introduction</p><p>What are Control Charts?</p><p>When Should They Be Used?</p><p>Main steps in constructing control charts</p><p>Summary</p>