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((Short description|Statistical measure that quantifies the robustness of a manufacturing process))
((Manufacturing)) 
'''Process Window Index''' ('''PWI''') is a [[statistical measure]] that quantifies the robustness of a manufacturing process, e.g. one which involves heating and cooling, known as a thermal process. In manufacturing industry, PWI values are used to calibrate the heating and cooling of soldering jobs (known as a thermal profile) while baked in a [[reflow oven]].

PWI measures how well a process fits into a user-defined process limit known as the specification limit. The specification limit is the tolerance allowed for the process and may be statistically determined. Industrially, these specification limits are known as the ''process window'', and values that a plotted inside or outside this window are known as the process window index.

Using PWI values, processes can be accurately measured, analyzed, compared, and tracked at the same level of [[statistical process control]] and [[quality control]] available to other manufacturing processes.

==Statistical process control==
[[Process capability]] is the ability of a process to produce output within [[Specification (technical standard)|specified limits]].<ref name="nist">((cite web|url=http://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm|title=What is Process Capability?|accessdate=2008-06-22|work=[http://www.itl.nist.gov/div898/handbook/index.htm NIST/Sematech Engineering Statistics Handbook]|publisher=[[National Institute of Standards and Technology]]))</ref>  To help determine whether a manufacturing or business process is in a state of statistical control, process engineers use [[control chart]]s, which help to predict the future performance of the process based on the current process.<ref name="juran">((cite book|last=Godfrey|first= A. B|title=Juran's Quality Handbook|publisher=[[McGraw-Hill]] |date=September 1, 2000|edition=5th|isbn=9780070340039))</ref>

[[Image:ControlChart.svg]]
[[Image:PWI.svg|thumb|Process Window Index for a thermal process. Green blurbs denote that the PWIs are within specification, red depicts out of specification.]]
To help determine the capability of a process, statistically determined upper and lower limits are drawn on either side of a process [[arithmetic mean|mean]] on the control chart.<ref name="juran" /> The control limits are set at three [[standard deviation]]s on either side of the process mean, and are known as the upper control limit (UCL) and lower control limit (LCL) respectively.<ref name="juran" /> If the process [[data plot]]ted on the control chart remains within the control limits over an extended period, then the process is said to be stable.<ref name="juran" /><ref name="pwi" />
 
The tolerance values specified by the end-user are known as specification limits – the upper specification limit (USL) and lower specification limit (LSL) respectively.<ref name="juran" /> If the process [[data plot]]ted on a control chart remains within these specification limits, then the process is considered a capable process, denoted by <math>\hat{C}_{pk}</math>.<ref name="juran" /><ref name="pwi" />

Manufacturing industry has developed customized specification limits known as Process Windows.  Within this process window, values are plotted. The values relative to the process mean of the window are known as the Process Window Index. By using PWI values, processes can be accurately measured, analyzed, compared, and tracked at the same level of [[statistical process control]] and [[quality control]] available to other manufacturing processes.<ref name="pwi">((cite book|last=Hall|first=Jim|author2=Zarrow, Phil|title=PWI: Process Optimization Made Simple|publisher=Circuits Assembly Magazine|url=http://www.kicthermal.com/pwi/PWI--Process%20Optimization%20Made%20Simple%20(CA%202002-02).pdf|date=February 2002|access-date=2008-12-10|archive-url=https://web.archive.org/web/20110713145535/http://kicthermal.com/pwi/PWI--Process%20Optimization%20Made%20Simple%20(CA%202002-02).pdf|archive-date=2011-07-13|url-status=dead))</ref>

=== Control limits ===
((More citations needed section|date=September 2022))
'''Control limits''', also known as '''natural process limits''', are horizontal lines drawn on a [[statistical process control|statistical process]] [[control chart]], usually at a distance of ±3 [[standard deviation]]s of the plotted [[statistic|statistic's]] [[mean]], used to judge the stability of a process.<ref>((Cite book |url=https://www.aiag.org/quality/automotive-core-tools/spc |title=Statistical Process Control (SPC) Reference Manual |publisher=Automotive Industry Action Group (AIAG) |year=2005 |edition=2))</ref>

Control limits should not be confused with ''tolerance limits'' or ''specifications,'' which are completely independent of the [[Frequency distribution|distribution]] of the plotted sample statistic. Control limits describe what a process is capable of producing (sometimes referred to as the “voice of the process”), while tolerances and specifications describe how the product should perform to meet the customer's expectations (referred to as the “voice of the customer”).

==== Use ====
((see also|Control chart))
Control limits are used to detect signals in process data that indicate that a process is not in control and, therefore, not operating predictably. A value in excess of the control limit indicates a special cause is affecting the process. 

To detect signals one of several rule sets may be used (((section link|Control chart#Rules for detecting signals))). One specification outlines that a signal is defined as any single point outside of the control limits. A process is also considered out of control if there are seven consecutive points, still inside the control limits but on one single side of the mean.

For [[normal distribution|normally distributed]] statistics, the area bracketed by the control limits will on average contain 99.73% of all the plot points on the chart, as long as the process is and remains in statistical control. A false-detection rate of at least 0.27% is therefore expected.

It is often not known whether a particular process generates data that conform to particular distributions, but the [[Chebyshev's inequality]] and the [[Vysochanskij–Petunin inequality]] allow the inference that for any [[unimodal]] distribution at least 95% of the data will be encapsulated by limits placed at 3 sigma.

==PWI in electronics manufacturing==
((main|Reflow soldering))
[[Image:Process Window Index (bullseye).svg|thumb|A graphical representation of the Process Window Index for a thermal profile]]

An example of a process to which the PWI concept may be applied is soldering.  In [[soldering]], a thermal profile is the set of time-temperature values for a [[reflow soldering|variety of processes]] such as slope, thermal soak, reflow, and peak.<ref name="lead">((cite web|url=http://www.leadfreemagazine.com/pages/pdf/pain_out_of_reflow.pdf |title=Taking the Pain Out of Pb-free Reflow|last=Houston|first=Paul N|author2=Brian J. Louis |author3=Daniel F. Baldwin |author4=Philip Kazmierowicz  |publisher=Lead-Free Magazine|page=3|accessdate=2008-12-10))</ref> 

Each thermal profile is ranked on how it fits in a process window (the specification or tolerance limit).<ref name="KIC">((cite web|url=http://kicthermal.com/products/solar-industry.html?page=shop.product_details&flypage=flypage.tpl&category_id=6&product_id=16&vmcchk=1|title=A Method for Quantifying Thermal Profile Performance|publisher=KIC Thermal|accessdate=2010-09-30|archiveurl=https://web.archive.org/web/20110713145755/http://kicthermal.com/products/solar-industry.html?page=shop.product_details&flypage=flypage.tpl&category_id=6&product_id=16&vmcchk=1|url-status=dead|archivedate=2011-07-13))</ref> Raw temperature values are normalized in terms of a percentage relative to both the process mean and the window limits. The center of the process window is defined as zero, and the extreme edges of the process window are ±99%.<ref name="KIC" /> A PWI greater than or equal to 100% indicates that the profile does not process the product within specification. A PWI of 99% indicates that the profile  runs at the edge of the process window.<ref name="KIC" /> For example, if the process mean is set at 200&nbsp;°C, with the process window calibrated at 180&nbsp;°C and 220&nbsp;°C respectively; then a measured value of 188&nbsp;°C translates to a process window index of &minus;60%.  A lower PWI value indicates a more robust profile.<ref name="lead" /><ref name="KIC" /> For maximum efficiency, separate PWI values are computed for peak, slope, reflow, and soak processes of a thermal profile. 

To avoid   [[thermal shock]] affecting production, the steepest slope in the thermal profile is determined and leveled. Manufacturers use custom-built software to accurately determine and decrease the steepness of the slope. In addition, the software also automatically recalibrates the PWI values for the peak, slope, reflow, and soak processes. By setting PWI values, engineers can ensure that the reflow soldering work does not overheat or cool too quickly.<ref name="lead" />

==Formula==
[[Image:Lead Free Process Window Index.svg|thumb|Example of a Process Window Index for peak, soak, and slope values]]
The Process Window Index is calculated as the [[Worst case analysis|worst case]] (i.e. highest number) in the set of thermal profile data. For each profile statistic the percentage used of the respective process window is calculated, and the worst case (i.e. highest percentage) is the PWI.

For example, a thermal profile with three [[thermocouple]]s, with four profile statistics logged for each thermocouple, would have a set of twelve statistics for that thermal profile. In this case, the PWI would be the highest value among the twelve percentages of the respective process windows. 

The formula to calculate PWI is:<ref name="SMT">((cite web|url=http://smt.pennnet.com/display_article/167071/35/ARTCL/none/none/1/Step-2:-Process-Control/|title=Process Control|last=Kazmierowicz|first=Phil |publisher=SMT Magazine|year=2003|accessdate=2008-12-10))</ref>

: <math>
\text{PWI} = 100 \times \max_{i=1\dots N \atop j=1\dots M}
\left\{\left|
\frac{\text{measured value}_{[i,j]} - \text{average limits}_{[i,j])) {\text{range}_{[i,j]}/2}
\right|\right\}
</math>

where:<ref name="SMT" />
: ''i'' = 1 to ''N'' (number of thermocouples)
: ''j'' = 1 to ''M'' (number of statistics per thermocouple)
: measured value [''i'',&nbsp;''j''] = the [''i'',&nbsp;''j'']<sup>th</sup> statistic's measured value
: average limits [''i'',&nbsp;''j''] = the average of the high and low (specified) limits of the [''i'',&nbsp;''j''']<sup>th</sup> statistic
: range [''i'',&nbsp;''j''] = the high limit minus the low limit of the [''i'',&nbsp;''j'']<sup>th</sup> statistic

==See also==
* [[Acceptable quality limit]]
* ((section link|Control chart#Chart details))
* [[Reflow soldering]]
* [[Wave soldering]]

==References==
((reflist))

[[Category:Electronics manufacturing]]
[[Category:Industrial_processes]]
[[Category:Brazing and soldering]]
[[Category:Statistical charts and diagrams]]
[[Category:Statistical process control]]
[[Category:Statistical distance]]
[[Category:Quality control]]

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