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Process Window Index (PWI) is a
statistical measure In statistics, as opposed to its general use in mathematics, a parameter is any measured quantity of a statistical population that summarises or describes an aspect of the population, such as a mean or a standard deviation. If a population exa ...
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 A reflow oven is a machine used primarily for reflow soldering of surface mount electronic components to printed circuit boards (PCBs). In commercial high-volume use, reflow ovens take the form of a long tunnel containing a conveyor belt along wh ...
. 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 Statistical process control (SPC) or statistical quality control (SQC) is the application of statistical methods to monitor and control the quality of a production process. This helps to ensure that the process operates efficiently, producing ...
and quality control available to other manufacturing processes.


Statistical process control

Process capability The process capability is a measurable property of a process to the specification, expressed as a process capability index (e.g., Cpk or Cpm) or as a process performance index (e.g., Ppk or Ppm). The output of this measurement is often illustra ...
is the ability of a process to produce output within specified limits. To help determine whether a manufacturing or business process is in a state of statistical control, process engineers use
control chart Control charts is a graph used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1) The hourly status is arranged on the graph, and the occurrence of abnormalit ...
s, which help to predict the future performance of the process based on the current process. To help determine the capability of a process, statistically determined upper and lower limits are drawn on either side of a process
mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the '' ari ...
on the control chart. The control limits are set at three standard deviations on either side of the process mean, and are known as the upper control limit (UCL) and lower control limit (LCL) respectively. If the process
data plot A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were u ...
ted on the control chart remains within the control limits over an extended period, then the process is said to be stable. The tolerance values specified by the end-user are known as specification limits – the upper specification limit (USL) and lower specification limit (LSL) respectively. If the process
data plot A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were u ...
ted on a control chart remains within these specification limits, then the process is considered a capable process, denoted by \hat_. 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 Statistical process control (SPC) or statistical quality control (SQC) is the application of statistical methods to monitor and control the quality of a production process. This helps to ensure that the process operates efficiently, producing ...
and quality control available to other manufacturing processes.


Control limits

Control limits, also known as natural process limits, are horizontal lines drawn on a statistical process
control chart Control charts is a graph used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1) The hourly status is arranged on the graph, and the occurrence of abnormalit ...
, usually at a distance of ±3 standard deviations of the plotted statistic's
mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the '' ari ...
, used to judge the stability of a process. Control limits should not be confused with ''tolerance limits'' or ''specifications,'' which are completely independent of the
distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations * Probability distribution, the probability of a particular value or value range of a vari ...
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

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 (). 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 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 In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from th ...
and the Vysochanskij–Petunin inequality allow the inference that for any
unimodal In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object. Unimodal probability distribution In statistics, a unimodal p ...
distribution at least 95% of the data will be encapsulated by limits placed at 3 sigma.


PWI in electronics manufacturing

An example of a process to which the PWI concept may be applied is soldering. In
soldering Soldering (; ) is a process in which two or more items are joined by melting and putting a filler metal (solder) into the joint, the filler metal having a lower melting point than the adjoining metal. Unlike welding, soldering does not involv ...
, a thermal profile is the set of time-temperature values for a variety of processes such as slope, thermal soak, reflow, and peak. Each thermal profile is ranked on how it fits in a process window (the specification or tolerance limit). 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%. 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. For example, if the process mean is set at 200 °C, with the process window calibrated at 180 °C and 220 °C respectively; then a measured value of 188 °C translates to a process window index of −60%. A lower PWI value indicates a more robust profile. For maximum efficiency, separate PWI values are computed for peak, slope, reflow, and soak processes of a thermal profile. To avoid
thermal shock Thermal shock is a type of rapidly transient mechanical load. By definition, it is a mechanical load caused by a rapid change of temperature of a certain point. It can be also extended to the case of a thermal gradient, which makes different pa ...
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.


Formula

The Process Window Index is calculated as the
worst case In computer science, best, worst, and average cases of a given algorithm express what the resource usage is ''at least'', ''at most'' and ''on average'', respectively. Usually the resource being considered is running time, i.e. time complexity, b ...
(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 A thermocouple, also known as a "thermoelectrical thermometer", is an electrical device consisting of two dissimilar electrical conductors forming an electrical junction. A thermocouple produces a temperature-dependent voltage as a result of th ...
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: : \text = 100 \times \max_ \left\ where: : ''i'' = 1 to ''N'' (number of thermocouples) : ''j'' = 1 to ''M'' (number of statistics per thermocouple) : measured value 'i'', ''j''= the 'i'', ''j''sup>th statistic's measured value : average limits 'i'', ''j''= the average of the high and low (specified) limits of the 'i'', ''jsup>th statistic : range 'i'', ''j''= the high limit minus the low limit of the 'i'', ''j''sup>th statistic


See also

*
Acceptable quality limit The acceptable quality limit (AQL) is the worst tolerable process ''average'' (''mean'') in percentage or ratio that is still considered acceptable; that is, it is at an acceptable quality level.Dodge, Y. (2003) ''The Oxford Dictionary of Statisti ...
* *
Reflow soldering Reflow soldering is a process in which a solder paste (a sticky mixture of powdered solder and flux) is used to temporarily attach one or thousands of tiny electrical components to their contact pads, after which the entire assembly is subjec ...
*
Wave soldering Wave soldering is a bulk soldering process used for the manufacturing of printed circuit boards. The circuit board is passed over a pan of molten solder in which a pump produces an upwelling of solder that looks like a standing wave. As the ci ...


References

{{reflist Electronics manufacturing Industrial_processes Brazing and soldering Statistical charts and diagrams Statistical process control Statistical distance Quality control