Process window index

Last updated April 23, 2024

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 specified limits.^[1] To help determine whether a manufacturing or business process is in a state of statistical control, process engineers use control charts, which help to predict the future performance of the process based on the current process.^[2]

Process Window Index for a thermal process. Green blurbs denote that the PWIs are within specification, red depicts out of specification. PWI.svg — 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 mean on the control chart.^[2] 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.^[2] If the process data plotted on the control chart remains within the control limits over an extended period, then the process is said to be stable.^[2]^[3]

The tolerance values specified by the end-user are known as specification limits – the upper specification limit (USL) and lower specification limit (LSL).^[2] If the process data plotted on a control chart remains within these specification limits, then the process is considered a capable process, denoted by ${\hat {C}}_{pk}$ .^[2]^[3]

The 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.^[3]

Control limits

Control limits, also known as natural process limits, are horizontal lines drawn on a statistical process control chart, usually at a distance of ±3 standard deviations of the plotted statistic's mean, used to judge the stability of a process.^[4]

Control limits should not be confused with tolerance limits or specifications, which are completely independent of the 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

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 (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 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

A graphical representation of the PWI 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 variety of processes such as slope, thermal soak, reflow, and peak.^[5]

Each thermal profile is ranked on how it fits in a process window (the specification or tolerance limit).^[6] 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%.^[6] 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.^[6] 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.^[5]^[6] 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.^[5]

Formula

The PWI is calculated as the 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 thermocouples, 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:^[7]

{\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\}

where:^[7]

i = 1 to N (number of thermocouples)

j = 1 to M (number of statistics per thermocouple)

measured value [i, j] = the [i, j]^th statistic's measured value

average limits [i, j] = the average of the high and low (specified) limits of the [i, j']^th statistic

range [i, j] = the high limit minus the low limit of the [i, j]^th statistic

Related Research Articles

<span class="mw-page-title-main">Thermocouple</span> Electrical device for measuring temperature

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 the Seebeck effect, and this voltage can be interpreted to measure temperature. Thermocouples are widely used as temperature sensors.

Six Sigma (6σ) is a set of techniques and tools for process improvement. It was introduced by American engineer Bill Smith while working at Motorola in 1986.

A ball grid array (BGA) is a type of surface-mount packaging used for integrated circuits. BGA packages are used to permanently mount devices such as microprocessors. A BGA can provide more interconnection pins than can be put on a dual in-line or flat package. The whole bottom surface of the device can be used, instead of just the perimeter. The traces connecting the package's leads to the wires or balls which connect the die to package are also on average shorter than with a perimeter-only type, leading to better performance at high speeds.

Surface-mount technology (SMT), originally called planar mounting, is a method in which the electrical components are mounted directly onto the surface of a printed circuit board (PCB). An electrical component mounted in this manner is referred to as a surface-mount device (SMD). In industry, this approach has largely replaced the through-hole technology construction method of fitting components, in large part because SMT allows for increased manufacturing automation which reduces cost and improves quality. It also allows for more components to fit on a given area of substrate. Both technologies can be used on the same board, with the through-hole technology often used for components not suitable for surface mounting such as large transformers and heat-sinked power semiconductors.

Control charts are graphical plots used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. The hourly status is arranged on the graph, and the occurrence of abnormalities is judged based on the presence of data that differs from the conventional trend or deviates from the control limit line. Control charts are classified into Shewhart individuals control chart and CUSUM(CUsUM)(or cumulative sum control chart)(ISO 7870-4).

<span class="mw-page-title-main">Engineering tolerance</span> Permissible limit or limits of variation in engineering

Engineering tolerance is the permissible limit or limits of variation in:

a physical dimension;
a measured value or physical property of a material, manufactured object, system, or service;
other measured values ;
in engineering and safety, a physical distance or space (tolerance), as in a truck (lorry), train or boat under a bridge as well as a train in a tunnel ;
in mechanical engineering, the space between a bolt and a nut or a hole, etc.

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 more specification-conforming products with less waste scrap. SPC can be applied to any process where the "conforming product" output can be measured. Key tools used in SPC include run charts, control charts, a focus on continuous improvement, and the design of experiments. An example of a process where SPC is applied is manufacturing lines.

A reflow oven is a machine used primarily for reflow soldering of surface mount electronic components to printed circuit boards (PCBs).

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 circuit board makes contact with this wave, the components become soldered to the board. Wave soldering is used for both through-hole printed circuit assemblies, and surface mount. In the latter case, the components are glued onto the surface of a printed circuit board (PCB) by placement equipment, before being run through the molten solder wave. Wave soldering is mainly used in soldering of through hole components.

Reflow soldering is a process in which a solder paste is used to temporarily attach anywhere from one to thousands of tiny electrical components to their contact pads, after which the entire assembly is subjected to controlled heat. The solder paste reflows in a molten state, creating permanent solder joints. Heating may be accomplished by passing the assembly through a reflow oven, under an infrared lamp, or by soldering individual joints with a hot air pencil.

<span class="mw-page-title-main">Rework (electronics)</span> Refinishing operation of an electronic printed circuit board assembly

In electronics, rework is the repair or refinish of a printed circuit board (PCB) assembly, usually involving desoldering and re-soldering of surface-mounted electronic components (SMD). Mass processing techniques are not applicable to single device repair or replacement, and specialized manual techniques by expert personnel using appropriate equipment are required to replace defective components; area array packages such as ball grid array (BGA) devices particularly require expertise and appropriate tools. A hot air gun or hot air station is used to heat devices and melt solder, and specialised tools are used to pick up and position often tiny components. A rework station is a place to do this work—the tools and supplies for this work, typically on a workbench. Other kinds of rework require other tools.

The process capability is a measurable property of a process to the specification, expressed as a process capability index or as a process performance index. The output of this measurement is often illustrated by a histogram and calculations that predict how many parts will be produced out of specification (OOS).

Solder paste is used in the manufacture of printed circuit boards to connect surface mount components to pads on the board. It is also possible to solder through-hole pin in paste components by printing solder paste in and over the holes. The sticky paste temporarily holds components in place; the board is then heated, melting the paste and forming a mechanical bond as well as an electrical connection. The paste is applied to the board by jet printing, stencil printing or syringe; then the components are put in place by a pick-and-place machine or by hand.

The process capability index, or process capability ratio, is a statistical measure of process capability: the ability of an engineering process to produce an output within specification limits. The concept of process capability only holds meaning for processes that are in a state of statistical control. This means it cannot account for deviations which are not expected, such as misaligned, damaged, or worn equipment. Process capability indices measure how much "natural variation" a process experiences relative to its specification limits, and allows different processes to be compared to how well an organization controls them. Somewhat counterintuitively, higher index values indicate better performance, with zero indicating high deviation.

Selective soldering is the process of selectively soldering components to printed circuit boards and molded modules that could be damaged by the heat of a reflow oven or wave soldering in a traditional surface-mount technology (SMT) or through-hole technology assembly processes. This usually follows an SMT oven reflow process; parts to be selectively soldered are usually surrounded by parts that have been previously soldered in a surface-mount reflow process, and the selective-solder process must be sufficiently precise to avoid damaging them.

Flat no-leads packages such as quad-flat no-leads (QFN) and dual-flat no-leads (DFN) physically and electrically connect integrated circuits to printed circuit boards. Flat no-leads, also known as micro leadframe (MLF) and SON, is a surface-mount technology, one of several package technologies that connect ICs to the surfaces of PCBs without through-holes. Flat no-lead is a near chip scale plastic encapsulated package made with a planar copper lead frame substrate. Perimeter lands on the package bottom provide electrical connections to the PCB. Flat no-lead packages usually, but not always, include an exposed thermally conductive pad to improve heat transfer out of the IC. Heat transfer can be further facilitated by metal vias in the thermal pad. The QFN package is similar to the quad-flat package (QFP), and a ball grid array (BGA).

In statistical quality control, the individual/moving-range chart is a type of control chart used to monitor variables data from a business or industrial process for which it is impractical to use rational subgroups.

A thermal profile is a complex set of time-temperature data typically associated with the measurement of thermal temperatures in an oven. The thermal profile is often measured along a variety of dimensions such as slope, soak, time above liquidus (TAL), and peak.

<span class="mw-page-title-main">Graping</span> Phenomenon occurring to unreflowed [[solder]].

Graping is a phenomenon marked by the appearance of unreflowed solder particles on top of the solder mass. The solder that is partially coalesced resembles a cluster of grapes, hence the derivation of the phenomenon’s name.

Stencil printing is the process of depositing solder paste on the printed wiring boards (PWBs) to establish electrical connections. It is immediately followed by the component placement stage. The equipment and materials used in this stage are a stencil, solder paste, and a printer.

References

↑ "What is Process Capability?". NIST/Sematech Engineering Statistics Handbook . National Institute of Standards and Technology . Retrieved 2008-06-22.{{cite web}}: External link in |work= (help)
1 2 3 4 5 6 Godfrey, A. B (September 1, 2000). Juran's Quality Handbook (5th ed.). McGraw-Hill. ISBN 9780070340039.
1 2 3 Hall, Jim; Zarrow, Phil (February 2002). PWI: Process Optimization Made Simple (PDF). Circuits Assembly Magazine. Archived from the original (PDF) on 2011-07-13. Retrieved 2008-12-10.
↑ Statistical Process Control (SPC) Reference Manual (2 ed.). Automotive Industry Action Group (AIAG). 2005.
1 2 3 Houston, Paul N; Brian J. Louis; Daniel F. Baldwin; Philip Kazmierowicz. "Taking the Pain Out of Pb-free Reflow" (PDF). Lead-Free Magazine. p. 3. Retrieved 2008-12-10.
1 2 3 4 "A Method for Quantifying Thermal Profile Performance". KIC Thermal. Archived from the original on 2011-07-13. Retrieved 2010-09-30.
1 2 Kazmierowicz, Phil (2003). "Process Control". SMT Magazine. Retrieved 2008-12-10.

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[nist-1] "What is Process Capability?". NIST/Sematech Engineering Statistics Handbook . National Institute of Standards and Technology . Retrieved 2008-06-22.{{cite web}}: External link in |work= (help)

[juran-2] 1 2 3 4 5 6 Godfrey, A. B (September 1, 2000). Juran's Quality Handbook (5th ed.). McGraw-Hill. ISBN 9780070340039.

[pwi-3] 1 2 3 Hall, Jim; Zarrow, Phil (February 2002). PWI: Process Optimization Made Simple (PDF). Circuits Assembly Magazine. Archived from the original (PDF) on 2011-07-13. Retrieved 2008-12-10.

[4] Statistical Process Control (SPC) Reference Manual (2 ed.). Automotive Industry Action Group (AIAG). 2005.

[lead-5] 1 2 3 Houston, Paul N; Brian J. Louis; Daniel F. Baldwin; Philip Kazmierowicz. "Taking the Pain Out of Pb-free Reflow" (PDF). Lead-Free Magazine. p. 3. Retrieved 2008-12-10.

[KIC-6] 1 2 3 4 "A Method for Quantifying Thermal Profile Performance". KIC Thermal. Archived from the original on 2011-07-13. Retrieved 2010-09-30.

[SMT-7] 1 2 Kazmierowicz, Phil (2003). "Process Control". SMT Magazine. Retrieved 2008-12-10.

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